2018 Poster Abstracts

Projection of pinhole diffraction trap array into cold atom cloud for quantum computing using atomic qubits

Presenting Author: Sergio Aguayo, California Polytechnic State University
Contributing Author(s): Alexandra Crawford, Justin Jee, Katharina Gillen

Measurement-based linear optics

Presenting Author: Rafael Alexander, University of New Mexico CQuIC
Contributing Author(s): Natasha Gabay Peter Rohde Nicolas Menicucci

Ion-electrode distance scaling of surface electric-field noise

Presenting Author: Da An, University of California Berkeley
Contributing Author(s): D. An, C. Mattheisen, E. Urban, M. Lewin-Berlin, D. Gorman, N. Daniilidis, H. Haeffner

Demonstrations of EPR steerable polarization-entangled photon states

Presenting Author: Evan Atchison, Harvey Mudd College
Contributing Author(s): Chen Jie Xin, Colter Downing, Theresa W. Lynn

Towards full characterization of photonic gates with weak local oscillators

Presenting Author: Arik Avagyan, National Institute of Standards and Technology, Boulder
Contributing Author(s): Emanuel, Knill Scott, Glancy

Damping bases on symmetric subspace for individual dissipation of N TLA

Presenting Author: William Álvarez, National Autonomous University of Mexico
Contributing Author(s): Pablo Barberis Blostein

Optically pumped semiconductor lasers for atomic physics

Presenting Author: Shaun Burd, National Institute of Standards and Technology, Boulder
Contributing Author(s): D. T. C. Allcock, J-P. Penttinen, T. Leinonen, D. H. Slichter, R. Srinivas, M. Guina, D. Leibfried, D. J. Wineland

Testing the Robustness of Robust Phase Estimation

Presenting Author: Karl Burkhardt, Georgia Tech Research Institute
Contributing Author(s): Creston Herold, Brian McMahon, Adam Meier

Waveguide integrated superconducting single photon detectors for efficient NV entanglement generation

Presenting Author: Srivatsa Chakravarthi, University of Washington
Contributing Author(s): Michael Gould, Kai-Mei Fu

Many-body-localization transition in matchgate-dominated quantum circuits

Presenting Author: Adrian Chapman, University of New Mexico
Contributing Author(s): Akimasa Miyake

Automating quantum algorithms design

Presenting Author: Lukasz Cincio, Los Alamos National Laboratory
Contributing Author(s): Yigit, Subasi Francesco, Caravelli Patrick, Coles Andrew, Sornborger

Adiabatic quantum computing solution of the knapsack problem

Presenting Author: Mark W. Coffey, Colorado School of Mines
Contributing Author(s):

Qubit channel parameter estimation with very noisy initial states

Presenting Author: David Collins, Colorado Mesa University
Contributing Author(s):

The accuracy of physical processes for estimating parameters associated with single qubit channels depends on the physical systems used to probe the channel, the choices of measurements, processing of measurement outcomes and the choices of probe input states. These can be assessed using the quantum Fisher information per channel invocation as a measure of the estimation accuracy. The resulting optimal estimation protocols usually require that the initial states that are used to generate the input states are pure. We consider qubit channel parameter estimation when the available initial states are mixed with very low initial purity; these occur in situations such as nuclear magnetic resonance (NMR). We compare two protocols: one where the input states into the channel are uncorrelated states generated independently from the individual qubit initial states and the other where the input states are prepared from the same initial states using a particular multi-qubit correlating preparatory unitary. We compare these, in the limit as the purity approaches zero, for the cases where the channel is invoked on one out of n qubits. We show that for unital channels the correlated state protocol enhances the quantum Fisher information by a factor between n and n-1. We also show that for a broad class of non-unital channels, there is no enhancement possible to lowest order in purity, regardless of the input state. Read this article online: https://arxiv.org/abs/1706.03552

Entanglement and secret key agreement capacities of bipartite quantum interactions and read-only memory devices

Presenting Author: Siddhartha Das, Louisiana State University
Contributing Author(s): Stefan Baeuml, Mark M. Wilde

A bipartite quantum interaction or bidirectional quantum channel corresponds to the most general quantum interaction that can occur between two quantum systems. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret key agreement. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity that we introduce, called the bidirectional max-Rains information. Our upper bound on the secret key agreement capacity of a bipartite quantum interaction is given by a related quantity, called the bidirectional max-relative entropy of entanglement. Observing that quantum reading is a particular kind of bipartite quantum interaction, we leverage our bounds from the bidirectional setting to deliver bounds on the capacity of a task that we introduce, called private reading of a quantum memory cell. Given a set of quantum channels, the goal of private reading is for an encoder to form codewords from these channels, in order to establish secret key with a party who controls one input and one output of the channels, while a passive eavesdropper has access to the environment of the channels. We derive both lower and upper bounds on the capacities of private reading protocols. We then extend these results to determine achievable rates for the generation of entanglement between two distant parties who have coherent access to controlled point-to-point channels.

Sensing behind metallic shields and storing information in atomic vapors using electromagnetically induced transparency

Presenting Author: Kenneth DeRose, Miami University
Contributing Author(s): Kefeng Jiang, Hong Cai, Stone Oliver, Linzhao Zhuo, Samir Bali

We consider two distinct applications of electromagnetically induced transparency in warm Rubidium vapor: magnetometric sensing of conductive targets behind thick metallic barriers for security screening; the use of twisted light to store topological information in atomic vapors. Experimental progress toward achieving these twin goals is described.

Loss unlimited quantum communications

Presenting Author: Dawei Ding, Stanford University
Contributing Author(s): Saikat Guha

The maximum rate of quantum-secured communication over an optical channel with two-way authenticated public communication, under an all-powerful quantum adversary, is -log(1-eta) secure bits/mode, where eta is the channel's transmissivity, no matter how high the transmit power is. Since eta = e^{-alpha L} in a length L fiber, and -log(1-eta) ~ 1.44 eta for eta << 1, the rate decays exponentially with L. We propose a reverse-reconciliation-based protocol but with the assumption of a slightly weakened Eve. We assume that Eve's copy of the first round of the reverse public communication is corrupted by a tiny amount of additive noise. However, Eve is still assumed to hear the remainder of the public communication noiselessly, wiretap the transmitted-but-lost photons perfectly, and can do arbitrary collective measurements. We show that with this seemingly inconsequential weakening of the conventional eavesdropping model, Alice and Bob can achieve a private communication rate of (1/2)log(1+ 4 eta N_S) bits/mode on the pure-loss channel using a simple laser-light modulation and homodyne detection, N_S being the mean transmit photon number per mode. The rate of our protocol has no upper limit, regardless of how lossy the channel is, for a high enough transmit power. Our protocol also works with arbitrary i.i.d. noise (not necessarily Gaussian) injected by Eve in every use, and the error probability decays super-exponentially with the block length n. Read this article online: https://drive.google.com/file/d/1Li4k523S9HeNWEOVLl0VwqBl9ZLYkKfM/view?usp=sharing

Fundamental work cost of quantum processes

Presenting Author: Philippe Faist, California Institute of Technology
Contributing Author(s): Renato Renner

Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nano scale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure---the coherent relative entropy---which measures information relative to the Gibbs weight of each microstate. The coherent relative entropy enjoys properties expected from an information measure, and in the limit of many independent copies (i.i.d. limit), we obtain the difference of the quantum relative entropies. The generality of our framework ensures not only that our results hold in the context of other thermodynamic frameworks such as thermal operations, but also in any information-theoretic resource theory where a given operator is to be preserved by free operations. We also derive a new upper bound on the amount of work which can be extracted in a state transition, instead of requiring a specific process to be implemented. From our microscopic thermodynamic model, we recover the macroscopic second law as emergent. Our approach furthermore may be consistently applied at any level of knowledge, for instance, from either the microscopic or macroscopic observer's point of view, clarifying the role of the observer in thermodynamics and allowing to systematically analyze Maxwell-demon-like examples. Read this article online: https://arxiv.org/abs/1709.00506

Diamond magnetic imaging of single paramagnetic biocrystals

Presenting Author: Ilja Fescenko, University of New Mexico CHTM
Contributing Author(s): Abdelghani Laraoui, Janis Smits, Nazanin Mosavian, Pauli Kehayias, Jong Seto, Lykourgos Bougas, Andrey Jarmola, Victor Acosta

Quantum sensors based on diamond nitrogen-vacancy (NV) centers have emerged as a powerful platform for detecting nanomagnetism in biological samples. With this technique, magnetic images of individual nanoparticles exhibiting ferromagnetism and super-paramagnetism have been recorded, but observation of paramagnetic nanoparticles has remained a challenge, owing to their weaker signatures. Of particular interest are paramagnetic hemozoin nanocrystals, which are a byproduct of the breakdown of hemoglobin by malaria parasites. The prevention of hemozoin formation is a primary target of antimalarial drugs, but the molecular mechanism for hemozoin formation is poorly understood. We have performed magnetic imaging of individual hemozoin nanocrystals using optically detected magnetic resonance of a near-surface layer of NV centers on a diamond chip. We measured the magnetic properties of individual hemozoin crystals and unambiguously confirmed their paramagnetic nature. We compared numerous individual natural and synthetically-produced hemozoin nanocrystals and observed heterogeneity in their paramagnetic properties. The results are in good agreement with a magnetostatic model informed by independent measurements of nanocrystal morphology and chemical composition. The translation of this tool to the study of living malarial cell cultures could shed new light on the formation dynamics of hemozoin and their interaction with antimalarial drugs.

