2011 Poster Abstracts

Strong interactions of single atoms and photons near a dielectric boundary

Daniel Alton, California Institute of Technology

D. J. Alton (1), N. P. Stern (1), Takao Aoki (1,3), H. Lee (2), E. Ostby (2), K. J. Vahala (2), and H. J. Kimble (1). (1) Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, CA 91125, USA. (2) T. J. Watson Laboratory of Applied Physics 128-95, California Institute of Technology, Pasadena, CA 91125, USA. (3) present address: Department of Physics, Kyoto University, Kyoto 606-8502, Japan. Quantum control of strong interactions between a single atom and one photon has been achieved within the setting of cavity quantum electrodynamics (cQED) [1]. To move beyond proof-of-principle experiments involving one or two conventional optical cavities to more complex scalable systems that employ N >> 1 microscopic resonators requires localization of atoms on distance scales ~100 nm from a resonator's surface where an atom can be strongly coupled to a single intracavity photon. A promising candidate for the realization of such systems is a system of microtoroidal resonators that are optically coupled via tapered nanofibers [2]. Cavity QED interactions between falling single atoms and single intracavity photons in such a system has been achieved in the strong coupling regime [3], followed by demonstrations of dynamic regulation of photon transport [4,5]. Recent study allows observations of perturbative surface effects mediated by atom's radiative interactions, due to its proximity to the dielectric boundary of the resonator, and cQED dynamics in the strong coupling regime [6]. In this initial step into a new regime of cQED, we use real-time detection and high-bandwidth feedback to select and monitor the motion of a single Cesium atom through the evanescent field of a microtoroid. Direct temporal and spectral measurements along with simulations reveal the manifestly quantum nature of strongly coupled atom-cavity dynamics, and the significant role the Casimir effect and light forces play in the atom dynamics. This interplay is significant and important in determining the dynamics of cQED systems involving strongly interacting single atoms in close proximity to resonator boundaries. This work thereby sets the stage for trapping strongly interacting atoms near micro- and nano-scopic optical resonators. References: [1] H. J. Kimble, Nature 453, 1023-1030 (2008). [2] S. M. Spillane, et al., Phys. Rev. A 71, 013817 (2005). [3] T. Aoki, et al., Nature 442, 671-674 (2006). [4] B. Dayan, et al., Science 319, 1062 (2008). [5] T. Aoki, et al., Phys. Rev. Lett. 102, 083601 (2009). [6] D. J. Alton, et al., Nature Physics, online: 21 November 2010, doi:10.1038/nphys1837. This work is supported by NSF, NSSEFF, Northrop Grumman Corporation, ARO, and DARPA.

Fault-tolerant quantum computing with color codes

Jonas Anderson, University of New Mexico

Quantum computers have the promise of algorithms with exponential speed-ups over the best known classical algorithms. To achieve these speed-ups we have to combat the noise that occurs in quantum systems. This is the biggest obstacle in current attempts to build a quantum computer. Quantum error correction provides a path to fault-tolerant quantum computation (FTQC). Typical schemes for FTQC rely on concatenation, however, these schemes suffer from low accuracy thresholds (on the order of one part in 10,000) or high resource overheads (millions of physical qubits per logical qubit to achieve thresholds on the order of one percent). Topological surface codes introduced by Kitaev offer another route to fault tolerance with more modest overheads and thresholds approaching 1%. In addition these codes have a natural architecture that is local in two dimensions, namely the code can be implemented on a square lattice. The recently introduced topological color codes share many properties with surface codes, such as the ability to perform syndrome extraction locally in two dimensions. In addition, some families of color codes admit a transversal implementation of the entire Clifford group. These families are constructed on the 4.8.8 lattice. We estimate the code threshold using several methods including a self-avoiding walk bound, a combinatorial counting bound, a mapping onto the two-dimensional three-body random-bond Ising model, and Monte Carlo simulations. Our findings apply to two distinct models for syndrome measurement errors: a phenomenological model in which syndrome measurements are modeled as stochastically erring with probability at most p and a low-level model in which the individual components of the circuits carrying out syndrome measurements are modeled as stochastically erring with probability at most p. Our numerical estimate for the threshold in the phenomenological model is approximately 3% while our numerical estimate for the threshold with the circuit model is approximately 8.5 x 10^(-4). We find a better threshold than the toric code for the phenomenological model. The circuit model on the other hand performs worse than the toric code for a similar model. We believe this is due to the more complex circuitry involved in the 8-body parity checks. Our results give an estimate for the threshold for fault-tolerant quantum memory for the 4.8.8 color codes. The threshold for magic state distillation is likely to be higher than this value. Typical thresholds for distillation are around 15%. Also, using similar methods as those for surface codes, the logical CNOT gate can be implemented by code deformation in a single code block instead of between pairs of code blocks. In light of this information the threshold for fault-tolerant quantum memory for the color codes becomes the threshold for FTQC.

Quantum Control and Measurement in the 133Cs Full Hyperfine Ground Manifold

Brian Anderson, University of Arizona

Quantum systems with Hilbert space dimension greater than two (qudits) are often considered as carriers of quantum information. The use of qudit systems could prove advantageous for information processing tasks, provided that good laboratory tools for robust qubit manipulation and readout can be developed. We have successfully implemented a protocol for arbitrary state mapping in the 16-dimensional hyperfine ground manifold of the Cesium 133 atom, using only DC, rf and microwave magnetic fields and thus avoiding the photon scattering and decoherence characteristic of schemes that rely on optical fields. Our control waveforms are designed to provide robustness against errors and inhomogeneities in the control fields, and this has allowed us to achieve state mapping fidelities of 98% or better in the laboratory. We are currently investigating a procedure involving successive applications of state mapping waveforms, in the hope that this will allow us to separate qudit initialization and readout errors from state mapping errors, and thus to reliably measure state mapping fidelities in excess of 99%. We are also working to implement a scheme for arbitrary quantum state reconstruction via continuous weak measurement, which will add a crucial diagnostic tool to our toolbox.

