# 2014 Talk Abstracts

## 1. Towards an Efficient Decoder for Quantum LDPC Codes

Jonas Anderson, Université de Sherbrooke

(Session 9a : Friday from 5:30pm - 6:00pm)

Quantum low-density parity-checking (LDPC) codes can greatly reduce the overhead associated with fault-tolerant quantum computation (FTQC) by providing a nonzero-rate code family with low-weight stabilizer generators. In principle this means that as the code distance grows so does the number of encoded qubits thus allowing FTQC with constant overhead [1]. Exact decoding of classical LDPC codes is computationally difficult, but approximate decoders such as the belief propagation (BP) decoder are known to work well. For quantum LDPC codes much less is known and BP without modifications is plagued with issues due to degeneracy and short cycles in the Tanner graph. Here we improve upon the work of Poulin and Chung [2] by modifying BP to correct for some of the effects of message passing on a Tanner graph with cycles. Our technique uses nonlinear message weights to offset the additional correlations picked up due to cycles. For physical error rates an order of magnitude below pseudothreshold, arguably the most important regime for FTQC, we improve upon the best-known decoding schemes by an order of magnitude. We will also discuss ideas to further improve upon these schemes. [1] Daniel Gottesman, “What is the Overhead Required for Fault-Tolerant Quantum Computation?” arxiv.org/1310.2984. [2] David Poulin and Yeojin Chung, “On the iterative decoding of sparse quantum codes” Quantum Information and Computation, Vol. 8, No. 10 (2008) 0987–1000.

## 2. Towards practical quantum simulators for quantum chemistry

Alan Aspuru-Guzik, Harvard University

(Session 8 : Friday from 1:45pm - 2:30pm)

My first talk about quantum computing for chemistry was at SQUINT 2005. Back then, I presented a gate-model approach for the simulation of quantum chemistry. In this talk, almost a decade later, I will present two approaches that are much less demanding on the requirements of the quantum device, yet are able to simulate Fermionic Hamiltonians such as those of molecular quantum chemistry. First, I will talk about the variational quantum eigensolver approach for solving chemistry problems in an arbitrary {\sl hardware ansatz}. I will follow by describing an approach for the simulation of quantum chemistry using adiabatic quantum computers. Both approaches are scalable and good candidates for an early implementation of quantum devices that could carry out a simulation of practical relevance to medical or industrial applications.

## 3. Robust and high-sensitivity nonorthogonal coherent state discrimination

Francisco Elohim Becerra, University of New Mexico

(Session 3 : Thursday from 2:15pm - 2:45pm)

Measurements for accessing the information contained in quantum states are limited by the inherent noise of these states. Strategies for nonorthogonal state discrimination for optimally extracting information from these states have fundamental interest in quantum mechanics and can allow for communications approaching the quantum limits. Conventional measurements for nonorthogonal state discrimination of coherent states with different phases implement a direct phase-sensitive detection, and can ideally reach the standard quantum limit (SQL). However, measurement strategies based on the quantum properties of these states can allow for better measurements which surpass the SQL and approach the ultimate measurement limits allowed by quantum mechanics. We present the demonstration of a receiver based on adaptive measurements and single-photon counting that unconditionally discriminates multiple nonorthogonal coherent states below the SQL. We also discuss the potential of photon-number-resolving detection to provide robustness under realistic conditions for an adaptive coherent receiver with detectors with finite photon-number resolution.

## 4. Quantum assisted sensing with diamond spins

Ania Bleszynski-Jayich, University of California Santa Barbara

(Session 13 : Saturday from 4:15pm - 5:00pm)

Nitrogen-vacancy (NV) centers in diamond are atomic-scale spin systems with remarkable quantum properties that persist to room temperature. They are highly sensitive to a wide variety of fields (magnetic, electric, thermal) and are easy to initialize, read-out, and manipulate on the individual spin level; thus they make excellent nanoscale sensors. The NV’s sensitivity is a double-edged sword however; environmental fluctuating fields are also a source of decoherence. We use the NV to probe these fluctuating fields, both their frequency spectrum and spatial character, and we mitigate their induced decoherence through engineered CVD diamond growth and quantum control of the NV. I will also present my group’s work on quantum assisted sensing of strain fields on the nanoscale. We demonstrate strain coupling of a single NV spin to a high quality factor mechanical mode of a single-crystal diamond mechanical resonator. This hybrid system has exciting prospects for a phonon-based approach to integrating NVs into quantum networks.

## 5. Simulating Hamiltonian evolution on a quantum computer

Richard Cleve, University of Waterloo

(Session 2 : Thursday from 10:45am - 11:30am)

I will explain various quantum algorithms that have been proposed for simulating the evolution of a quantum state under a Hamiltonian, including my recent joint work (with Dominic Berry, Andrew Childs, Robin Kothari, and Rolando Somma) that dramatically improves the running time as a function of the precision of the output data.