Minimizing ancilla and garbage qubits in reversible function specifications

Presenting Author: Erik Gabrielsen, Southern Methodist University, Dallas
Contributing Author(s): Mitchell A. Thornton

As quantum computers become a practical reality, there is a need for development tools to enable their usage without requiring developers to assimilate detailed knowledge of quantum informatics processing (QIP). As developers begin to generate new software for quantum computers, a need will arise to generate quantum computer (QC) programs that adhere to the requirements for QIP. For example, a developer who wishes to apply Grover’s search algorithm for a custom searching application will need to at least specify the oracle in some form. As a consequence of the axioms of quantum mechanics, QIP operations are mathematically modeled as unitary transformations over finite Hilbert spaces. Therefore, such operations are necessarily reversible, meaning that the underlying transformations are bijective. It is necessary to convert irreversible functions into reversible forms to adhere to QC paradigms and to minimize quantum cost. To achieve this goal, we created the RTT methodology to produce reversible specifications of an irreversible function while minimizing the number of required ancilla and garbage qubits. To validate the functionality and effectiveness of the RTT method, we implemented the algorithms and ran them in an environment where benchmark irreversible functions were used and mapped to reversible forms. In each case we were able to create reversible forms of these functions that use less ancilla and garbage qubits than those present in the RevLib collection.

Towards a controlled test of the indistinguishability of a pair of well-separated composite particles

Presenting Author: Neil Glikin, University of California Berkeley
Contributing Author(s): Erik Urban, Boerge Hemmerling, Hartmut Haeffner

The symmetrization postulate is a fundamental tenant of nonrelativistic quantum mechanics. It imposes heavy restrictions on the allowed states of systems of identical particles as compared to systems of particles which are distinguishable, and applies to composite particles as well as fundamental ones. The physical manifestation of the consequential statistics of such restrictions is observable in many physical phenomena, and has been directly experimentally probed, for example, via spectroscopy of ensembles of many homonuclear diatomic molecules. We describe experiments towards the goal of demonstrating the indistinguishability of a single pair of 40-Ca+ ions. Using a surface-electrode Paul trap with concentric annular electrodes as a platform, we engineer a Hamiltonian similar to one which describes a homonuclear diatomic molecule in two dimensions. Such a platform should provide the necessary circular symmetry for observing indistinguishability, while allowing for precise control of the parameters of the Hamiltonian, as well as direct control of the rotational and vibrational state of the two-ion system. Using this system, we hope to study the emergence of indistinguishability under controlled conditions even for particles which are always separated by many micrometers.

Perfectly polarized light

Presenting Author: Aaron Goldberg, University of Toronto
Contributing Author(s): Daniel James

There have been numerous recent proposals for characterizing polarization of quantum states of light. We show that the accepted class of perfectly polarized states, with polarization determined using the readily-measurable Stokes parameters, is severely lacking in terms of both pure and mixed states. By appealing to symmetry and geometry arguments we determine all of the states corresponding to perfect polarization, and show that the accepted class of completely polarized states is only a subset of our result. We use this result to reinterpret the canonical degree of polarization, commenting on its interpretation for classical and quantum light. Our results are necessary for any further characterizations of light's polarization. Read this article online: https://arxiv.org/abs/1710.06869, https://journals.aps.org/pra/accepted/4b075N73X691381e16288913f440c96de05193fdc

Resilience of measurement protocols for out-of-time-ordered correlators

Presenting Author: Jose Raul Gonzalez Alonso, Chapman University
Contributing Author(s): Nicole Yunger Halpern, Justin Dressel

Out-of-time-ordered-correlators (OTOCs) have emerged as a useful tool to study quantum chaos and the scrambling and delocalization of information in many-body systems. While challenging, their experimental measurement has been achieved in NMR and trapped ion systems. In this work, we study the effect of experimental nonidealities on two measurement protocols, namely, one based on quantum clocks and the other on sequential weak measurements. For concreteness, we consider circuit implementations for the spin chain and kicked-top that may be achieved with current hardware.

Structured filtering

Presenting Author: Christopher Granade, Microsoft Research
Contributing Author(s): Nathan Wiebe

A major challenge facing parameter estimation in physics, including cutting-edge techniques such as sequential Monte Carlo methods, stems from the inability of existing approaches to robustly deal with experiments that have multiple equally plausible explanations. We address this problem by proposing a form of particle filtering that clusters the hypotheses that comprise the sequential Monte Carlo approximation before applying a resampler, allowing better approximations of posterior distributions. Through a new graphical approach to thinking about such models, we are able to devise an artificial intelligence–based strategy that automatically learns the shape and number of the clusters in the support of the posterior. We demonstrate the power of our approach by applying it to randomized gap estimation and a form of low circuit-depth phase estimation where existing methods from the physics literature either exhibit much worse performance or even fail completely. Read this article online: http://iopscience.iop.org/article/10.1088/1367-2630/aa77cf/meta

Measurement-based control of quantum chaos

Presenting Author: Sacha Greenfield, Carleton College
Contributing Author(s): Andre Carvalho, Arjendu K. Pattanayak

Recent results from Pokharel et al. observe quantum chaos in the Duffing oscillator without a corresponding classical attractor. In related work, Eastman et al. report measurement-angle-dependent chaos at the same parameters. We have investigated how semiclassical chaos arises for classically periodic systems, demonstrating that the choice of measurement scheme acts as a ``knob'' giving rise to the chaos. In doing this, we show that the semiclassical Duffing oscillator acts as a ``centroid'' oscillator in position and momentum coupled to a ``spread'' oscillator in the position-variance and its rate of change. We apply this new understanding to demonstrate measurement-based control of chaos.

Qhord: music, visualization, and playing quantum mechanics

Presenting Author: Aaron Grisez, Chapman University
Contributing Author(s): Justin Dressel, Michael Seaman

The Qhord Project is developing tools to encourage meaningful conversations about technologies involving quantum concepts. Our goal is to promote collaboration between the quantum computing community and experts in other fields that can benefit from upcoming technologies. Here, we present our flagship development: a mobile application which lets users interact with and learn from an accurate quantum mechanical simulation through a musical interface. We explore the issues surrounding the inaccessibility to quantum physics and offer viable solutions to generate more public interaction with science experts.

One from many: Scalar estimation in a multiparameter context

Presenting Author: Jonathan Gross, University of New Mexico CQuIC
Contributing Author(s): Carlton M. Caves

It is difficult to formulate achievable sensitivity bounds for quantum multiparameter estimation. Consider a specialized case: many parameters of a Hamiltonian are unknown and one seeks an estimate for a specific linear combination of these parameters. This problem exhibits genuine multiparameter behavior, though it is superficially similar to single-parameter estimation. The application of geometric reasoning proves the conditions, necessary and sufficient, for saturating the fundamental and attainable bound in this context.

Collective spin squeezing of atoms in magnetic field-sensitive states

Presenting Author: Daniel Hemmer, University of Arizona
Contributing Author(s): Senthilnathan Lingasamy, Ezad Shojaee, Ivan Deutsch, Poul Jessen

Collective spin squeezing can be generated from a QND measurement of the relevant spin component through quantum backaction. When starting from a spin coherent state (SCS), our experiment can generate more than 3 dB of metrologically relevant spin squeezing, closely matching theoretical predictions. Our main objective is now to use control of the internal atomic spin to improve squeezing. For example, we can coherently map the internal spins from the SCS to a “cat” state, which increases the QPN by a factor of 2f=8 relative to the SCS [1]. This leads to increased backaction and entanglement produced by our QND measurement. The squeezing in this cat state basis can in principle be mapped back to the spin SCS basis where it will correspond to squeezing of the physical spin. A preliminary result suggests that up to 8 dB of metrologically useful squeezing can be generated if there are no control errors. Going forward, the main experimental challenge appears to be fluctuating background magnetic fields at frequencies up to tens of kHz, which interfere with control of the magnetic field-sensitive internal atomic spin states. We report on progress using a combination of mu-metal and aluminum shielding to suppress these fields. Once these fields have been suppressed to an acceptable level, we can use composite pulse sequences to measure and correct for control errors due to remaining experimental imperfections. [1] L.M. Norris et al., Phys. Rev. Lett. 109, 173603 (2012)

Group representations and generalized phase spaces

Presenting Author: Christopher Jackson, University of New Mexico CQuIC
Contributing Author(s): Carl Caves, Ivan Deutsch, Akimasa Miyake, Ninnat Dangniam, Ezad Shojaee, Gopi Muraleedharan, Adrian Chapman, Mitchell Brickson

Given a group and representation, a generalized phase space is the orbit of some fiducial state. For example, the most studied phase space of boson quadratures can be described as the Fock space representation of the Weyl-Heisenberg group acting on the vacuum state. In general, if the representation is irreducible, then Wigner functions over the phase space provide an alternative (but equivalent) way to represent quantum information. If the orbit is generated from a state of highest weight, then the phase space can be represented by a single constraint, quadratic in the density operator. With a better understanding of generalized phase spaces, we have done many things such as: 1) Measure the rank of an unknown state with Haar random measurements and generalize the Porter-Thomas distribution. 2) Show that an independent sequence of Haar random weak measurements limit to the POVM consisting of coherent state projectors. 3) Easily prove that an independent sequence of random group elements limit to a Haar random element and calculate the rate of convergence. 4) Calculate Wigner functions relative to Fermion Gaussian states/measurements and show they are not positive, contrary to some expectations.