Superconducting nanowire single-photon detector on a distributed Bragg reflector and self-aligned fiber-coupling

Burm Baek, National Institute of Standards and Technology

Numerous recent demonstrations have shown the high performance and usefulness of superconducting nanowire single-photon detectors (SNSPDs) in high-fidelity quantum optics measurements especially at telecommunication wavelengths. Tailoring detectors for a specific target wavelength is achieved by embedding the active superconducting layer in a carefully designed optical multilayer structure. Our approach is growing the superconducting layer with dielectric top coating on a distributed Bragg reflector (DBR). This enables efficient and simple butt-coupling of an optical fiber. We have developed SNSPDs in optical structures based on dielectric and GaAs DBRs. The devices on a dielectric DBR use a silicon wafer that enabled us to realize a robust and efficient self-alignment with the optical fiber by micromachining the chip. On the other hand, the devices on GaAs platform open the possibility of achieving optical quantum circuit on a chip by integrating single-photon sources such as a quantum dots with detectors.

Time-optimal synthesis of unitary transformations

Allen David Boozer, University of New Mexico

Many applications in quantum information science rely on the ability to coherently control the state of a quantum system. In a typical control problem, the system in question is described by a Hamiltonian containing several control parameters that we are free to vary, and we would like to determine the values of these parameters such that the time evolution of the system implements a desired unitary transformation. I will describe a simple toy model of such a control problem involving a spin-1/2 particle in a magnetic field, and present analytic solutions for the values of the control parameters needed to implement a given unitary transformation in the least possible amount of time. I will also describe a generalization of these solutions to the problem of inhomogeneous control.

Quantum Information Processing using Scalable Techniques

Ryan Bowler, National Institute of Standards and Technology

Ryan Bowler, David Hanneke, John Jost, Jonathan Home*, Yiheng Lin, Ting Rei Tan, Dietrich Leibfried, David Wineland Ion Storage Group, National Institute of Standards and Technology, Boulder, Colorado We have previously demonstrated the combination of the fundamental building blocks required for large-scale quantum information processing using trapped atomic ions [1, 2]. Qubits are stored in a magnetic-field insensitive hyperfine-state superpositions in ⁹Be⁺, and information transport is accomplished by moving the ions themselves with time-varying potentials applied to the electrodes of a multi-zone radiofrequency trap. We have characterized the repeatability of a multi-qubit operation involving a combination of one- and two-qubit gates with transport of trapped-ion qubits over macroscopic distances, demonstrating no loss of gate fidelity due to transport [1]. One limitation of our previous experiments was the two-qubit gate fidelity; a geometric phase gate [3] required a complicated pulse sequence to be compatible with our magnetic-field insensitive qubit manifold. We have switched to a two-qubit gate that works directly on the field-insensitive states [4] and have implemented it in a manner insensitive to drifts in optical phase [5]. Another limitation of our previous work was the large amount of sympathetic cooling of ²⁴Mg⁺ ions required to combat the motional excitation acquired from imperfect ion transport. We have developed controls for our trap potentials that significantly reduce this excitation and have decreased transport times, dramatically increasing our operation speed. This work is supported by NSA, IARPA, DARPA, Sandia, and the NIST Quantum Information Program. [1] J. P. Home, et al., Science 325, 1227 (2009) [2] D. Hanneke, et al., Nature Phys. 6, 13 (2010) [3] D. Leibfried, et al., Nature 422, 412 (2003) [4] A. Sørensen and K. Mølmer, Phys. Rev. Lett. 82, 1971 (1999) [5] P. J. Lee, et al., J. Opt. B 7, S371 (2005) * current address: ETH, Zurich Switzerland

Simulation of quantum spin models with 2D ion arrays in a Penning trap#

Joe Britton, National Institute of Standards and Technology

We discuss progress towards simulating a transverse Ising model on a 2D triangular lattice of several hundred ions in a Penning trap. Optical dipole forces can be used to implement either a ferromagnetic or anti-ferromagnetic interaction. An anti-ferromagnetic interaction on a triangular lattice exhibits spin frustration whose properties are hard to simulate on a classical computer. We trap several hundred 9Be+ ions in a Penning trap with a 4.5 T magnetic field. Ion clouds in a Penning trap rotate, and through precise control of the rotation frequency with rotating electric fields, the ions form a single plane oriented perpendicular to the trap magnetic field. Through their mutual Coulomb repulsion, the ions naturally form ordered triangular lattices. Our two-level system or qubit is the 124 GHz electron spin-flip transition in the ground state of 9Be+ [1]. Our initial effort uses an optical dipole force from two interfering, off-resonant laser beams to globally interact with all the ions and excite, in an internal state-dependent manner, the axial center-of-mass motion of the planar array. This produces an infinite range Ising interaction where the interaction strength is independent of the distance between ions. With a transverse magnetic field implemented with 124 GHz microwaves, this system exhibits a quantum phase transition which can be compared with calculations (benchmarked). More complicated distance-dependent interactions are obtained by employing a different time dependence (beat note) of the optical dipole force [2]. #Supported by the DARPA OLE program. *In collaboration with M.J. Biercuk (Phys Dept., Univ. Sidney) and H. Uys (CSIR, Pretoria, South Africa) and J.J. Bollinger (NIST, Boulder) [1] M.J. Biercuk et al., QIC 9, 920-949 (2009). [2] D. Porras and J.I. Cirac, Phys. Rev. Lett. 92, 207901 (2004).

Harmonic oscillators coupled at the single quantum level

Kenton Brown, National Institute of Standards and Technology

K. R. Brown, C. Ospelkaus, Y. Colombe, A. C. Wilson, D. Leibfried, & D. J. Wineland
Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA

We have recently built a surface electrode ion trap for ⁹Be⁺ ions (ion-to-surface distance = 40 μm) that incorporates electrodes cooled to 4.2 K. The small dimensions and low heating rate in this apparatus have enabled a first demonstration of quantized Coulomb interaction between ions held in separate trapping potentials (arxiv:1011.0473, accepted for publication in Nature). This system demonstrates a building block for quantum information processing and quantum simulation, and is a natural precursor to experiments in hybrid quantum systems. The trap is housed within a cold copper enclosure that shields it from magnetic field fluctuations, and the small ion-to-surface distance makes possible radial trapping frequencies > 30 MHz. We will present recent results and discuss potential applications that exploit these advantageous features.