## 6. Probabilistic protocols in quantum information? Probably not.

Joshua Combes, University of New Mexico

(Session 13 : Saturday from 5:00pm - 5:30pm)

Probabilistic protocols in quantum information are an attempt to improve performance by occasionally reporting a better result than could be expected from a deterministic protocol. Here we show that probabilistic protocols can never improve performance beyond the quantum limits on the corresponding deterministic protocol. To illustrate this result we examine three common probabilistic protocols: probabilistic amplification, weak value amplification, and probabilistic metrology. In each of these protocols we show explicitly that the optimal deterministic protocol is better than the corresponding probabilistic protocol when the probabilistic nature of the protocol is correctly accounted for.

## 7. Shortcuts to adiabaticity in many-body systems

Adolfo del Campo, Los Alamos National Laboratory

(Session 9b : Friday from 5:00pm - 5:30pm)

The evolution of a system induced by counter-diabatic driving mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need of auxiliary non-local interactions for matter-waves. Here experimentally realizable driving protocols are presented for a large class of single-particle, many-body, and non-linear systems without demanding the spectral properties as an input. The method is applied to the fast decompression of quantum fluids realizing a dynamical quantum microscope, as well as to the fast transport of ion chains.

## 8. Trapped-ion quantum information processing experiments at NIST

John Gaebler, National Institute of Standards and Technology

(Session 1 : Thursday from 9:15am - 9:45am)

We report experiments towards scalable quantum information processing with laser-cooled trapped ions. Quantum information is stored in internal (hyperfine ground) states of ions and gate operations are performed with laser and microwave fields. We describe the current status of quantum information experiments using multi-zone trap arrays to investigate the basic tasks of a quantum information processor including transport of ions between zones and sympathetic cooling. In one recent experiment we created an entangled steady state of two trapped ions using dissipation. The steady state can be maintained for a duration of several times the entanglement generation duration and the entanglement fidelity is currently limited by identified technical issues. We also briefly describe recent progress with other quantum-information-focused experiments in our group including the generation of entanglement between two ions held in distinct but coupled trap zones, efforts to reduce the electric field noise from trap surfaces, superconducting photon detectors and junctions for switching the transport pathway of ions in multi-zone traps structures. *This work is supported by IARPA, ONR, and the NIST Quantum Information Program.

## 9. Quantum gate set tomography

John Gamble, Sandia National Laboratories

(Session 11 : Saturday from 10:15am - 10:45am)

In this talk, I will discuss a recently-proposed framework called "gate set tomography" (GST) for self-consistently characterizing an entire set of quantum logic gates on a black-box quantum device. Until recently, protocols for quantum tomography relied on a pre-existing and perfectly calibrated reference frame for the measurements used to characterize a device. GST eschews this artificial separation entirely, instead characterizing quantum processes, preparations, and measurements concurrently. I will then describe an explicit closed-form protocol for linear-inversion GST, whose reliability is independent of pathologies such as local maxima of the likelihood function. This initial estimate can then be refined using standard likelihood maximization techniques. Finally, I discuss recent experimental implementations of GST for single qubits in both ion traps and electrostatically defined quantum dot systems. This work was supported in part by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

## 10. Understanding the effects of leakage in superconducting quantum error detection circuits

Joydip Ghosh, University of Calgary

(Session 9a : Friday from 4:30pm - 5:00pm)

The majority of quantum error detection and correction protocols assume that the population in a qubit does not leak outside of its computational subspace. For many existing approaches, however, the physical qubits do possess more than two energy levels and consequently are prone to such leakage events. Analyzing the effects of leakage is therefore essential to devise optimal protocols for quantum gates, measurement, and error correction. In this talk, I discuss the role of leakage in a two-qubit superconducting quantum error detection circuit. We simulate the repeated ancilla-assisted measurement of a single Z operator for a data qubit, record the outcome at the end of each measurement cycle, and explore the signature of leakage events in the obtained readout statistics. An analytic model is also developed that closely approximates the results of our numerical simulations. We find that leakage leads to destructive features in the quantum error detection scheme, making additional hardware and software protocols necessary.

## 11. Practical and Fast Gaussian State Estimation

Scott Glancy, National Institute of Standards and Technology

(Session 11 : Saturday from 11:45am - 12:15pm)

Many experiments on quantum systems involve the preparation and measurement of Gaussian states of a multi-system continuous variable Hilbert space. Examples include optical and microwave systems involving squeezing and linear interactions and nanomechanical resonators described with second order Hamiltonians. The state space that these systems access is much smaller than the full Hilbert space and can be fully characterized with a 2Nx2N covariance matrix and 2N means vector, where N is the number of individual modes or resonators. We describe here a very simple and fast method for estimating the covariance matrix and means vector from homodyne (or quadrature) measurement data collected at arbitrary phases. The method computes observed means of simple functions of the homodyne (phase, quadrature) pairs, which are easily related to the covariance matrix and means vector. We characterize uncertainty through a parametric bootstrap strategy. Our method is particularly useful for the analysis of large data sets.