Quasi-local stabilization of multipartite quantum pure states

Presenting Author: Salini Karuvade, Dartmouth College
Contributing Author(s): Peter D. Johnson, Francesco Ticozzi, Lorenza Viola

Dissipative quantum control techniques under realistic resource constraints are attracting increasing attention across quantum information processing. A multipartite pure state is quasi-locally stabilizable (QLS) by continuous-time Markovian dynamics if it can be prepared using Hamiltonian as well as Lindblad noise operators that obey a fixed locality constraint. We provide a necessary and sufficient condition for a target pure state to be QLS with respect to a fixed locality constraint. We show that the QLS property of the pure state is determined by the existence of a Hamiltonian that is QL relative to the specific constraint and leaves the pure state invariant while having no other eigenstates in a certain subspace of the Hilbert space which is determined by the dissipative action. In particular, we focus on quantum states that are the unique ground states of QL (in general frustrated) Hamiltonians and show that they need not be stabilizable using QL resources alone. We illustrate this by using the paradigmatic W-state on N qubits, under a fixed nearest-neighbor locality constraint. We also discuss control strategies for approximately stabilizing unique ground states of QL Hamiltonians in one dimension, in cases where exact QL stabilization is not feasible.

OTOC for a few qubits

Presenting Author: Alex Kiral, Carleton College
Contributing Author(s): Arjendu Pattanayak

The behavior of out-of-time-ordered-correlators (OTOCs) in nonlinear dynamical quantum systems is of interest to understand many-body physics and eigenstate thermalization. We explore the behavior of the OTOC in the quantum kicked top model, a standard model used to study chaotic systems, with a small number of qubits (2 to 6), and present analysis showing the dependence of OTOCs on initial conditions, time, kick strength and number of qubits which gives insight into the asymptotic limits of this behavior and its relationship to the classical limiting system dynamics.

Quantum simulation of electronic structure with linear depth and connectivity

Presenting Author: Ian Kivlichan, Harvard University
Contributing Author(s): Jarrod McClean, Nathan Wiebe, Craig Gidney, Alán Aspuru-Guzik, Garnet Chan, Ryan Babbush

As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the fermionic swap network, we can simulate a Trotter step of the electronic structure Hamiltonian in exactly N depth and with N^2/2 two-qubit entangling gates, and prepare arbitrary Slater determinants in at most N/2 depth, all assuming only a minimal, linearly connected architecture. We conjecture that no explicit Trotter step of the electronic structure Hamiltonian is possible with fewer entangling gates, even with arbitrary connectivities. These results represent significant practical improvements on the cost of all current proposed algorithms for both variational and phase estimation based simulation of quantum chemistry. Read this article online: https://arxiv.org/abs/1711.04789

Measurement contextuality and Planck's constant

Presenting Author: Lucas Kocia, National Institute of Standards and Technology, Maryland
Contributing Author(s): Peter Love

Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, hbar, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of hbar. We show that contextual measurements in finite-dimensional systems\ have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order hbar^0 terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is equivalent to orders of hbar as a resource within the WWM formalism. This explains why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres-Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, we find that qubit Pauli observables lack an order hbar^0 contribution in their Weyl symbol and so exhibit contextuality regardless of the state being measured. As a result, the WWM formalism is shown to be an excellent candidate for use in the development of classical algorithms for quantum simulation that treat contextuality, or higher orders of hbar, as a resource. Read this article online: https://arxiv.org/abs/1711.08066

Stabilizing quantum dynamics through coupling to a quantized environment

Presenting Author: Meenu Kumari, University of Waterloo
Contributing Author(s): Shohini Ghose, Eduardo Martin-Martinez, Achim Kempf

Quantum systems can be very sensitive to perturbations such as changes to external control parameters. Past studies on fidelity decay and, in particular, studies related to quantum chaos, have shown that such perturbations can lead to a significant decrease in the fidelity of the quantum system. We present a method to stabilize quantum systems against such perturbations in the sense that a finite lower bound to the fidelity decay can be ensured. To this end, we show that it is possible to improve the fidelity of quantum systems against perturbations to the external control parameters by implementing the external control parameters through the coupling with a quantum ancilla, or environment, that is in a state with suitable uncertainties. We illustrate the method in the model of the quantum kicked top. The new method is applicable to any system, including highly fragile chaotic systems. We illustrate that the effective evolution of the system is characterized by a channel which is non-Markovian. We illustrate that non-Markovianity is important for attaining the desired robustness in the fidelity. The new method should be implementable in experiments. Read this article online: https://arxiv.org/abs/1711.07906

Noisy propagation of coherent states in a lossy Kerr medium

Presenting Author: Ludwig Kunz, University of Warsaw
Contributing Author(s): Matteo G. A. Paris,Konrad Banaszek

We identify and discuss nonlinear phase noise arising in Kerr self-phase modulation of a coherent light pulse propagating through an attenuating medium with third-order nonlinearity in a dispersion-free setting. This phenomenon, accompanying the standard unitary Kerr transformation of the optical field, is described with high accuracy as Gaussian phase diffusion with parameters given by closed expressions in terms of the system properties. The irreversibility of the nonlinear phase noise ultimately limits the ability to transmit classical information in the phase variable over a lossy single-mode bosonic channel with Kerr-type nonlinearity. Our model can be also used to estimate the amount of squeezing attainable through self-phase modulation in a Kerr medium with distributed attenuation.

Compensating for bandwidth limitations in radio-frequency control waveforms

Presenting Author: Kevin Kuper, University of Arizona
Contributing Author(s): Nathan Lysne, Poul Jessen

Exercising accurate control over quantum systems is necessary for quantum computation and analog quantum simulation. As our ability to control these systems continues to improve, new limitations inherent in the specific control toolbox used can surface. On our testbed of electronic ground state Cs atoms, we have improved our control over the atoms’ spin states to a point where bandwidth and slew-rate limitations on the control fields have a noticeable impact on the control fidelity. So far, we numerically search for control waveforms using a gradient ascent algorithm to optimize control fidelity, with piecewise constant phases of the control fields serving as control variables. This greatly reduces the computational overhead, but results in waveform discontinuities that cannot be faithfully reproduced in the laboratory. Assuming linear response in our chain of amplifiers and magnet coils, the actual magnetic field waveform is given by the convolution of the input waveform with a response function that can be independently measured. This poster discusses possible methods for improving the control fidelity, with special attention given to designing input waveforms that limit or correct for the effects of finite bandwidth and/or slew-rate.

Imaging individual 25-nm superparamagnetic nanoparticles using diamond magnetic microscopy

Presenting Author: Abdelghani Laraoui, University of New Mexico CHTM
Contributing Author(s): Nazanin Mosavian, Janis Smits, Ilja Fescenko, Victor Acosta University of New Mexico, Dept. of Physics and Center for High Technology Materials Andrey Jarmola ODMR Technologies, El Cerrito, CA, and University of California-Berkeley, Dept of Physics.

Nitrogen-vacancy (NV) centers in diamond are presently been investigated for quantum information processing and as quantum sensors for studying magnetism at the nanometer scale. This is facilitated by their unique properties, including the long electron spin coherence time (exceeding one millisecond) and superb photostability at room temperature. The goal of this research is to develop new strategies based on NV centers for high throughput, high spatio-temporal resolution characterization of individual magnetic nanoparticles (MNPs) for biomedical imaging and nanotechnology applications. We doped a diamond chip with a near-surface (<200 nm="" layer="" of="" nv="" centers="" and="" used="" it="" to="" perform="" wide="" field="" magneto-optical="" microscopy="" by="" optically="" detecting="" the="" magnetic="" resonance="" frequencies="" we="" measured="" static="" dynamic="" properties="" 15-25="" individual="" superparamagnetic="" nanoparticles="" correlated="" them="" with="" their="" morphology="" determined="" from="" atomic="" force="" transmission="" electron="" images="" reveal="" dipole="" patterns=""> 20 uT) from small clusters of MNPs as well as weaker signatures (~8 uT) from individual MNPs. This study will provide a fundamental understanding of the effect of size, surface structure, and inter-particle dipolar interactions on MNP magnetic properties.

Multi-platform quantum information system for secure communication at KRISS and NSR

Presenting Author: Jae Hoon Lee, Korea Research Institute of Standards and Science
Contributing Author(s): Yonuk Chong

We present current research being conducted at KRISS (Korea Research Institute for Standards and Science) and NSR (National Security Research Institute) in South Korea for studying multi-platform quantum information systems geared towards the research of secure quantum communications. The project’s goal is to fully integrate multiple teams (photonic qubit, atomic qubit, superconducting qubit, quantum communication theory, and quantum communication hardware development) to demonstrate a lab-scale distributed quantum direct communication (QDC) network composed of hybrid quantum systems. Currently, our main research topics are to develop qudit encoded photons transferred via multicore fibers, single photon sources from SiV nano diamonds, superconducting single photon detectors, signal processing boards for QDC protocols, superconducting and atomic qubits for quantum information processing, and nanophotonic devices for atom-photon coupling.