This work is supported by IARPA, DARPA, ONR, and the NIST Quantum Information Program.

chievable concurrences for three qubits

Orest Bucicovschi, UCSD Department of Mathematics

We investigate the set of achievable values - the cornu concursoris - for the three pairwise concurrences of a state of three qubits. Taking advantage of the algebraic simplification of the expressions for the concurrences of generalized X-states we begin by showing that in this case it is the intersection of the convex hull of the Roman Steiner surface with the positive octant in the space of concurrences. Next we give three distinct proofs that this is true for any pure state of three qubits. Finally we show that the cornu concursoris is the solution of a linear matrix inequality involving three other entanglement invariants.
This is joint work with David A.Meyer and Jon R. Grice

Precision Measurements of the System Detection Efficiency of Optical Fiber-Coupled Transition-Edge Sensors

Brice Calkins, National Institute of Standards and Technology

The development of optical-wavelength single-photon detectors at extremely high (near unity) system detection efficiencies is of great interest in the fields of quantum optics and quantum information. However, high-precision measurement is required in order to verify detection efficiencies in the 90-100% range. The lack of an optical detection standard at the single-photon level means that this measurement must be made by attenuating a more powerful source, which can be calibrated to an optical power standard at photon fluxes 5 to 10 orders of magnitude higher. We report on experimental techniques for conducting these precision measurements both in continuous and pulsed-power modes, utilizing fiber-coupled milliWatt diode lasers, variable optical attenuators, and NIST-calibrated nanoWatt to milliWatt optical power meters. Using these methods we measured system detection efficiencies upwards of 95% for fiber-coupled optical Transition-Edge Sensor devices tuned to a variety of near-IR wavelengths.

Adiabatic Topological Quantum Computing with Surface Codes

Chris Cesare, Center for Quantum Information and Control, University of New Mexico

We present a model of quantum computation that marries the gapped robustness of adiabatic algorithms with the topological protection afforded by classes of quantum stabilizer codes. Computations are realized by code deformations augmented with the ability to prepare several special states, and the result of the computation is accessed by measuring the (topological) logical operators for each qubit involved. We demonstrate how to create code defects and then braid these defects adiabatically to perform gates between encoded logical qubits.

Ion Fluorescence Collecting by a Reflective Optical Trap Design

Chen-Kuan Chou, University of Washington

Chen-Kuan Chou, Gang Shu, Nathan Kurz, Thomas Noel, John Wright, Boris Blinov, University of Washington. Efficiently collecting ion fluorescence is critical for many aspects of trapped ion quantum computation and information, such as qubit state readout and entanglement generation. To address this issue, we developed a novel ion trap combining a spherical mirror with trap electrodes. With the advantage of optical alignment and little photon blocking, it collects >20% of the photons emitted from a single ion. The large spherical aberration can be compensated by a customized aspheric lens. Hopefully we can reach the diffraction limit, with which >70% fiber coupling efficiency is achievable. The trap's simple design can be easily adapted into more complex trap systems.

Al+ quantum-logic clocks for fundamental physics, geodesy, and quantum metrology*

Chin-wen Chou, National Institute of Standards and Technology

Laser-cooled trapped atoms have long been recognized as providing the basis for very accurate spectroscopy and clocks. Ultimate inaccuracies below 10^-18 are projected from the time-dilation of trapped ions that move at laser-cooled velocities. The Al+ ion is an attractive candidate for high accuracy, owing to its narrow electronic transition in the optical regime and low sensitivity to ambient field perturbations. Precision spectroscopy on Al+ is enabled by quantum information techniques. The motion of Al+ is cooled sympathetically via the Coulomb interaction with a simultaneously-trapped laser-cooled auxiliary ion. With conditional logic, the internal state of an Al+ is transferred to the auxiliary ion, mediated by the collective motion of the ions. Detecting the state of the auxiliary ion effectively projects the state of the Al+ ion. Clocks based on Al+ are approaching inaccuracy of 10^-18, but further control of atomic motion is needed to reach this goal. Nevertheless, the current inaccuracy of 8.6x10^-18 has enabled a geo-potential-difference measurement from the gravitational red shift corresponding to a height change of 37+/-17 cm. We have also observed quantum coherence of Al+ clock ions that corresponds to a record Q-factor of 3x10^16. We have also compared the Al+ resonance frequency to that of a single Hg+ ion to place limits on the temporal variation of the fine-structure constant. *work supported by ONR and AFOSR

Ion-photon networks for scalable quantum computing

Susan Clark, University of Maryland

Trapped ions connected by photons are a promising avenue for large-scale quantum computing and quantum information transfer. Previous experiments with photonically connected, distant, trapped ions establish ion entanglement, ion teleportation, and the generation of private random numbers. Here, we report advances toward combining these photonic gates between distant ions with Coulombic gates between nearby ions in order to demonstrate a scalable quantum network. Specifically, we show individual optical addressing of single ions, allowing photonic entanglement to be performed separately from the Coulomb gates. Also, we show increased robustness to phase noise from optical gates and dephasing from motional states of both the Coulomb two-ion and single-ion gates via the use of a composite pulse sequence similar to spin echo. These improvements are important steps to the realization of a scalable ion-photon network. This research was supported by IARPA through ARO contract, the ARO MURI program, the AQUTE program. the NSF PIF Program, and the NSF Physics Frontier Center at JQI.