## 12. The effect of realistic noise models on quantum error correction thresholds

Mauricio Gutierrez, Georgia Institute of Technology

(Session 9a : Friday from 5:00pm - 5:30pm)

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code (QECC). In this context, it is common to model the noise as a depolarizing channel by inserting Pauli gates randomly throughout the circuit [1]. However, it is not clear how sensitive a code's threshold is to the noise model, and whether or not a depolarizing channel is a good approximation for realistic non-stabilizer errors. Within the stabilizer formalism, we have shown that for a single qubit more accurate approximations can be obtained by including in the noise model Clifford operators and Pauli operators conditional on measurement [2]. Independent work by Magesan et al. has also shown the utility of adding Clifford operators to error models [3]. We now examine the feasibility of employing these error approximations at the single-qubit level to obtain better estimates of a QECC's threshold. For several codes and various noise models, we simulate an error-correction step and compute the pseudo-threshold by determining the noise strength above which encoding reduces the qubit fidelity. We compare the pseudo-threshold values for the real noise with its Pauli and expanded Pauli approximations. In most cases, the expanded Pauli channel provides a significantly better approximation to the real pseudo-threshold suggesting that our expanded error models will lead to more accurate stabilizer-based threshold estimations for realistic noise models. [1] A.M. Steane, Phys. Rev. A 68, 042322 (2003) [2] M. Gutiérrez, L. Svec, A. Vargo, and K. R. Brown, Phys. Rev. A. 87, 030302(R) (2013) [3] E. Magesan, D. Puzzuoli, C. E. Granade, D. G. Cory, Phys. Rev. A 87, 012324 (2013)

## 13. Spacetime, quantum cloning and black holes

Patrick Hayden, Stanford University

(Session 7 : Friday from 10:30am - 11:15am)

Reconciling black hole evaporation with the unitarity of quantum mechanics is an endeavour frought with conceptual difficulties. Not least among them is the apparent need for quantum cloning or, equivalently, violations of the monogamy of entanglement. The most recent and confusing incarnation of this problem is the so-called firewall paradox, which interprets monogamy violations as an indication that black holes may not have interiors. This talk will begin with a more pedestrian question: understanding all the ways in which quantum information can be replicated in Minkowski spacetime. It turns out that there is an amazing variety, perhaps an indication that we should not be so worried about apparent violations of no-cloning in situations in which the causal structure of spacetime is itself in doubt. Towards the end, I will return to the black hole firewall problem and sketch some of the quantum information theoretic ideas that have been proposed as possible resolutions.

## 14. Period Finding with Adiabatic Quantum Computation

Itay Hen, University of Southern California

(Session 9a : Friday from 4:00pm - 4:30pm)

We outline an efficient quantum-adiabatic algorithm that solves Simon's problem, in which one has to determine the period', or xor-mask, of a given black-box function. We show that the proposed algorithm is exponentially faster than its classical counterpart and has the same complexity as the corresponding circuit-based algorithm. Together with other related studies, this result supports a conjecture that the complexity of adiabatic quantum computation is equivalent to the circuit-based computational model in a stronger sense than the well-known, proven polynomial equivalence between the two paradigms. We also discuss the importance of the algorithm and its implications for the existence of an optimal-complexity adiabatic version of Shor's integer factorization algorithm and the experimental implementation of the latter.

## 15. Single charged impurities inside a Bose-Einstein condensate

Sebastian Hofferberth, Universität Stuttgart

(Session 1 : Thursday from 8:30am - 9:15am)

We investigate the interaction of a single electron as well as a single ion with a Bose-Einstein condensate (BEC). The charge impurities are produced by exciting exactly one atom from the BEC to a Rydberg state. Since the ionic core and the Rydberg electron have vastly different mass and interaction range with the surrounding ground state, we can consider both parts separately. Firstly, for low-L Rydberg states, the electron wavefunction is fully immersed in the BEC, and we observe electron-phonon coupling. We observe that single electron excite collective modes of the whole condensate. Alternatively, for high-L states the electron can be moved completely outside of the BEC, enabling us to study the interaction of the ionic core with the BEC. We are currently studying ion-ground state Feshbach resonances and investige the possibility of trapping the ion inside the BEC without any external electric fields.