Electric field noise in surface ion traps

Presenting Author: Maya Lewin-Berlin, University of California Berkeley
Contributing Author(s): Crystal Noel, Clemens Matthiesen, Hartmut Haeffner

Trapped ions provide a suitable platform for quantum information applications due to their long coherence times and controllable quantum states. The planar Paul trap uses a flat surface with microfabricated electrodes to suspend ions in a harmonic potential. The benefit of this architecture is its scalability; it can be extended to create a fast, compact, multi-qubit system. However, an ion trapped close to a surface has increased sensitivity to electric field noise. This leads to so called ‘anomalous heating’ of the ions, thus limiting our ability to perform computations. We seek to characterize and remove the source of this noise. To this end, we are trapping ions with a diverse range of electrode materials and measuring the response of these materials to in-situ annealing and sputtering treatments.

Deterministic spin squeezing with continuous feedback control

Presenting Author: Senthilnathan Lingasamy, University of Arizona
Contributing Author(s): Daniel Hemmer, Ivan Deutsch, Poul Jessen

We demonstrate preparation of a deterministically squeezed collective spin state of about a million Cs atoms using continuous quantum non-demolition (QND) measurement and real-time radio-frequency (RF) magnetic field feedback. In our experiment, laser-cooled Cs atoms are optically pumped to the |f=4,mf=4> state and a pi/2 RF pulse is applied to steer the spins to the desired spin coherent state (SCS). After this initial state preparation, we perform a QND measurement of the Fz component of the collective spin with an off-resonant probe laser beam. The measured value is fed to a controller that applies real-time RF feedback. By doing so, we are able to correct for state preparation errors and deterministically squeeze the variance of the SCS (standard quantum limit) to the ‘shot-noise limit’. This feedback control strategy can be extended to perform real-time atomic magnetometry.

State preparation and measurement of light with orbital angular momentum with high quality using spatial light modulators

Presenting Author: Xijie Luo, University of New Mexico
Contributing Author(s): F. E. Becerra

The Orbital Angular Momentum (OAM) degree of freedom of light provides access to a high dimensional space, which is an ideal platform for applications in communication and quantum information. However, the characterization of photons in OAM states and superpositions becomes more challenging as the dimension of the space increases. We investigate the performance of different methods used for preparation of states and projective measurements in OAM, and methods to correct for experimental imperfections. We use a spatial light modulator (SLM) to control the phase and amplitude of light for state preparation. Detection of OAM modes and superpositions is achieved by a second SLM which transforms the input state onto a Gaussian mode, and a single mode fiber works as a spatial filter. The use of SLMs to compensate for differences in efficiencies of different OAM modes allows for a good performance in state preparation and measurements. These methods are essential for our future investigations in efficient protocols for quantum state tomography of OAM states in high dimensions.

Building a general-purpose analog quantum simulator from cold-atom qudits

Presenting Author: Nathan Lysne, University of Arizona
Contributing Author(s): Kevin Kuper Poul Jessen Karthik Chinni Ivan Deutsch

Control over quantum devices has advanced such that analog quantum simulators (AQS) are being used to study quantum phase transitions and other complex many body phenomenon. However, as of yet there is no clear understanding as to how imperfections in the control of the AQS itself impacts the outcome of a simulation. Investigating this relationship is paramount as these platforms grow in scale and complexity beyond classical verification. Utilizing new advances in our control protocol to quickly drive any desired unitary transformation in a d = 16 dimensional Hilbert space, we use the atomic spin of neutral Cs atoms in the electronic ground state as a general-purpose quantum simulator capable of stroboscopically examining a variety of disparate systems in time with high fidelity (>99%). In particular, we will report on initial investigations of Hamiltonians that exhibit chaos and hypersensitivity (the quantum kicked top), quantum phase transitions (the Lipkin-Meshkov-Glick model), and others with fundamental features of interest to quantum simulation. Experimentally, we have demonstrated that our AQS faithfully captures the evolution of the quantum state over hundreds of time steps, as well as salient global features. Beyond verifying that we are capable of varied simulation tasks, with this high fidelity of control we are able to reintroduce errors in a deliberate fashion to study how our AQS is impacted, in both numerical modeling and experiment.

Semiclassical to classical transition for nonlinear stochastic quantum dynamics

Presenting Author: Andrew Maris, Carleton College
Contributing Author(s): Moses Misplon, Sharan Ganjam, Sacha Greenfield, and Arjendu Pattanayak

We present results on the transition from semiclassical to classical behavior of a nonlinear chaotic quantum system as a function of coupling to the environment as well as system size. These results show several surprises about the behavior of the semiclassical Lyapunov exponents and the range of validity of the classical equations, and in particular how they depend upon the degree of chaos in the classical or semiclassical system.

From non-stoquastic to stoquastic Hamiltonians

Presenting Author: Milad Marvian, University of Southern California
Contributing Author(s): Itay Hen, Daniel Lidar

Non-stoquastic Hamiltonians cannot be efficiently simulated with quantum Monte Carlo techniques due to the infamous sign problem. We study the conditions under which seemingly non-stoquastic Hamiltonians are still simulable by QMC. We argue that this drives a novel definition of stoquasticity that is based on the computational complexity required to transform non-stoquastic Hamiltonians into simulable stoquastic ones. We provide several examples and results motivating this definition.

Nonclassical effects in multilevel electromagnetically induced transparency

Presenting Author: Mitch Mazzei, Miami University
Contributing Author(s): Perry Rice

We examine a simple multilevel system that can exhibit Electromagnetically Induced Transparency/Absoprtion. We explore nonclassical behavior in the EIT/EIA regime, and elsewhere. Methods developed in the simple regime are applied to degenerate EIT systems. The spectra and nonclassical behavior in these systems are discussed. We propose a multilevel photonic memory in this system, as well as a scheme for improving the lifetime of such a memory utilizing the phenomena of superradiance and subradiance. We are examining pulses that excite the bright states of an atomic ensemble/fiber system, writing a state, and then shifting the system to a dark state for storage.

Mitigating errors in quantum simulation problems through additional measurements

Presenting Author: Jarrod McClean, Google
Contributing Author(s):

One of the promising early applications for pre-fault-tolerant quantum computers is the simulation of quantum systems, including the electronic structure problem for quantum chemistry. We recently introduced the quantum subspace expansion (QSE) as a means to extend near-term variational methods to excited states without the need for additional coherence time in the quantum device. It relies only upon additional quantum measurements of a prepared input state and the solution of a polynomially sized generalized eigenvalue problem on a classical computer. In addition, this method was also predicted to mitigate certain incoherent errors in the presence of noise on real quantum devices. This prediction has recently been experimentally verified on superconducting quantum devices. Here we review these results in the context of upcoming near-term experiments and expand the theoretical foundations for the conditions under which error mitigation or correction is expected when using this technique. Read this article online: https://arxiv.org/pdf/1603.05681.pdf, https://arxiv.org/abs/1707.06408

Verification of spectroscopic techniques using noise injection

Presenting Author: Brian McMahon, Georgia Tech Research Institute
Contributing Author(s): Creston Herold

Noise processes in quantum computing architectures limit gate performance, and correlations between gate errors in algorithms are not fully understood. In this work, we validate noise spectroscopy techniques by measuring injected amplitude and phase noise. For this purpose, we developed FPGA code to generate tailored noise spectra. The code was implemented on a NIST Digital-Servo controller, but it can be added to any FPGA design. Using these techniques, we can characterize amplitude and dephasing noise intrinsic to our system and study noise correlations in longer sequences such as algorithms.

Approximate t-designs by random quantum circuits with nearly optimal depth

Presenting Author: Saeed Mehraban, Massachusetts Institute of Technology
Contributing Author(s): Aram Harrow

We prove that poly(t) n^{1/D}-depth local random quantum circuits with two qudit nearest-neighbor gates on a D-dimensional lattice with n qudits are approximate t-designs in various measures. These include the ``monomial'' measure, meaning that the monomials of a random circuit from this family have expectation close to the value that would result from the Haar measure. Previously, the best bound was poly(t) n due to Brandao-Harrow-Horodecki (BHH) for D=1. We also improve the ``scrambling'' and ``decoupling'' bounds for spatially local random circuits due to Brown and Fawzi. One consequence of our result is that assuming the polynomial hierarchy (PH) is infinite and that certain counting problems are #P-hard ``on average'', sampling within total variation distance from these circuits is hard for classical computers. Previously, exact sampling from the outputs of even constant-depth quantum circuits was known to be hard for classical computers under the assumption that PH is infinite. However, to show the hardness of approximate sampling using this strategy requires that the quantum circuits have a property called ``anti-concentration'', meaning roughly that the output has near-maximal entropy. Unitary 2-designs have the desired anti-concentration property. Thus our result improves the required depth for this level of anti-concentration from linear depth to a sub-linear value, depending on the geometry of the interactions.