Number theoretic application of a spin network model

Mark Coffey, Colorado School of MInes

We present a scalable spin-1/2 network capable of performing calculations of interest to number theory [1]. Among these computations are primality testing and factoring. The fully connected network model is realizable with superconducting phase qubits, and very probably with other solid-state spin implementations. The spin network model offers the prospect to perform interesting calculations in quantum information processing with a modest number of qubits. Joint work with Ron Deiotte. [1]M. W. Coffey and R. Deiotte, Europhys. Lett. 90:40006 (2010).

A Comparison Study of the Temperature Dependence of Anomalous Heating in Identically Fabricated Surface Electrode Ion Traps

Robert Cook, Sandia National Labs

A significant source of decoherence in trapped ion quantum computation is heating in the ions' motional degrees of freedom. The source and mechanism for this anomalous heating is poorly understood but has shown a nonlinear dependence on several trap parameters, specifically the temperature of the trap electrodes. Cooling the trap to cryogenic temperatures has been able to reduce the heating rate by several orders of magnitude. Recent results with superconducting electrodes showed no significant change in the heating rate across the superconducting transition, suggesting that the source of anomalous heating is primarily due to surface effects in the electrode. Therefore variations in the fabrication process could play an important role in these mechanisms. Here we compare the heating rate of a linear surface electrode trap mounted to a liquid helium bath cryostat to that of an identically fabricated trap in a room temperature UHV chamber.

A computational quest for quantum subsystem codes

Gregory Crosswhite, University of Washington

Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to active quantum error correcting schemes as well as to the design of self-correcting quantum memories. Previous approaches for investigating these codes have focused on applying theoretical analysis to look for interesting codes and to investigate their properties. In this talk we present an alternative approach that uses computational analysis to accomplish the same goals. Specifically, we present an algorithm that computes the optimal quantum subsystem code that can be implemented given an arbitrary set of measurement operators that are tensor products of Pauli operators. We then demonstrate the utility of this algorithm by performing a systematic investigation of the quantum subsystem codes that exist in the setting where the interactions are limited to 2-body interactions between neighbors on lattices derived from the convex uniform tilings of the plane.

Deterministic Random-Length Computation with Weakly Entangled Cluster States

Adam D'Souza, Institute for Quantum Information Science, University of Calgary

Universal quantum computation can be accomplished via single-qubit measurements on a highly entangled resource state, together with classical feedforward of the measurement results. The best-known example of such a resource state is the cluster state, on which judiciously chosen single-qubit measurements can be used to simulate an arbitrary quantum circuit with a number of measurements that is linear in the number of gates. We examine the power of the orbit of the cluster states under GL(2,C), also known as the SLOCC-equivalence class of the cluster state, as a resource for deterministic universal computation. We find that, under certain circumstances, these states do indeed constitute resources for such computations, but of random length.

Vacuum system for surface studies of ion traps

Nikolaos Daniilidis, University of California, Berkeley

Many current approaches to scalable quantum information processing rely on fabrication of miniaturized ion traps. One of the most resilient obstacles to operation of these devices is excessive "anomalous heating", caused by poorly understood electric field noise close to metallic surfaces. Recent measurements and evaluation of experimental data has indicated that anomalous heating may be related to surface adsorbates on trap electrodes and is likely related to sources of noise and dissipation encountered in other fields. In order to attack this problem, we are constructing a vacuum system combining ion trapping capabilities with analytical and surface cleaning tools.

Quantum Algorithms for geometry using continuous quantum walks in Rⁿ

Aaron Denney, University of New Mexico

Quantum walks have been the basis for several interesting results in quantum algorithms, from evaluating a NAND tree in time O(n^1/2), to recovering hidden non-linear structures in finite fields. Taking the continuous limit of a continuous time quantum walk on a lattice yields nothing more than the time-dependent Schrödinger equation. We show two uses for such evolution, in solving geometric, rather than algebraic problems. In both cases we recover geometric information about an initial state. In R² we can sample efficiently from the evolute of a plane curve. In Rⁿ, given a symmetric enough state concentrated near an n-sphere, we can efficiently locate its center, in constant a number of samples, as compared to O(n) samples required classically.

Local equivalence of topological order: Kitaev code and color codes

Guillaume Duclos-Cianci, Université de Sherbrooke

We demonstrate that distinct topological codes can be mapped onto each other by local transformations. The existence of such a local mapping can be interpreted as saying that these codes belong to the same topological phase. When used as quantum error-correcting codes, the local mapping also enables us to use any decoding algorithm suitable for one of these codes to decode other codes in the same topological phase. We illustrate this idea with the topological color code and the topological subsystem color code that are found to be locally equivalent to two copies of Kitaev toric code. We are therefore able to decode these two codes that had no previously known efficient decoding algorithm, and find error thresholds comparable to previously estimated optimal values. These local mappings could have additional use for fault-tolerant quantum computation. In particular, one could in principle take advantage of the features (transversal gates, topological gates, etc.) of all the codes that are locally equivalent by switching between them during the computation in a fault-tolerant fashion.

Efficient Generation of Quantum States of Light via Four Wave Mixing in Optical Fiber

Shellee Dyer, National Institute of Standards and Technology

Collaborators: Sae Woo Nam, Burm Baek, NIST The generation and manipulation of single photon states in optical fiber has the exciting possibility of high-efficiency detection, because it avoids the potential losses involved in coupling the single-photon states to single-mode optical fiber for long distance transmission and detection. However, several challenges remain for fiber-based generation and manipulation of quantum states. One key challenge arises from the low nonlinearity coefficient of optical fiber, which necessitates fiber lengths on the order of 100s of meters for high efficiency four-wave mixing. The dispersion, and hence the phase matching, in the optical fiber is not consistent throughout such long lengths, and this limits the four-wave mixing efficiency. Other key challenges include optical losses involved in filtering the strong pump signals from the single photon states, background signals due to Raman generation in the optical fiber, and optical source purity limitations. We discuss these challenges in the context of our progress towards efficient wavelength conversion of single photon states.