## 16. Quantum process tomography of near-unitary maps

Amir Kalev, University of New Mexico

(Session 11 : Saturday from 11:15am - 11:45am)

We study the problem of quantum process tomography given the prior information that the implemented map is near to a unitary map on a d-dimensional Hilbert space. In particular, we show that a perfect unitary map is completely characterized by a minimum of d^2 + d measurement outcomes. This contrasts with the d^4 measurement outcomes required in general. To achieve this lower bound, one must probe the system with a particular set of d states in a particular order. This order exploits unitarity but does not assume any other structure of the map. We further numerically study the behaviors of two of compressed sensing estimators based on correct or faulty prior information caused by noise. The results show two important features: (1) When we have accurate prior information, one can drastically reduce the required data needed; (2) Different estimators applied to the same data are sensitive to different types of noise. The estimators could, therefore, be used as indicators of particular error models and to validate the use of prior assumptions for compressed sensing quantum process tomography. Finally, we consider the more general case of noisy quantum maps, with a low level of noise. Our study indicates that transforming to the interaction picture, where the noiseless map is represented by a diagonal operator, can provide a useful tool to identify the noise structure. This, in turn, can lead to a substantial reduction in the numerical resources needed to estimate the noisy map.

## 17. Certifying violations of local realism

Emanuel Knill, University of Colorado at Boulder

(Session 12 : Saturday from 1:45am - 2:30pm)

Many applications of quantum systems require measurements that verify the presence of sufficiently strong quantum correlations. The probability of the following unwanted event must be extremely small: The event where the correlations are not sufficiently strong but one is nevertheless convinced that they are strong enough. Important examples of quantum correlation occur in experiments showing violations of Bell's inequalities, which are thought to invalidate local realism. This is a review of how such violations are quantified and robustly certified, with or without predetermined Bell's inequalities.

## 18. True Quantum Precision and Unique Optimal Probes in presence of Decoherence.

Sergey Knysh, NASA Ames Research Center

(Session 13 : Saturday from 5:30pm - 6:00pm)

Quantum instruments derived from composite systems allow greater measurement precision than their classical counterparts due to coherences maintained between the N component elements; spins, atoms or photons. Typical decoherence that plagues real-world devices can be dephasing, particle loss, thermal excitation and relaxation. All these adversely affect precision (mean squared error), whether one is measuring time or phase, or even the noise amplitude itself. We develop a novel technique that uncovers the uniquely optimal probe states of the N qubits' alongside new tight bounds on precision under local and collective mechanisms of these noise types above.   For large quantum ensembles (where numerical techniques fail), the problem reduces by analogy  to finding the ground state of a 1-D particle in a potential well, with the shape of the well dictated by the type and strength of decoherence. Under collective dephasing alone we find that optimal estimation of phase and noise parameter can be effected simultaneously, utilizing the same optimal probe and measurement scheme. The formalism is applied to real-world devices such as the Mach-Zehnder interferometer and atom clocks.

## 19. Optimal quantum-enhanced interferometry using a laser power source

Matthias Lang, University of New Mexico

(Session 9c : Friday from 5:00pm - 5:30pm)

We consider an interferometer powered by laser light (a coherent state) into one input port and ask the following question: what is the best state to inject into the second input port, given a constraint on the mean number of photons this state can carry, in order to optimize the interferometer’s phase sensitivity? This question is the practical question for high-sensitivity interferometry. We answer the question by considering the quantum Cramer-Rao bound for such a setup. The answer is squeezed vacuum, if there are no photon losses in the interferometer. For a lossy interferometer, the squeezed vacuum is the best choice for the practical case where the laser power is much bigger than the power put into the squeezing.

## 20. Symmetry-Protected Topological Entanglement

Iman Marvian, University of Southern California

(Session 9b : Friday from 5:30pm - 6:00pm)

We propose an order parameter for the Symmetry-Protected Topological (SPT) phases which are protected by an Abelian on-site symmetry. This order parameter, called the SPT entanglement, is defined as the entanglement between A and B, two distant regions of the system, given that the total charge (associated with the symmetry) in a third region C is measured and known, where C is a connected region surrounded by A and B and the boundaries of the system. In the case of 1-dimensional systems we prove that at the limit where A and B are large and far from each other compared to the correlation length, the SPT entanglement remains constant throughout a SPT phase, and furthermore, it is zero for the trivial phase while it is nonzero for all the non-trivial phases. Moreover, we show that the SPT entanglement is invariant under the low-depth local quantum circuits which respect the symmetry, and hence it remains constant throughout a SPT phase in the higher dimensions as well. Finally, we show that the concept of SPT entanglement leads us to a new interpretation of the string order parameters and based on this interpretation we propose an algorithm for extracting the relevant information about the SPT phase of the system from the string order parameters.