Trapped atoms and polarimetry in a nanofiber-based quantum interface

Presenting Author: David Melchior, University of Arizona
Contributing Author(s): Poul Jessen

We describe an experiment to trap and control the collective spin of cold cesium atoms using the evanescent-wave field of a tapered optical fiber (nanofiber). Probe light propagating through the nanofiber is strongly mode-matched to atoms trapped in the evanescent mode, resulting in a high expected optical depth on the order of 10^2. When probe laser light interacts with a trapped atomic sample with high optical depth, the polarization of the light undergoes Faraday rotation proportional to the atomic magnetization. For sufficiently high atom-light coupling, polarimetry of this probe light can measure the magnetization with resolution better than the spin projection noise, at which point measurement back-action can be used for quantum control of the spin. Here, we report experimental progress towards detecting cold atoms samples around a nanofiber, including resonant absorption of ~10% from a single atom.

Entanglement swapping of photons in the spectral-temporal domain

Presenting Author: Sofiane Merkouche, University of Oregon
Contributing Author(s): Valerian Thiel, Alex Davis, Brian Smith

Entanglement is one of the most distinguishing features of multi-partite quantum systems and, appropriately, a crucial resource in quantum information science. An important technique to aid in harnessing this resource is entanglement swapping, which enables entanglement of distant quantum systems and thereby the long-range distribution of quantum correlations, in addition to shedding light on the fundamental nature and extent of quantum non-locality. Our work investigates how to achieve entanglement swapping and characterize the entanglement of photon pairs entangled in the continuous spectral-temporal degree of freedom. This allows unprecedented control over a large Hilbert space and can be applied to the spatial-momentum degrees of freedom as well.

Lower dimensional sections of qutrit state space using 3-dimensional vectors

Presenting Author: Vinod Mishra, US Army Research Laboratory
Contributing Author(s):

The qutrit having three internal states comes next in complexity after qubit as a resource for quantum information processing. A qutrit state density matrix is of order 3 and depends on 8 parameters. Whereas the qubit density matrix can be easily visualized using Bloch sphere representation of its states, at the same time this simplicity is unavailable for the 8-dimensional state space of a qutrit. Earlier work tried to capture the complexity of the Qutrit State Space (QtSS) by studying its 2 and 3 dimensional sections. Recently an alternative approach to study the QtSS using 3 dimensional vectors has become available. In this work we use them to study 2, 3, and other higher order sections. Read this article online: https://arxiv.org/abs/1611.02701

All bipartitions of a Dicke state

Presenting Author: Marcos Moreno, Universidade Federal de Pernambuco
Contributing Author(s): Fernando Parisio

We analytically derive a closed form for a Schmidt decomposition of any bipartition of a system composed by an arbitrary number n of qubits in a Dicke state with an arbitrary number k of excitations. This decomposition is the key to some fundamental results, for instance it reveals the optimal set of entanglement witnesses for detecting entanglement in the vicinity of any balanced Dicke state, this result is used to characterise the loss of entanglement of these states against noise and unbalanced coefficients.

Master equation for adiabatic quantum computing

Presenting Author: Evgeny Mozgunov, University of Southern California
Contributing Author(s):

We present a spatially local Master equation for open system dynamics of a two-dimensional lattice of qubits in contact with a fast bath. The complete positivity of the evolution can be achieved via a previously known procedure of coarse-graining - time-averaging over a finite time. We show that the equation has a wider range of validity than the Lindblad equation with Davies generators. In particular, we do not require coupling to be exponentially weak in the system size. If the state remains a low bond dimension Matrix Product State throughout the evolution, the local equation can be simulated in time polynomial in system size. We also show how a widely used form \Delta^2/W of the tunneling rate through a potential barrier can be derived from this equation. Here \Delta is the splitting between states on the opposite sides of the barrier and W is the noise bandwidth. Read this article online: https://arxiv.org/abs/1611.04188

Boson sampling of multiple quantum random walkers on a lattice

Presenting Author: Gopikrishnan Muraleedharan, University of New Mexico CQuIC
Contributing Author(s): Ivan H. Deutsch, Akimasa Miyake

A quantum device capable of performing an information-processing task more efficiently than current state of the art classical computers is said to demonstrate “quantum supremacy”. One path to achieving this is via “sampling complexity”; random samples are drawn from a probability distribution by measuring a complex quantum state in a defined basis. Surprisingly, a gas of identical noninteracting bosons can yield sampling complexity due solely to quantum statistics, dubbed “boson sampling,” in the context of identical photons scattering from a linear optical network. We study here an analogous problem in case of multiple boson continuous-time quantum random walkers on a lattice, e.g., bosonic atoms in an optical lattice.Results are presented for the special case of a 1D lattice with nearest neighbor and uniform hopping amplitude.We demonstrate that the sampling problem is classically tractable until the time of evolution passes the logarithmic scale in the number of particles.We also conjecture that this problem is classically hard beyond the logarithmic scale. We present a protocol for generating any arbitrary unitary transformation using microwave induced transport in a spinor lattice.By using this protocol we try to approximate a Haar-random unitary map on a single boson, and quantum statistics yields the many-body complexity. We quantify the degree of randomness of the unitarity map using different techniques from random matrix theory, unitary t-designs and Renyi entropy.

Memory assisted quantum cryptography networks

Presenting Author: Mehdi Namazi, Stony Brook University
Contributing Author(s): Mael Flament, Bertus Jordaan, Alessia Scriminich, Giuseppe Vallone, Reihaneh Shahrokhshahi, Paolo Villoresi, Eden Figueroa

The construction of an interconnected set of many quantum devices that performs long distance quantum communication is now within experimental reach. Therefore, it is of utmost relevance to engineer elementary networks of a few quantum nodes and quantum channels in order to understand and harness the potential of these novel architectures. We report the realization of a quantum communication network capable of performing memory-assisted measurement-device-independent quantum key distribution (MDI-QKD). We interconnect several quantum modules, each assigned to perform different tasks, achieving all capabilities needed for quantum cryptography. The components of our network are: (i) two independent random polarization qubit generators, (ii) two fiber based quantum communication channels, (iii) two portable quantum memories and (iv) a qubit decoder and reading station. Random qubits are sent over kilometers long links and coupled into a pair of dual-rail room temperature quantum memories. After storage and retrieval, the qubits are analyzed in a four-detector polarization setup. We achieve quantum bit error rates (QBER’s) of up to 3%, already fulfilling all the requirements needed to perform the BB84 and memory-assisted MDI-QKD protocols. This network will be the core of our four-memory entanglement distribution quantum repeater prototype. Read this article online: https://arxiv.org/abs/1609.08676, https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.8.034023

Microscopy of strontium atoms with optical tweezers and lattices

Presenting Author: Matthew Norcia, University of Colorado JILA
Contributing Author(s): Aaron Young, Adam Kaufman

I will present progress towards a new microscopy platform for quantum science that uses strontium atoms confined in a combination of optical tweezers and lattices. This platform will enable us to take advantage of the rich internal structure of strontium, including long-lived optically excited states and narrow-linewidth transitions, the flexibility and rapid cycle time of optical tweezers for creating low-entropy states, and the well-defined potentials provided by optical lattices for enabling high-fidelity coherent evolution. We intend to apply this new platform to problems in quantum simulation and computation.

Guiding atoms with a tapered optical nanofiber

Presenting Author: Adrian Orozco, Sandia National Laboratories
Contributing Author(s): Grant Biedermann, Jongmin Lee, Rustin Nourshargh

Light Pulse Atom Interferometry (LPAI) utilizes stimulated Raman transitions to split, redirect, and recombine atomic wavepackets along a single dimension. We investigate the implementation of LPAI in optical atomic guides that constrain the transverse motion, specifically, the evanescent mode surrounding a tapered optical fiber (TOF). TOFs have the potential to increase the detection fidelity of atomic states while simultaneously reducing the power required to drive LPAI pulse sequences. In addition, the micron-scale confinement in TOF guides can be leveraged to probe fundamental physics of near-surface dynamics such as inverse square law violations and Casimir-Polder force measurements.

Quantum simulations of 1D systems with Rydberg polaritons

Presenting Author: Hudson Pimenta, University of Toronto
Contributing Author(s): Aaron Goldberg, Josiah Sinclair, Kent Bonsma-Fisher

A dark polariton is a quasiparticle emerging in the context of electromagnetically-induced transparency (EIT). It consists of a superposition of a photonic and a collective atomic excitation that is very long-lived, owing to the conditions that minimize dissipation associated with EIT. The dark polaritons may be made to interact through the choice of Rydberg atoms, which experience very strong van der Waals interaction due to their huge polarizability. We discuss a protocol for implementing quantum many-body physics through Rydberg dark polaritons, particularly in the context of one-dimensional systems.