Integrated Photodetector for Fluorescence Detection in Trapped Ion Qubits

Amira Eltony, Massachusetts Institute of Technology

Integrated trapped ion quantum computation systems have recently made advances building on silicon chip technology by incorporating a variety of devices including optical fibers, MEMs cantilevers, and control electronics. This integration seeks to improve gate fidelities, fault tolerance thresholds, and scalability, but state detection efficiency relies on fluorescence detection, which is largely still implemented with bulk optics and conventional photomultipliers or image intensified charge coupled detectors. Here, we present a system designed to integrate a photodiode in close proximity with a microfabricated ion trap, for improved fluorescence detection. This design faces a significant challenge because the typical power emitted is on the order of picowatts and there is no internal gain mechanism in a PIN photodiode as there is in a PMT detector, thus requiring detection of photocurrents on the order of hundreds of femtoamps. Furthermore, the responsivity of photodiodes drops by as much as an order of magnitude during cooling to 4 K due to carrier freeze-out. Our approach places the photodiode immediately below a surface electrode trap fabricated with transparent electrodes, made of indium tin-oxide (ITO), on a quartz substrate. Assuming a noiseless amplifier, 99% state detection fidelity could be accomplished within 10 microseconds using the generated photocurrent from this photodiode configuration. We describe the fabrication and operation of our ITO trap, above which single ions have been trapped at cryogenic temperatures, and characterize trap behavior, including stability, compensation, and ion heating rates.

Neutral Atom Trapping with the Diffraction Pattern from a Circular Aperture for the Generation of a 2D Array of Optical Dipole Traps

Andrew Ferdinand, California Polytechnic State University, San Luis Obispo

Neutral atom quantum computing is a promising approach to creating a quantum computer. Recently, the neutral atom quantum computing community has made progress towards demonstrating the feasibility of neutral atom quantum computing. The qubits are formed by the motional or internal states of the neutral atoms. The initialization, readout, and a universal set of quantum gates of neutral atoms trapped in optical dipole traps have been experimentally demonstrated as well. An intrinsic advantageous characteristic of using neutral atoms is the weak interaction of neutral atoms with the environment, which can result in long coherence times. One aspect of neutral atom quantum computing that has caused difficulty is the ability to create a scalable system of qubits of which each qubit can also be addressed individually. Addressing each atom individually allows the initialization and readout of each qubit and single qubit gates. It would be advantageous to also have the ability to manipulate the position of each atom, allowing qubits to be brought into close proximity to facilitate two qubit gates. We plan on trapping rubidium atoms in the dipole traps formed by the localized intensity minima or maxima produced in the diffraction pattern immediately behind a circular aperture. Blue or red detuning of the trapping laser dictate whether the rubidium atoms are trapped in the minima or maxima, each of which has advantages and disadvantages in the context of quantum computing. The position of the trap sites, and therefore trapped atoms, can be manipulated through the angle at which the trapping laser beam is incident on the circular aperture. This technique potentially has the ability to produce a scalable system of qubits while allowing each qubit to be individually addressed. We anticipate demonstrating these trapping techniques by first cooling and trapping rubidium atoms with a magneto-optical atom trap (MOT). Once the atoms are successfully trapped in the MOT, the diffraction pattern immediately behind a 100μm diameter pinhole will be projected onto the cloud of trapped atoms, which then will be transferred to the dipole trap sites. Once this is accomplished we will measure the trap properties and compare them to our computational results. In this presentation we summarize our computational results for these traps and will report our experimental progress to date. This work was performed in collaboration with Dani May, Bert D. Copsey, Grant Rayner, Jennifer Rushing, Glen D. Gillen, and Katharina Gillen-Christandl (PI). We acknowledge helpful discussions with Thomas D. Gutierrez, Ivan H. Deutsch, and Marianna Safronova. This work was supported by the National Science Foundation Grant No. PHY-0855524.

Quantum systems as embarrassed colleagues: what do tax evasion and state tomography have in common?

Chris Ferrie, Institute for Quantum Computing, University of Waterloo

Quantum state estimation (a.k.a. "tomography") plays a key role in designing quantum information processors. As a problem, it resembles probability estimation -- e.g. for classical coins or dice -- but with some subtle and important discrepancies. We demonstrate an improved classical analogue that captures many of these differences: the "noisy coin". Observations on noisy coins are unreliable -- much like soliciting sensitive information such as one's tax preparation habits. So, like a quantum system, it cannot be sampled directly. Unlike standard coins or dice, whose worst-case estimation risk scales as the inverse of N for all states, noisy coins (and quantum states) have a worst-case risk that scales as the inverse of the square root of N and is overwhelmingly dominated by nearly-pure states. The resulting optimal estimation strategies for noisy coins are surprising and counterintuitive. We demonstrate some important consequences for quantum state estimation -- in particular, that adaptive tomography can recover the inverse of N risk scaling of classical probability estimation.

Characterization of high-purity, pulsed squeezed light at telecom wavelengths from pp-KTP for quantum information applications

Thomas Gerrits, National Institute of Standards and Technology

Pure optical squeezing in a single mode is highly desirable for quantum information applications such as continuous variable quantum computing and the generation of optical Schrödinger cat states. To generate optical cat states, photons are subtracted from squeezed light. Both the created quantum state and the subtracted photons must overlap with all modes (spatial, spectral, temporal) of the measurement apparatus, i.e. the homodyne detector and the photon-subtraction-arm single-mode fiber. This implies that the squeezed state must be in a single mode, allowing for all the subtracted photons to match the mode of the local oscillator. To date, high levels of mode-matched squeezing (matched to the mode of the local oscillator) have been achieved with cavity squeezing using a cw laser source. However, no pure squeezing in a single mode that qualifies for unambiguous photon subtraction has been shown so far. In pulsed experiments, which allow for true heralding of the created state, the purity and intensity of the measured squeezing is generally low due to mode-matching difficulties. Recent theoretical predictions have held that a squeezing in a single mode can in principle be achieved by engineering a parametric down-conversion source in which the spatial and spectral output modes are exactly tailored to match the local oscillator modes of the homodyne detection apparatus. We will present the experimental realization of such a source at telecom wavelengths, i.e. 1570 nm. The source is a periodically poled KTP crystal that delivers circular joint spectral distributions and a Hong-Ou-Mandel interference visibility of 97%. The measured g(2) values fit the theoretical predictions of single mode outputs (thermal and squeezed vacuum) very well. These results suggest that the squeezed vacuum is close to the spatial mode of the collection optics, i.e. single mode fiber. We will present various photon counting techniques to characterize the single mode character of two-mode and single-mode squeezed states.