## 21. An on-chip toolset for surface-electrode trap based quantum processors

True Merrill, Georgia Tech Research Institute

(Session 1 : Thursday from 9:45am - 10:15am)

Increasing the size and complexity of ion-trap quantum computing experiments requires improvements in automation, hardware, and control.  We report on several technologies which incorporate control electronics, diffractive ion imaging optics, and quantum control techniques for microwave gates in microfabricated surface-traps.  We demonstrate a compact, in-vacuum 80 channel digital-to-analog converter (DAC) system controlling a surface-electrode trap.  The DAC system transports  40Ca+ ions for over 70 m at 1 m/s without cooling, and the measured 0.8 quanta/ms  ion-heating rate is comparable to external DAC systems.  A second project incorporates diffractive Fresnel mirrors onto a trap surface for enhanced ion imaging and state detection.  Optics for light collimation and refocusing are demonstrated, achieving a ~8.3 x enhancement in the total fluorescence signal.  We comment on possible limits to asynchronous ion-qubit readout and strategies to mitigate decoherence from stray photons during measurement processes. Finally, we discuss composite pulse techniques for gates on 171Yb+ qubits that yield accurate quantum control despite classical control errors.

## 22. Symmetry-protected topological ordered phases and their use for quantum computation

Akimasa Miyake, University of New Mexico

(Session 4 : Thursday from 4:30pm - 5:00pm)

Collective phenomena, like superconductivity and magnetism, are usually robust features of quantum many-body systems. They only depend on a few key parameters of a system Hamiltonian, and often symmetries are sufficient enough to characterize different (quantum) phases associated with different collective behaviors. Through remarkable progress at the crossover between quantum information and quantum many-body physics, it gets more and more clear that certain strongly-correlated ground states could be harnessed for quantum information processing, based on their underlying entanglement structure and thus inherent complexity. For example, some concrete models of topological orders are most known by the application to quantum error correction. Here we address a question: "to what extent computational usefulness of quantum many-body ground states would be determined ubiquitously by symmetries, without the system Hamiltonian specified in detail?" Our approach may be also applicable to how quantum state preparation and verification can be made without detailed knowledge about the system, in the context of quantum simulation. This is a joint work with Jacob Miller.

## 23. Topological defect formation and dynamics in ion Coulomb crystals

Heather Partner, Physikalisch-Technische Bundesanstalt

(Session 8 : Friday from 3:00pm - 3:30pm)

Topological defects (kinks) in laboratory systems have attracted recent interest because of their universal nature. In our system, kinks form during nonlinear quenches from the linear to zigzag phase in Coulomb crystals of about 30 172Yb+ ions in a segmented linear trap. I will present our experimental study of probabilistic kink creation in the context of the Kibble-Zurek mechanism, which predicts a scaling for defect creation as a function of quench rate, and discuss the effects of inhomogeneity and finite size in such systems. In addition, I will describe the dynamics of such defects and how they can be controllably modified. These methods provide a toolbox for using kinks to study phase transitions and soliton physics, and as a potential carrier of quantum information.

## 24. Optimal dissipative encoding and state preparation for topological order

Fernando Pastawski, California Institute of Technology

(Session 9b : Friday from 4:30pm - 5:00pm)

We study the suitability of dissipative (non-unitary) processes for (a) encoding logical information into a topologically ordered ground space and (b) preparing an (arbitrary) topologically ordered state. We give a construction achieving (a) in time O(L) for the LxL-toric code by evolution under a geometrically local, time-independent Liouvillian. We show that this scaling is optimal: even the easier problem (b) takes at least O(L) time when allowing arbitrary (possibly time-dependent) dissipative evolution. For more general topological codes, we obtain similar lower bounds on the required time for (a) and (b). These bounds involve the code distance and the dimensionality of the lattice. The proof involves Lieb-Robinson bounds, recent cleaning-lemma-type arguments for topological codes, as well as uncertainty relations between complementary observables. By allowing general locality-preserving evolutions (including, e.g., circuits of CPTPMs), our results extend earlier work characterizing unitary state preparation.

## 25. An atomic superfluid Bose-Einstein condensate in a ring

William Phillips, Joint Quantum Institute/National Institute of Standards and Technology

(Session 6 : Friday from 8:30am - 9:15am)

A Bose-Einstein condensate extending around a ring-shaped trap that is interrupted by a repulsive barrier can exhibit behavior similar to that of a superconducting loop interrupted by a weak link or Josephson junction. [ See, for example, K. Wright, R. Blakestad, C. Lobb, W. Phillips, and G. Campbell, Phys. Rev. Lett 110, 025302 (2013). DOI: 10.1103/PhysRevLett.110.025302]. We observe controllable, discrete phase slips (jumps in the phase winding number around the ring) and hysteretic behavior. Analogies to the superconducting circuit can describe much of the behavior of this atomtronic circuit. This work was partially supported by the ONR, the NSF, and the ARO.