Optimal control and non-Markovian effects in driven open quantum systems

Presenting Author: Pablo Poggi, Universidad de Buenos Aires (Argentina)
Contributing Author(s): Nicolas Mirkin, Diego Wisniacki

Non-Markovian effects arising in open quantum systems evolution have been a subject of increasing interest over the past decade. One of the most appealing features of non-Markovianity (NM) is that it captures scenarios where loss of information and coherence are reversible, and thus a temporary backflow of information from the environment to the system is possible. In this work we first tackle the issue of how the presence of a driving field can affect the non-Markovian features of open quantum system dynamics. By studying a paradigmatic model of a two-level system coupled to an structured bath, we show that the driving can greatly enhance the degree of non-Markovianity with respect to the undriven case. Then, we present an extensive numerical study about the role played by non-Markovian effects when controlling such systems. We find that the regions which were originally more non-Markovian are compatible with the regions where the best control is achieved. However, we also observe that the driving-field-induced change of the degree of NM does not necessarily lead to an improvement in the fidelities achieved. Read this article online: http://iopscience.iop.org/article/10.1209/0295-5075/118/20005/meta

Experimental dynamical decoupling on IBM quantum experience

Presenting Author: Bibek Pokharel, University of Southern California
Contributing Author(s): Namit Anand, Benjamin Fortman, Daniel Lidar

One of the fundamental challenges in the physical realization of quantum computing and quantum information processing tasks is fighting decoherence---the loss of coherence due to the inevitable coupling of a quantum system to its environment. Dynamical decoupling (DD) is one of the powerful techniques proposed to combat this challenge. In this work, we investigate the performance of DD sequences on the IBM Quantum Experience (IBM QE). The IBM QE is a cloud-based platform that allows remote access to a 5-qubit quantum computer (labelled ibmqx4) and a 16-qubit quantum computer (labelled ibmqx5). We compare the performance of several genetic-algorithm optimized DD sequences and randomized dynamical decoupling (RDD) on this superconducting quantum computer. We show that, in general, performing DD helps in maintaining quantum coherence for longer times than free evolution. Our results elucidate the performance of DD as a defense against decoherence in this experimental setup.

Fundamental limits of photodetectors

Presenting Author: Saul Propp, University of Oregon
Contributing Author(s): Steven van Enk

Starting from the most basic model of photodetection in the single-photon limit, we add different ingredients such as intermediate states, side channels, and quantum amplification mechanisms to create a general theory of photodetection applicable to all physical platforms. When these ingredients are added individually, we see two-way trade-off relations for five standard figures-of-merit: dead time, quantum efficiency, dark count rate, and time and frequency resolution. Adding both intermediate states and an atomic side channel, we observe a non-monotonic three-way trade-off between quantum efficiency and time and frequency resolution. We discuss how to extend this model further (detection of multiple photons, classical fluctuations, coupling to fermionic continuum states) as well as the mathematical machinery we used to generate this model (POVMs, theory of pseudomodes, quantum trajectory method).

Enhanced cooperativity of quantum measurement for spin squeezing of atoms coupled to a nanophotonic waveguide

Presenting Author: Xiaodong Qi, University of New Mexico CQuIC
Contributing Author(s): Yuan-Yu Jau, Jongmin Lee, Ivan Deutsch

We study the enhancement of cooperativity in the atom-light interface near a nanophotonic waveguide for application to quantum nondemolition (QND) measurement of atomic spins. Here the cooperativity per atom is determined by the ratio between the measurement strength and the decoherence rate. Counterintuitively, we find that by placing the atoms at an azimuthal position where the guided probe mode has the lowest intensity, we increase the cooperativity. This arises because the QND measurement strength depends on the interference between the probe and scattered light guided into an orthogonal polarization mode, while the decoherence rate depends on the local intensity of the probe. Thus, by proper choice of geometry, the ratio of good to bad scattering can be strongly enhanced for highly anisotropic modes. We apply this to study spin squeezing resulting from QND measurement of spin projection noise via the Faraday effect in two nanophotonic geometries, a cylindrical nanofiber and a square waveguide. By using a two-color scheme to cancel the tensor light shift, we find, with about 2500 atoms using realistic experimental parameters, \( \sim 6 \) dB and \( \sim 13 \) dB of squeezing can be achieved on the nanofiber and square waveguide, respectively. Read this article online: https://i2000s.github.io/en/2017/11/20/squint-2018-poster.html

Noise-enabled ratchets in cold atom dissipative lattices

Presenting Author: Anthony Rapp, Miami University
Contributing Author(s): Patrick Janovick, Samir Bali

By shining an additional laser beam onto a 3D dissipative optical lattice we introduce a propagating modulation, in either intensity or polarization, that “ripples” through the lattice and “drags” along some cold atoms. The underlying physical mechanism is discussed, and data presented to elucidate the interplay between noise (spontaneous emission) and directed motion. Our goal is to implement Brownian ratchets in optical lattices with efficiencies rivaling those of naturally occurring biomolecular motors. Biomolecular motors outperform current artificial nanomotors, no matter what choice of architecture, by at least an order of magnitude. We hope to achieve our goal by exploiting the unparalleled flexibility offered by optical lattices in tuning the coupling between the atomic ratchet and environmental fluctuations.

Information scrambling of one dimensional symmetry protected topological phases from thermalized boundaries via tensor networks

Presenting Author: Sayonee Ray, University of New Mexico CQuIC
Contributing Author(s): Arpan Bhattacharyya

An emerging area of study is a 1D MBL-SPT (many body localized-symmetry protected topological) bulk with a thermalized boundary which possesses a corresponding quantum anomaly characterizing the SPT bulk. The SYK model is one of them. The thermalizing and information scrambling nature of SYK has been studied from the point of view of level statistics, tripartite mutual information, out-of-time-order correlator (OTOC) etc. We aim at addressing the questions related to information scrambling of a thermalized boundary into a fermionic MBL-SPT bulk and their bulk-boundary correspondence. We consider the Kitaev Majorana wire with a SYK-like model at the boundary, with a constant strength of interaction between four Majoranas, and study the dynamics of thermalization. We aim at studying the time evolution of the GS of the boundary Hamiltonian using tensor network methods, to arrive at a bulk description consistent with the boundary. This can be generalized to SYK boundaries with random fourfermion interactions. Other possible directions of work are using a BDI-SPT bulk with thermalized boundaries like the Sherrington-Kirkpatrick model. Similar calculations for a different SPT bulk (like the AIII and CII classes) with a SYK boundary might also reveal interesting aspects.

Teaching quantum information science to nonscience students

Presenting Author: Michael Raymer, University of Oregon
Contributing Author(s):

Many universities require nonscience students to take a few science courses, which unfortunately are sometimes dumbed-down version of introductory physics, chemistry, or computer science courses. At the University of Oregon we have taken a different approach – we offer a course called Quantum Mechanics for Everyone, in which we attempt to teach, using almost no math, the basic ideas behind quantum science, including state space, projective measurements, Born rule, quantum key distribution, Bell inequality, entanglement, teleportation, quantum computing, atomic clocks, etc. After several years of experimenting, I wrote a book that is used for the course and also sells well as a popular (trade) book, titled Quantum Physics: What Everyone Needs to Know. This poster will present the key methods, with examples, we use in teaching this successful course.

Investigations of the quantum alternating operator ansatz

Presenting Author: Eleanor Rieffel, NASA - Ames Research Center
Contributing Author(s): Stuart Hadfield, Zhihui Wang, Bryan O'Gorman, Davide Venturelli, Rupak Biswas

The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation, and which have the potential to significantly expand the breadth of quantum computing applications. Here, we present investigations of the Quantum Alternating Operator Ansatz [1], an extension of the framework defined by Farhi et al. [2] in their Quantum Approximate Optimization Algorithm, including design criteria, mappings of specific problems [1], compilation to near-term hardware [3], and early results. [1] Stuart Hadfield, Zhihui Wang, Bryan O'Gorman, Eleanor G. Rieffel, Davide Venturelli, Rupak Biswas, From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz, arXiv:1709.03489 [2] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem. arXiv:1412.6062 [3] Davide Venturelli, Minh Do, Eleanor G. Rieffel, Jeremy Frank, Compiling Quantum Circuits to Realistic Hardware Architectures using Temporal Planners, arXiv:1705.08927 Read this article online: https://arxiv.org/abs/1709.03489

Towards a low noise system for generating entangled photons in orbital angular momentum

Presenting Author: Nate Ristoff, University of New Mexico
Contributing Author(s): A.R. Ferdinand F.E. Becerra

Orbital angular momentum (OAM) of light can be used to increase the information capacity of a communication channel because it allows for multilevel encoding. In quantum communication, multilevel encoding can be used to increase secret key rates in quantum key distribution, while quantum memories based on atomic ensembles can allow for extending communication to long distances. Photon pairs entangled in OAM modes generated from atomic ensembles are readily compatible with atomic quantum memories. We report on the progress towards developing a source of entangled photons in OAM from atomic ensembles with very low levels of noise, that can in principle allow for characterization and control over the OAM spectrum. This source will be based on a cold ensemble of cesium atoms, for which we will employ a variety of techniques to reduce the levels of noise and improve fidelities in the correlation measurements in OAM such as narrow-band frequency filtering and optimized projective measurements with spatial light modulators. This source of entangled photons in OAM will be used for investigations of quantum correlations in high dimensions and entanglement transfer between photons and atoms..

Van Trees information in pure quantum states

Presenting Author: Marco Rodriguez , National Autonomous University of Mexico
Contributing Author(s): Pablo Barberis Blostein

In the context of parameter estimation in quantum systems, the Van Trees information is the maximization of the generalized Fisher information over the set of all POVMs. The Van Trees information gives us a bayesian lower bound of a quantum estimator. Since the set of POVMs is not countable, the Van Trees information is too difficult to calculate. However, in pure quantum states, the calculation of Van Trees information is possible to attain. The aim of this work is to present a theorem that allow us to calculate the Van Trees information when the state of our quantum system is pure. We proved that the maximization of the generalized Fisher information over the set of all POVMs is equivalent to maximize over a subset of extremal two outcomes-POVMs.