Lessons and Innovations in Maximum Likelihood Quantum State Tomography

Scott Glancy, National Institute of Standards and Technology

S. Glancy, E. Knill, M. Girard, F. Mallet, and Thomas Gerrits

As the quality and size of our quantum devices improve, we must continue to improve our methods for testing these devices and analyzing their behavior. One important tool that we use is quantum state tomography (or quantum state estimation), which allows the estimation of the quantum state from a collection of measurements, each performed on identically prepared copies of the system. In this talk I will describe a few improvements to maximum likelihood quantum state tomography: a new iterative method to find the maximum likelihood state, a stopping criterion, and a resampling strategy to estimate confidence intervals.

At NIST we have been engaged in performing tomography for two experiments in continuous variable systems. The first produces superpositions of optical coherent states (such superpositions are sometimes called “Schrödinger cat”states) by photon subtraction from a squeezed light pulse, and the second produces squeezed states of itinerant microwave fields. I will describe lessons learned from analyzing the data of these experiments, focusing on challenges unique to tomography of continuous variable systems.

Entanglement of Spin Waves among Four Quantum Memories

Akihisa Goban, California Institute of Technology

Akihisa Goban(1), Kyung Soo Choi(1), Scott B. Papp(1)*, Steven J. van Enk(2) and H. Jeff Kimble(1) (1) Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125, USA (2) Department of Physics, University of Oregon, Eugene, Oregon 97403, USA E-mail address: agoban@caltech.edu Abstract; Quantum networks are composed of quantum nodes that interact coherently through quantum channels, and open a broad frontier of scientific opportunities [1]. We will review recent experiments with atomic ensembles in the Caltech Quantum optics group, directed toward the realization of quantum networks utilizing collective strong interaction between matter and light [2]. In particular, we demonstrate a quantum interface for measurement-induced quadripartite entanglement stored in four atomic memories [3]. Here, the entangled state for the four atomic ensembles is created by quantum interference in the measurement process. The heralded atomic state is ideally a quadripartite (i.e, N = 4 quantum systems) entangled state, a so-called W state. The individual atomic components for the entangled W state of the four ensembles are then coherently converted into four propagating beams of light, comprising a photonic W state via collective emissions of the spin waves. The full quadripartite entanglement is unambiguously confirmed by way of the operational metric of quantum uncertainty relations [4]. By controlling the spin-wave statistics, we observe statistical transitions from quadripartite entangled states to tripartite entangled, bipartite entangled and fully separable states. Also, we examine the dissipative dynamics of multipartite entanglement for the four quantum memories by monitoring the temporal decay of entanglement and observe the successive crossings of the boundaries for three-mode, two-mode entangled state, and separable state. Here, the decoherence for the atomic W state is governed by the temporal transitions of the initial collective state into a subradiant state due to the motional dephasing of the spin waves. Finally, we will discuss the extensions of our work to the investigation of the entanglement order for condensed-matter systems in thermal equilibrium. The comparison between the characterization of multipartite entanglement and the relaxations of entanglement in quantum many-body systems suggests that our method of entanglement characterization could be applied to access the link between off-diagonal long-range order and multipartite entangled spin waves in thermalized quantum magnets. References [1] H. J. Kimble, Nature 453, 1023 (2008). [2] C. W. Chou, et al., Nature 428, 828 (2005). [3] K. S. Choi, et al., Nature 468, 412 (2010). [4] S. B. Papp, et al. Science 324, 764 (2009). * Present address: National Institute of Standards and Technology, Boulder, Colorado 80305, USA. ** This work is supported by NSF, NSSEFF, DOD, Northrop Grumman Corporation, and IARPA.

Optical Feshbach Resonances for Quantum Control

Krittika Goyal, University of New Mexico

Optical Feshbach resonances (OFRs) are a useful tool to control the interaction strength between atoms, particularly in alkaline-earth-like elements without ground state hyperfine structure and narrow intercombination lines. Both s-wave [1] and p-wave [2] OFRs have been theoretically explored in 171Yb, a spin-1/2 fermion. For spin polarized atoms p-wave OFRs along with magnetic fields and selection rules for polarized light yields a highly controllable system. We show how such control can be used to explore a toy model of three-color superfluidity in optical lattices. Experimental studies, however, show that the loss rate is well beyond that predicted by current theories of OFRs. The most likely reason for the disagreement between theory and experiment is current theoretical models consider coupling of the scattering state of the ground potential to only a single bound state of the excited potential. Due to large detunings from a particular bound state of the excited potential considered in OFRs this is likely to be inaccurate. We develop a technique to obtain the scattering length and loss rates in OFRs including the coupling of the scattering state of the ground potential to multiple bound and scattering states of the excited potential. [1] Reicenbach et. al., PRA, 80, 020701R [2] Goyal et. al., arXiv:1010.0465

Quantum Process Tomography by Direct Characterization of Quantum Dynamics Using Hyperentangled Photons

Trent Graham, University of Illinois at Urbana-Champaign

We use hyperentangled photons to experimentally implement an entanglement-assisted quantum process tomography technique known as Direct Characterization of Quantum Dynamics (DCQD). Specifically, we use hyperentanglement-assisted Bell State Analysis to measure the effect of a single-qubit quantum process on a specific set of entangled states. We are thus able to characterize quantum processes with exponentially fewer measurements than are required by standard quantum process tomography. Furthermore, we demonstrate how known errors in both the state preparation and Bell State measurement may be compensated for in the data analysis. Using these techniques we have obtained preliminary process fidelities as high as 98.7 ± 0.3% for a single-qubit process. Limitations of the technique and applications to multi-qubit processes will be discussed.