## 26. Spectrally Entangled Photon Pairs for Ultrafast Probing of Molecules

Michael Raymer, University of Oregon

(Session 3 : Thursday from 2:45pm - 3:15pm)

We introduce a new method, called entangled photon-pair two-dimensional fluorescence spectroscopy (EPP-2DFS), to sensitively probe the nonlinear electronic response of complex molecular systems. The method incorporates a separated two-photon (Franson) interferometer, which generates time-frequency-entangled photon pairs, into the framework of a fluorescence-detected 2D optical spectroscopic experiment. The EPR-like correlations in time and frequency allow circumventing the usual restrictions imposed by the time-frequency uncertainty principle.

## 27. Classical command of quantum systems

Ben Reichardt, University of Southern California

(Session 12 : Saturday from 2:30pm - 3:15pm)

Can a classical experimentalist command an untrusted quantum system to realize arbitrary quantum dynamics, aborting if it misbehaves?  We give a way for a classical system to certify the joint, entangled state of a bipartite quantum system, as well as command the application of specific operators on each subsystem. This is accomplished by showing a strong converse to Tsirelson's optimality result for the CHSH game: the only way to win many games is if the bipartite state is close to the tensor product of EPR states, and the measurements are the optimal CHSH measurements on successive qubits. This leads directly to a scheme for device-independent quantum key distribution. Control over the state and operators can also be leveraged to create more elaborate protocols for reliably realizing general quantum circuits. Joint work with Falk Unger and Umesh Vazirani.

## 28. Quantum optics experiments at Earth-orbital scales and beyond

David Rideout, University of California, San Diego

(Session 9c : Friday from 4:30pm - 5:00pm)

A number of national and international entities are racing to set up satellite-based quantum communication infrastructure, which would allow the construction of a global network for quantum key distribution. The construction of such a network poses numerous technological challenges, considering that quantum entanglement has not yet been demonstrated at such scales. I will provide some details of a Canadian Space Agency funded mission to demonstrate quantum entanglement between the Earth's surface and Low Earth Orbit, and sketch some tests of fundamental physics which could be enabled by such satellites, ranging from verification of quantum mechanics to tests of spacetime discreteness from quantum gravity.

## 29. Tomography of Quantum Fields

Carlos Riofrio, Freie Universität Berlin

(Session 11 : Saturday from 10:45am - 11:15am)

Understanding the fundamental interactions in many-body physical systems is of great interest in current theoretical and experimental efforts. In particular, continuous many-body systems or fields are exciting because they offer the tools for performing quantum simulations of processes of non-equilibrium, equilibration and thermalization. In this context, the problem of developing tools for identifying and reconstructing the state or some aspect of such systems is needed on a practical level. In this talk, I will present a first approach in that direction and possible applications for reconstructing quantum fields from low order correlation functions readily measurable in current experiments. We concentrate on one dimensional systems with spatially limited entanglement which are well described by the continuous matrix product state (cMPS) formalism.

## 30. Mapping the topological phase diagram of superconducting qubit systems

Pedram Roushan, UCSB

(Session 10 : Saturday from 9:15am - 9:45am)

Building a practical quantum simulator requires a scalable architecture suitable for large numbers of qubits. By combining the high coherence Xmon qubits with an adjustable inductance, we have developed a new qubit architecture called g-mon, which has a tunable qubit-qubit interaction. To demonstrate this tunability, we have performed high fidelity single and two-qubit gates. Turning on the qubit-qubit interaction allows for fast multi-qubit operations implemented in less than 30 ns, achieving multi-qubit gate times approaching that of single qubit gates. Furthermore, we show the versatility of this system by mapping the topological phase diagram of interacting Hamiltonians. So far, experimental studies of topological invariants in condensed matter systems have been limited to transport measurements in non-interacting systems. Recently, it was proposed [1] that the topological properties of Hamiltonians can be inferred from quantum dynamics. Using superconducting g-mon qubits, we experimentally measure the Berry curvature, a quantity that reflects the geometrical properties of the eigenstates, for various eigenstates of the Hamiltonian of the system. We will discuss the phase diagram of various topological phases and the robustness of the measured Chern numbers. [1] Gritsev and Polkovnikov, PNAS, 109, 6457 (2012).

## 31. Quantum Behavior of Electro-mechanical Structures

Keith Schwab, Caltech

(Session 6 : Friday from 9:15am - 10:00am)

Electro-mechanical structures composed of a radio-frequency mechanical resonator parametrically coupled to a superconducting microwave frequency electrical resonator, offer an opportunity to study quantum behavior of both the electronic and mechanical degrees of freedom. We have recently demonstrated detection of a single motional quadrature with imprecision less than x_zp, and avoidance of the backaction due to the shot noise of the microwave field. We have also demonstrated the measurement of the imbalance between up and down conversion and will discuss the interpretation of these measurements. Finally, we have also recently demonstrated quantum squeezing of the motion using a reservoir engineering technique described by Aash Clerk et al and will present this new data.