Quantum noise in a PT symmetric system

Presenting Author: Jayson Rook, Miami University
Contributing Author(s): Perry Rice

A PT symmetric system is invariant under the combined action of parity and time-reversal. For a system of two coupled quantum oscillators, PT symmetry can occur by having one oscillator with gain and another with loss. Classically, when gain and loss coefficients are equal, the system exhibits a zero linewidth. Using quantum trajectory theory we find that the linewidth is not zero but scales as 1/, where is the average excitation number. This line-width is minimized near the exceptional point, where eigenvalues and eigenvectors coalesce. We make connections to an incoherently pumped, three-level laser, and electromagnetically induced transparency. We also consider this system as a heat engine, and investigate coherent pumping and nonclassical inputs.

Improving operator averaging in hybrid algorithms with approximate N-representability constraints

Presenting Author: Nicholas Rubin, Rigetti Computing
Contributing Author(s): Jarrod R. McClean Ryan Babbush

The two most well known hybrid classical/quantum algorithms require calculating expected values of Pauli operators by repeated state preparation and measurement. Accelerating the operator averaging step correlates directly with minimizing the total runtime of the algorithms. We derive an optimal bound on the number of measurements required to calculate the expected value of a sum of non-commuting Pauli operators to fixed precision that improves upon the bound derived from central limit theorem. To further reduce the required measurements, we propose the use of approximate N-representability constraints as a set of conditions for reconstructing marginals. These techniques take the form of projections onto the set of N-representable two-electron reduced density matrices (2-RDMs) enforcing non-negativity of the marginal, particle number conservation, and the appropriate magnetization of the targeted Fermionic state prepared on the quantum resource. Most importantly, the projection techniques restore physicality of the measured states corrupted by an error channel. We present the performance of the N-representability inspired 2-RDM reconstruction procedures on marginals mimicking real measured data. For small systems, the projection techniques give a significant reduction in the number of samples required for operator averaging to a given precision.

Wavelet-based representations of quantum field theory

Presenting Author: Yuval Sanders, Macquarie University
Contributing Author(s): Bryte Hagan, Dean Southwood, Sukhwinder Singh, Barry Sanders, Gavin Brennen

Here we present current results from our investigations into wavelet-based representations of quantum field theory. Specifically, we develop representations of one-dimensional free field theories for fermions and scalar bosons using the Daubechies wavelets, which are desirable due to their compact support and vanishing moments. We reproduce entanglement area laws with a resolution-dependent cutoff and generalize to fractal sets. The ground states of these one-dimensional free field theories have a holographic dual representation in terms of multiscale wavelet degrees of freedom. We show how an emergent geometry can be inferred from the scaling of mutual information between wavelet degrees of freedom in the bulk. At the critical point, the bulk has an anti-de-Sitter geometry with radius of curvature that depends on the Daubechies wavelet index. Our work has implications for resource-theory-based approaches to quantum field theory as well as applications to the development of quantum algorithms for simulating quantum field theory.

Machine learning of noise in single-qubit hardware

Presenting Author: Travis Scholten, University of New Mexico CQuIC
Contributing Author(s):

Techniques for characterizing quantum information processing hardware — e.g., as-built qubits — are generally based on ad-hoc or statistical methods for analyzing data. Machine learning provides a different paradigm for qubit characterization methods. It promises greater efficiency, the ability to handle large datasets, and automated tool-building. I will present progress toward these desiderata via two distinct but related projects. First, I demonstrate a support vector machine classifier that learns how to distinguish whether the noise afflicting a single-qubit QIP is predominantly stochastic or predominantly coherent. It analyzes data from the structured circuits used for gate set tomography (GST), but avoids all the standard statistical tools used for GST analysis. Second, I demonstrate how to automate the selection of a sparse subset of those circuits that is maximally useful for classifying such noise.​ Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Rényi relative entropies of quantum Gaussian states

Presenting Author: Kaushik Seshadreesan, University of Arizona
Contributing Author(s): Ludovico Lami, Mark Wilde

The quantum Rényi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory. On a different thread, quantum Gaussian states have been intensely investigated theoretically, motivated by the fact that they are more readily accessible in the laboratory than are other, more exotic quantum states. In this paper, we derive formulas for the quantum Rényi relative entropies of quantum Gaussian states. We consider both the traditional (Petz) Rényi relative entropy as well as the more recent sandwiched Rényi relative entropy, finding formulas that are expressed solely in terms of the mean vectors and covariance matrices of the underlying quantum Gaussian states. Our development handles the hitherto elusive case for the Petz-Rényi relative entropy when the Rényi parameter is larger than one. Finally, we also derive a formula for the max-relative entropy of two quantum Gaussian states, and we discuss some applications of the formulas derived here. Read this article online: https://arxiv.org/pdf/1706.09885.pdf

Bounding the energy-constrained quantum and private capacities of phase-insensitive quantum Gaussian channels

Presenting Author: Kunal Sharma, Louisiana State University
Contributing Author(s): Mark M. Wilde, Sushovit Adhikari, and Masahiro Takeoka

One of the main aims of quantum information theory is to characterize the capacities of quantum communication channels. Bosonic Gaussian channels are some of the most important channels to consider, as they model practical communication links in which the mediators of information are photons. Of particular interest is the bosonic thermal channel, which is a more realistic model than the pure-loss channel because it incorporates environmental imperfections. In our work, we establish three different upper bounds on the energy-constrained quantum and private capacities of bosonic thermal channels. We also discuss the closeness of these upper bounds to a known lower bound for different parameter regimes of background thermal radiation and transmission loss. In particular, our results establish strong limitations on any potential superadditivity of coherent information of the thermal channel. We also find improved achievable rates of private communication through bosonic thermal channels, by employing coding schemes that make use of displaced thermal states. Although we mainly focus on thermal channels, using the techniques developed in our work we also establish bounds on the energy-constrained quantum and private capacities of other important Gaussian channels such as quantum amplifier channels and additive-noise Gaussian channels. Hence, we establish bounds on energy-constrained quantum and private capacities of all phase-insensitive quantum Gaussian channels. Read this article online: https://arxiv.org/pdf/1708.07257.pdf

Single qubit quantum ring structures and applications

Presenting Author: Kaitlin Smith, Southern Methodist University, Dallas
Contributing Author(s): Mitchell Thornton, Duncan MacFarlane, Tim LaFave, Jr., William Oxford

Quantum ring structures (QRS) are building blocks for applications such as qubit storage, sensing elements, and oscillators. QRS architectures are motivated by the need to retain or modify the state of a flying qubit such as a photon and incorporate a feedback path so that the state-carrying particle can be spatially localized for a brief period of time. In one configuration of these architectures, referred to as Quantum Ring Oscillators (QRO), the feedback qubit state alternates in binary basis states with a period proportional to the delay of the circuit elements. Because the feedback state is not superimposed, it can be measured to determine the internal state of the oscillator which is superimposed. Circuits for information carrier injection, state extraction, and features of QRS/QRO are described in this work. When the overall transfer function for the feed-forward stage in a QRS is equivalent to a Pauli-X rotation, a QRO results. The second application is the use of the structure as the basis for a qubit storage element. The inclusion of rotation and controlled-rotation operators into the structure allow for any arbitrary qubit to be “stored” in the structure. Storage is achieved through continuous regeneration of the qubit state rather than attempting to preserve the same qubit.

Entangling trapped ions with a low-frequency magnetic field gradient

Presenting Author: Raghavendra Srinivas, National Institute of Standards and Technology, Boulder
Contributing Author(s): David Allcock, Daniel Slichter, Shaun Burd, Andrew Wilson, Dietrich Leibfried, David Wineland

Entangled states of trapped ions are typically generated using laser-induced spin-motion coupling. Spin-motion coupling with hyperfine qubits has also been demonstrated with microwave magnetic fields instead of lasers, thus eliminating photon scattering errors and offering potential benefits for scalability. These experiments have relied on either static magnetic field gradients or oscillating magnetic field gradients at GHz frequencies[1-4]. We present a method of spin-motion coupling using microwaves and a magnetic field gradient oscillating at MHz frequencies, related to the optical method discussed in [5]. We entangle the internal states of two trapped 25Mg+ ions in a cryogenic microfabricated surface-electrode trap and characterize the Bell-state fidelity. This implementation offers important technical advantages over both the static-gradient and GHz-gradient techniques. [1] Mintert and Wunderlich PRL 87, 257904 (2001) [2] Weidt et al. PRL 117, 220501 (2016) [3] Ospelkaus et al. Nature 476, 181 (2011) [4] Harty et al. PRL 117, 140501 (2016) [5] Ding et al. PRL 113, 073002 (2014)

Quantum-adiabatic like algorithms for linear systems of equations

Presenting Author: Yigit Subasi, Los Alamos National Laboratory
Contributing Author(s): Rolando Somma

We present a quantum method based on evolution randomization or adiabatic evolutions to prepare a quantum state that is proportional to the solution of the linear system of equations \(A \vec{x}=\vec{b}\). Our quantum algorithm is not obtained using equivalences between the circuit model and adiabatic quantum computing. We rather use simple Hamiltonians that are linear combinations of \(A\) and the projector in the initial state \(|b〉\) when \(A>0\). The coefficients in this combination may be unknown a priori but can be estimated by running the algorithm for several intermediate times. Our quantum algorithm requires being able to measure expectation values of \(A\) and \(|b〉〈b|\). The overall time complexity of our approach is polynomial in the condition number \(\kappa\) and polynomial in \(1/\epsilon\), where \(\epsilon\) is the target precision. The case of non-positive \(A\) can be studied similarly by replacing \(A \mapsto A^2\), increasing the condition number to \(\kappa^2\). Our results are important in that this problem could be solved using a restricted, maybe non-universal quantum computing device that can implement evolutions with such Hamiltonians only. Just like other quantum algorithms for this problem, our method may result in an exponential quantum speedup for particular efficient specifications of \(A\) and \(b\), and when the condition number is polylogarithmic in the dimension.