Symbolic Quantum Computation Simulation: An Open-Source Implementation in SymPy

Brian Granger, Cal Poly San Luis Obispo

Addison Cugini, Cal Poly San Luis Obispo, San Luis Obispo, CA Matt Curry, Cal Poly San Luis Obispo, San Luis Obispo, CA Brian E. Granger, Cal Poly San Luis Obispo, San Luis Obispo, CA The simulation of quantum computers on classical computers is an important part of quantum information science. There is a need to create software tools that i) help newcomers to learn the field, ii) enable practitioners to design and simulate quantum circuits, iii) assist in the development of new algorithms and iv) provide an open-source foundation for further research in the field. Towards these ends we have created a package, in the open-source symbolic computation library SymPy, that simulates the quantum circuit model of quantum computation using standard Dirac notation. This package builds on the extant powerful symbolic capabilities of SymPy to preform its simulations in a fully symbolic manner. As part of this work, we have extended SymPy to handle the Dirac notation in its most general and abstract form. This includes operators, states, inner/outer products, tensor products, commutators/anticommutators, basis sets, representations and Hilbert spaces. Building on this general foundation, we use object oriented design to abstract circuits as ordered collections of quantum gate and qubit objects. Gate objects can either be applied directly to the qubit objects or be represented as matrices in different bases. The package is also capable of performing standard quantum algorithms such as the quantum Fourier transform and Shor's algorithm. A variety of measurements types are also possible on qubits. In this poster, we describe the software and show examples of quantum circuits on single and multi qubit states that involve common algorithms, gates and measurements. We also outline the completely open development model used for SymPy and how new users can become involved in its development.

Atoms Talking to SQUIDs

Jonathan Hoffman, Joint Quantum Institute, Department of Physics, University of Maryland

Number-conserving Bogoliubov approximation for BEC

Zhang Jiang, University of New Mexico

We consider a BEC of $N$ ultra-cold atoms in a trapping potential. The many-body wave function of the BEC is "encoded" in the $N$-particle sector of an extended catalytic state, coherent state for the condensate mode and a state for the orthogonal modes. Using a time-dependent interaction picture, we move the coherent state to the vacuum, where all the field operators are small compared to $\{N\}^\{1/2\}$. The resulting Hamiltonian can then be organized by powers of $\{N\}^\{-1/2\}$. Requiring the terms of order $\{N\}^\{1/2\}$ to vanish, we get the GP equation for the condensate wave function. Going to the next order, $N^0$, we are able to derive equations equivalent to those found by Castin and Dum [Phys. Rev. A "57", 3008 (1998)] for a number-conserving Bogoliubov approximation. In contrast to other approaches, ours allows one to calculate the state evolution in the Schrödinger picture, and it also has advantages in discussing higher-order corrections and multi-component cases.

A Layered Architecture for Quantum Computing using Optically-Controlled Quantum Dots

Cody Jones, Stanford University

We are designing a quantum computer which takes advantage of the strong capabilities of device integration afforded by semiconductor fabrication. Our qubit is defined by the electron spin states of a charged quantum dot controlled by ultrafast optical pulses [1]. Optical control makes this system very fast, scalable to large problem sizes, and extensible to distributed architectures [2]. The design of this quantum computer centers on error correction in the form of a topological surface code, which requires only local and nearest-neighbor gates [3]. The framework of this architecture is flexible, providing techniques to analyze and compare other quantum computer designs. The system we propose uses charged quantum dots to store quantum information in the electron spin state [4]. The quantum dots are embedded in a planar distributed Bragg reflector (DBR) microcavity [5], and a transverse magnetic field separates the spin levels. Broadband optical pulses rotate the spin vector [1]; these optical pulses are controlled by arrays of MEMS micromirrors [6]. Dispersive readout provides measurement of the spin state [7]. We seek to design a quantum computer architecture which can be scaled to problems believed to be intractable for classical computation, such as Shor's algorithm. We estimate this can factor a 2048-bit number in about one week by taking advantage of ultrafast optical control. Additionally, this particular architecture attempts to take advantage of mature technologies from other fields wherever possible, such as the MEMS mirror arrays. We implement the surface code for quantum error correction; this has a strong influence on the physical design of this system (such as nearest-neighbor gates for a 2D array of quantum dots), but in principle other methodologies are compatible with this framework. References: [1] Press, D., Ladd, T. D., Zhang, B., and Yamamoto, Y. Nature456, 218--221 (2008). [2] Van Meter, R., Ladd, T. D., Fowler, A. G., and Yamamoto, Y. International Journal of Quantum Information8, 295--323 (2010). preprint available as arXiv:0906.2686v2 [quant-ph]. [3] Fowler, A. G., Stephens, A. M., and Groszkowski, P. Physical Review A80(052312) (2009). [4] Imamoglu, A., Awschalom, D. D., Burkard, G., DiVincenzo, D. P., Loss, D., Sherwin, M., and Small, A. Physical Review Letters83(20), 4204{4207 (1999). [5] Reitzenstein, S., Hofmann, C., Gorbunov, A., Strauss, M., Kwon, S. H., Schneider, C., Löffler, A., Höfling, S., Kamp, M., and Forchel, A. Applied Physics Letters90(251109) (2007). [6] Kim, C., Knoernschild, C., Liu, B., and Kim, J. IEEE Journal of Selected Topics in Quantum Electronics13(2), 322--329 (2007). [7] Berezovsky, J., Mikkelsen, M. H., Gywat, O., Stoltz, N. G., Coldren, L. A., and Awschalom, D. D. Science314(5807), 1916{1920 (2006).