## 32. Autonomously stabilized entanglement between two superconducting qubits

Shyam Shankar, Yale University

(Session 10 : Saturday from 8:30am - 9:15am)

Quantum error-correction codes are designed to protect an arbitrary state of a multi-qubit register against decoherence-induced errors, but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first step is to stabilize a non-equilibrium state of a simple quantum system such as a qubit or a cavity mode, in the presence of decoherence. Several groups have recently accomplished this goal using measurement-based feedback schemes. A next step is to prepare and stabilize a state of a composite system. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result[1] is achieved by an autonomous feedback scheme which combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative bath. Similar bath engineering techniques have recently been used for qubit reset, single qubit state stabilization, as well as for the creation and stabilization of states of multipartite quantum systems. Unlike conventional, measurement-based schemes, an autonomous approach which uses engineered dissipation to counteract decoherence, obviates the need for a complicated external feedback loop to correct errors. Instead the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building-block for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, will be an essential tool for the implementation of quantum-error correction. [1] http://dx.doi.org/10.1038/nature12802

## 33. Tensor networks and Symmetries

Sukhbinder Singh, Macquarie University, Sydney

(Session 9b : Friday from 4:00pm - 4:30pm)

Tensors networks methods, which are based on ideas of entanglement and renormalization group, have significantly progressed our understanding of strongly correlated quantum lattice systems in recent years. Examples of popular tensor network states include the matrix product state (MPS)[1], which results naturally from both Wilson’s numerical renormalization group[2] and White’s density matrix renormalization group(DMRG)[3], and the multi-scale entanglement renormalization ansatz (MERA) [4] which is based a specific RG scheme known as entanglement renormalization [5]. These tensor networks have been applied to the exploration of frustrated antiferromagnets, interacting fermions, quantum criticality, topological order and symmetry protected order, and more recently, the MERA has been used to explore[6] the holographic correspondence[7] of string theory. The careful incorporation[8] of lattice symmetries (both spacetime and internal symmetries) in tensor networks is playing an increasingly important role in these applications. In this talk I will outline some aspects of this role in the context of the MPS and the MERA where symmetries have been exploited to (i) target specific quantum number sectors of the Hilbert space, which subsequently also allows for the efficient simulation of lattice systems of anyons[9], (ii) identification of the quantum order of a ground state from its tensor network description[10], and (iii) to realize certain symmetry features of the holographic correspondence in the MERA. References [1] S. Ostlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995). [2] K.G. Wilson, Rev. Mod. Phys. 47, 4, 773 (1975). [3] S.R. White, Phys. Rev. Lett. 69, 2863 (1992). [4] G. Vidal, Phys. Rev. Lett. 101, 110501 (2008). [5] G. Vidal, Phys. Rev. Lett. 99, 220405 (2007). [6] B. Swingle, Phys. Rev. D 86, 065007 (2012). [7] J. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998). [8] S. Singh, R. N. C. Pfeifer, and G. Vidal, Phys. Rev. A 82, 050301 (2010). [9] S. Singh, R. N. C. Pfeifer, G. Vidal, and G. K. Brennen. arXiv:1311.0967 (2013). [10] S. Singh and G. Vidal. Phys. Rev. B 88, 121108(R) (2013).

## 34. A quantum fractional Fourier transform

Rolando Somma, Los Alamos National Laboratory

(Session 2 : Thursday from 11:30am - 12:00pm)

The Fourier transform (FT) is ubiquitous in signal processing, as it can be used to filter noise. The digital version, often named the discrete Fourier transform, when formulated on a basis of quantum states, is the quantum Fourier transform (QFT). The efficiency in the implementation of the QFT is the main reason for several quantum speedups, including the one for factoring and the one in phase estimation at the Heisenberg limit. The fractional FT (frFT) is a generalization of the FT. The frFT has recently gained attention in signal analysis as it can filter noise in scenarios where the FT is not useful. Quantum frFTs (QfrFTs), however, have never been analyzed or applied; We propose a QfrFT and show that a good approximation of this transformation can be implemented on a quantum computer with exponentially less resources than those required for its conventional implementation. We then analyze some problems in signal analysis (parameter estimation) for which our defined QfrFT is useful. Applications of the QfrFT for the simulation of continuous-variable quantum mechanics will also be considered.