Improved algorithms for quantum simulation of fermionic systems

Presenting Author: Kevin Sung, University of Michigan
Contributing Author(s): Zhang Jiang, Kostyantyn Kechedzhi, Vadim Smelyanskiy, Sergio Boixo

We present some quantum algorithms for the simulation of fermionic systems on one- and two-dimensional qubit arrays with nearest-neighbor interactions. We show how to prepare arbitrary fermionic Gaussian states with O(N^2) gates and O(N) depth. For the special case of Slater determinants, we improve an existing algorithm by exploiting a unitary symmetry. We also present an algorithm for performing the two-dimensional fermionic Fourier transform with O(N^1.5) gates and O(N^.5) depth. Read this article online: https://arxiv.org/abs/1711.05395

Photonic memory using engineered modes of a nanophotonic waveguide

Presenting Author: Tyler Thurtell, Miami University
Contributing Author(s): Perry Rice

An atomic ensemble of three-level atoms can store a photon state if the control field is manipulated properly. A limit is placed on the storage fidelity by spontaneous emission. The spontaneous emission rate of an ensemble of atoms can be modified by super and sub-radiance. It has recently been shown that selectively radiant states exist for which some modes are sub-radiant and others are super-radiant, that such states can be prepared in three level atoms undergoing EIT coupled to a nanofiber and that such states may exponentially improve storage fidelity. We use the Quantum Toolbox in Python(QuTIP) to integrate the master equation describing these systems and produce a numerical model of these results. The emission type is controlled via modification of the collapse operators. We then consider a variety of nanophotonic waveguides and fibers.

Universality of swap for qudits

Presenting Author: James van Meter, National Institute of Standards and Technology, Boulder
Contributing Author(s): Emanuel Knill

Using a representation theory approach, we derive conditions for which interactions with the swap Hamiltonian of qudits suffice for universal control of quantum information encoded in decoherence-free subsystems protected against all collective noise. In particular, we generalize a result of DiVincenzo et al. for the swap interactions of qubits by applying a theorem due to Marin concerning the structure of the Lie algebra generated by transpositions. As a consequence, we prove that encoded universality can also be implemented by swap interactions between three qudits, for any \(d\). Further, invoking the Littlewood-Richardson rules for tensor product decompositions, we show how any composite system of qudits can achieve encoded universality with the addition of at most \(d+1\) ancillae.

Quadrature histograms in maximum likelihood quantum state tomography

Presenting Author: Hilma Vasconcelos, National Institute of Standards and Technology, Boulder
Contributing Author(s): Jose Leonardo Silva, Scott Glancy

Quantum state tomography (QST) aims to determine the state of a quantum system from measured data and is an essential tool in quantum information. For continuous variable systems, such as quantum states of light, QST is often done by measuring statistics of the field amplitudes (or "quadratures") at different phases using homodyne detection. The quadrature-phase measurement outputs a continuous variable, and this can result in a very large data set and long computation time to reconstruct the state. However, one can histogram the continuous measurements into a small number of bins and make the reconstruction faster without losing too much information. We investigate different ways to determine the quadrature histogram bins for optical homodyne QST and show that high fidelity reconstruction can be maintained while significantly reducing the computation time.

Coherence properties of donor-bound electron spins in ZnO

Presenting Author: Maria Viitaniemi, University of Washington
Contributing Author(s): Xiayu Linpeng, Y. Kozuka, Cameron Johnson, Joseph Falson, Atsushi Tsukazaki, M. Kawasaki, and Kai-Mei Fu

Donor impurities in ZnO may be a promising solid state qubit candidate for photon-mediated quantum networks. Efficient and homogeneous transitions allow for optical control of the electron spin state. Long spin coherence times and strong donor nucleus-electron interactions show promise for incorporation into future quantum information processors. Here we demonstrate coherent control of the Ga donor in ZnO over small angles and present ensemble measurements of optical pumping, T1, T2* and T2. We find that T1 exceeds ~0.1 s at 2.5 T with a B^-3.5 dependence. We thus expect T1 to exceed 1s at fields less than 1 T. Measurements of ~20ns for T2* and ~30μs for the spin echo decoherence time (T2) are also described. We will discuss possible limitations on T2 including instantaneous spectral diffusion of donors (n~10^17 cm^-3) and Zn67 nuclear spins (4.1% of natural Zn). Through isotope purification and single donor isolation, we believe we will be able to significantly increase the spin coherence time. Funding acknowledgement: This material is based upon work supported by the National Science Foundation under Grant No. 1150647. K.M. F. also acknowledges the support from the Research Corporation for Science Advancement as a Cottrell Scholar.

Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels

Presenting Author: Mark Wilde, Louisiana State University
Contributing Author(s):

In the literature on the continuous-variable bosonic teleportation protocol due to [Braunstein and Kimble, Phys. Rev. Lett., 80(4):869, 1998], it is often loosely stated that this protocol converges to a perfect teleportation of an input state in the limit of ideal squeezing and ideal detection, but the exact form of this convergence is typically not clarified. In this paper, I explicitly clarify that the convergence is in the strong sense, and not the uniform sense, and furthermore, that the convergence occurs for any input state to the protocol, including the infinite-energy Basel states defined and discussed here. I also prove, in contrast to the above result, that the teleportation simulations of pure loss, thermal, pure amplifier, amplifier, and additive-noise channels converge both strongly and uniformly to the original channels, in the limit of ideal squeezing and detection for the simulations. For these channels, I give explicit uniform bounds on the accuracy of their teleportation simulations. These convergence statements have important implications for mathematical proofs that make use of the teleportation simulation of bosonic Gaussian channels, some of which have to do with bounding their non-asymptotic secret-key-agreement capacities. Read this article online: https://arxiv.org/abs/1712.00145

Two-qubit stabilizer circuits and recovery procedures

Presenting Author: Raymond Wong, University of California Santa Barbara
Contributing Author(s): Wim van Dam

Stabilizer operations play an integral part in several techniques that are fundamental to building a universal fault-tolerant quantum computer. Understanding the boundaries of their utility on general input is important to realizing a cost-effective strategy to running a quantum computation. We consider the problem of categorizing the different ways we may use stabilizer operations to reduce a two-qubit state down to one. We reveal two new findings from our investigation. First, we prove that for any postselected two-qubit stabilizer circuit, there exists an alternate that achieves the same output but uses at most one CNOT or SWAP gate surrounded by single qubit Clifford gates. In the process we identify three circuit forms characterizing all such alternative circuits. Second, we show that some postselected circuits have the capacity to “recycle” qubits. In particular, when one circuit fails to obtain a desired qubit, a second circuit may reuse the output to try recover one the input qubits that was used in the first. We design a recovery procedure involving multiple such circuits, thereby lowering demand to prepare another copy of that qubit. Under certain imputs, we can even cut down our qubit usage by as much as half.

Faster search by lackadaisical quantum walk

Presenting Author: Thomas Wong, Creighton University
Contributing Author(s):

Quantum walks, the quantum analogues of random walks, are the basis for several quantum algorithms. Contrary to some intuition, making a discrete-time quantum walk lazy by adding self-loops to each vertex, called a lackadaisical quantum walk, can actually speed up the quantum walk. In particular, the ballistic dispersion can be made faster, search on the complete graph (i.e., Grover's algorithm formulated as a quantum walk) can be improved by a constant factor, and search on the two-dimensional grid improves by a factor of the square root of the number of vertices. Read this article online: https://arxiv.org/abs/1706.06939, http://arxiv.org/abs/1703.10134, http://arxiv.org/abs/1502.04567

Optomechanical cooling with time dependent parameters

Presenting Author: Pablo Yanes-Thomas, National Autonomous University of Mexico
Contributing Author(s): Pablo Barberis Blostein

We model the laser cooling of a parametrically driven optomechanical cavity using a dissipation model that takes into account the modification of the quasi-energy spectrum caused by the driving. We construct a master equation for the mechanical object using Floquet operators. When the natural frequency of the mechanical object oscillates periodically around its mean value, we derive, using an adiabatic approximation, an analytical expression for its temperature. This expression depends both on the oscillator's mean frequency and that of the frequency's oscillations around its mean value. We find that the temperature can be lower than in the non-time dependent case. Our results raise the possibility of achieving lower temperatures for the mechanical object if its natural frequency can be controlled as a function of time.

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