## 35. New Tools for Unitary Control of Cold Atom Qudits

Hector Sosa Martinez, University of Arizona

(Session 9c : Friday from 4:00pm - 4:30pm)

Accurate and robust quantum control of single or coupled qubit systems is a key element of quantum information science. In practice, the actual physical building blocks (atoms, ions, superconducting devices) are often qudits with state space dimension d>2, and the available auxiliary levels have proven useful for information processing tasks such as implementing Toffoli gates with two-body interactions. More generally, large internal state spaces may prove a useful resource if good laboratory tools for qudit manipulation can be developed. As a laboratory test bed for such development, we have implemented a protocol to perform arbitrary unitary transformations in the 16 dimensional ground hyperfine manifold of individual 133Cs atoms, by driving this system with phase modulated rf and microwave magnetic fields and using the tools of optimal control to find appropriate control waveforms. Similar to what can be achieved for qubits, we show that accurate unitary control can be achieved in the presence of simultaneous static and dynamical perturbations and imperfections in the control fields, simply by optimizing with respect to the appropriate cost function when designing control waveforms. We anticipate this approach to prove helpful for control in less than ideal environments, such as atoms moving around in the light shift potential of a dipole trap. We are currently exploring the prospects for inhomogeneous quantum control, with the goal of performing different unitary transformations on qudits that see different light shifts from an optical addressing field. Ultimately this may lead to addressable unitary control similar to what has been demonstrated for atomic qubits in optical lattices.

## 36. Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries

Krysta Svore, Microsoft Research

(Session 8 : Friday from 2:30pm - 3:00pm)

We present a non-deterministic circuit decomposition technique for approximating an arbitrary single-qubit unitary to within distance epsilon that requires significantly fewer non-Clifford gates than deterministic decomposition techniques. We develop Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit Z-axis rotation to within distance epsilon, where the number of T gates scales as 1.26*log_2(1/\epsilon) - 3.53, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of 2.4 * log_2(1/\epsilon) - 3.28 can be achieved for arbitrary unitaries and a small range of epsilon, which is roughly twice as good as optimal deterministic decomposition methods.

## 37. On generating macroscopic superpositions via nonlinear dynamics of stopped light in a two-component Bose-Einstein condensate

Collin Trail, University of Calgary

(Session 9c : Friday from 5:30pm - 6:00pm)

We investigate a method for generating nonlinear phase shifts on superpositions of photon number states. The light is stored in a Bose-Einstein condensate via electromagnetically-induced transparency memory techniques. The atomic collisions are exploited to generate a nonlinear evolution for the stored state. The stored light is then revived with the nonlinear phase shift imprinted upon it. For the special case of a coherent state input we find that this method can be used to generate an optical cat state. We investigate the validity of using the Thomas-Fermi and mean-field approximations.

## 38. Mismatched quantum filtering and entropic information

Mankei Tsang, National University of Singapore

(Session 7 : Friday from 11:15am - 11:45am)

Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state preparation, quantum metrology, and quantum control. If the filter assumes a wrong model due to assumptions or approximations, however, the estimation accuracy is bound to suffer. I shall present formulas that relate the error penalty caused by quantum filter mismatch to the relative entropy between the true model and the nominal model, with one formula for Gaussian measurements, such as homodyne detection, and another for Poissonian measurements, such as photon counting. These formulas generalize recent seminal results in classical information theory and provide new operational meanings to relative entropy, mutual information, and channel capacity in the context of quantum experiments. See http://arxiv.org/abs/1310.0291 for details.

## 39. All-Optical Switching and Router via the Direct Quantum Control of Coupling between Cavity Modes

Jason Twamley, Macquarie University

(Session 12 : Saturday from 3:15pm - 3:45pm)

We describe a scheme to execute all-optical routing of photonic information by optically controlling the internal quantum state of a individual scatterer coupled to two independent cavity modes. We show that through this quantum control one can dynamically and rapidly modulate the cavity coupling. This allows all-optical modulation of intercavity couplings via ac Stark or shuffle (stimulated Raman adiabatic passage) control of the scatterer’s internal states, and from this modulation, we show that we can perform all-optical switching and all-optical routing with near-unit switching contrast and with high bandwidth. [1] K. Xia and J. Twamley, Phys Rev X 3, 031013 (2013)

## 40. A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians

Thomas Vidick, UC Berkeley

(Session 4 : Thursday from 3:45pm - 4:30pm)

Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an (inverse-polynomial) approximation, expressed as a matrix product state (MPS) of polynomial bond dimension. The algorithm combines many ingredients, including recently discovered structural features of gapped 1D systems, convex programming, insights from classical algorithms for 1D satisfiability, and new techniques for manipulating and bounding the complexity of MPS. Our result provides one of the first major classes of Hamiltonians for which computing ground states is provably tractable despite the exponential nature of the objects involved.