The validity of QDD

Wan-Jung Kuo, University of Southern California

For suppressing pure dephasing of a single qubit, Uhrig discovered an DD sequence (UDD) which is provably optimal in that it achieves to eliminate the dephasing to Nth order by applying the minimum number of N ideal pulses. For suppressing the general decoherence of one qubit, West et al proposed an efficient QDD scheme which is constructed by nesting two types of UDD sequences. From numerical study, QDD indeed seems to be able to decouple the general decoherence to Nth order by applying N^2 or (N+1)^2 pulses which is nearly optimal for low order N. However, the complete analytical proof of QDD has been missing. Wang and Liu proved the part for QDD with even order UDD on the inner level case. Recently we finally complete the proof for the validity of QDD.

Efficient tomography method for Matrix Product and Multi Scale Entangled states

Olivier Landon-Cardinal, Université de Sherbrooke

Quantum state tomography is essential to benchmark quantum devices but standard techniques fundamentally require a number of experiments and a post-processing effort that scales exponentially with the number of particles. However, by taking advantage of efficient representations of quantum states, such as matrix product states (MPS) or multi-scale entanglement renormalisation ansatz (MERA), we can do exponentially better. We describe a method for reconstructing a wide range of states from a small number of efficiently-implementable measurements and fast post-processing, namely all states well-approximated by MPS or MERA states. Examples of interest include GHZ, W and cluster states. Our method prevents the build-up of errors from both numerical and experimental imperfections and contains a built-in certification procedure. Moreover, in many cases, experimentalists are not interested in performing tomography in itself, but rather in comparing the experimental state to a desired goal state. We will thus discuss our ongoing effort to turn our approach into a simple and efficient Monte-Carlo certification procedure.

Dephasing of trapped-ion qubit due to Stark shift during shuttling

Hoi Kwan Lau, University of Toronto

We investigate a speed limit for quantum processing for trapped ion quantum computers using the Kielpinski-Monroe-Wineland (KMW) architecture [1]. The limiting speed for single-ion shuttling between a storage trap and a logic trap is constrained by the need to avoid excessive ion heating, and excessive dephasing due to Stark shifts. We find the path of an ion for which it gains a minimum phase is a cubic function of time. The total phase shift is quadratic in the duration of the shuttling trajectory, and an inverse cubic in the operational time scale. From these dependence relations, a limit of operational speed of ion-trap quantum computer is deduced. Without subsequent phase correction, the maximum speed an Calcium ion qubit can be transferred across a 100 micron-long trap, without excessive error, in about 10ns. [1] D. Kielpinski, C. Monroe, and D. J. Wineland, Nature (London) 417, 709 (2002).

Electromagnetically induced transparency on an array of artificial atoms

Patrick Leung, Institute for Quantum Information Science, University of Calgary

Electromagnetically induced transparency (EIT) has recently been demonstrated in a one-dimensional superconducting artificial atom in the microwave regime [1] and it is of interest to build quantum information devices with artificial atoms. Since one can flexibly engineer the properties of artificial atoms and the spatial dimension is reduced from three to one, artificial atoms has the potential to become a useful test bed for photonics. For instance, it is in theory impossible to induce a phase shift large enough for useful quantum gates with single photons via cross-phase modulation [2], and one may test the validity of the theory with microwave photons and artificial atoms. Here we develop the theory of a one-dimensional array of superconducting artificial atoms with EIT. Our theory shows how the absorption of the field in a one-dimensional array of atoms behaves similar to Beer's law and how the controlled field induces transparency in the array of atoms. Our theory also shows how EIT properties, such as the reduction of group-velocity, are achieved for microwave pulses in artificial atoms. [1] A.A. Abdumalikov Jr. et al, Phys. Rev. Lett., 104, 193601 (2010) [2] J. Gea-Banacloche, Phys. Rev. A, 81, 043823 (2010)

Enhanced Spontaneous Emission of a Trapped Ion in a Cavity QED System

Le Luo, Joint Quantum Institute

A micro-scale ion trap is integrated with an optical cavity to enhance the spontaneous emission from a single trapped ytterbium ion. Exciting the atom from the side of the cavity with a near resonant laser beam, we monitor the scattered photon output from an undriven cavity mode. Operating in the intermediate regime of cavity QED, we find an enhancement of the spontaneous emission into the cavity mode by more than a factor of 50 compared with the expected free-space emission into the same solid angle subtended by this mode. We investigate the spectrum of cavity photons as a function of the intensity of the excitation beam by varying the detuning between the atomic and cavity resonance. We also discuss the application of similar ion-cavity systems to enhance photon collection and thus improve the success probability of entangling remote ions. This research was supported by IARPA through ARO contract, the ARO MURI program, the NSF PIF Program, the AQUTE program, and the NSF Physics Frontier Center at JQI.

Single-ion Heisenberg-limited Quantum Phase Sensors

Warren Lybarger, Los Alamos National Laboratory

Warren E. Lybarger, Jr. (LANL), Rolando D. Somma (LANL), Diego Dalvit (LANL), John Chiaverini (MIT Lincoln Laboratory), and Malcolm G. Boshier (LANL) Abstract. We report on our efforts to construct a single-ion-qubit sensor capable of Heisenberg limited detection of external fields that can be efficiently coupled to the ion qubit. Based on a single-qubit iterative phase estimation algorithm (IPEA) [PRA 75, 012328 (2007)], a quadratic enhancement in quantum phase estimation precision is achieved when compared to standard shot-noise limited measurement protocols without using any entanglement. This approach also has the advantage that it does not require an understanding of the quantum Fourier transform, and it is readily related to more conventional approaches for measuring phases. The bit-by-bit estimation of an unknown phase only requires standard quantum information processing (QIP) protocols in addition to the use of single-qubit rotations that are each of a relative phase that is conditioned on all previous classical outcomes in the measurement sequence. Successful implementation of the IPEA will demonstrate a working quantum circuit with relatively immediate and useful applications in basic science, remote sensing, and clock synchronization. We also describe the potential application of novel ion trap architectures previously put forth [PRA 77, 022324 (2008)][ W. E. Lybarger, Jr., Ph.D. Thesis, UCLA (2010)] to the problem of miniaturizing the IPEA experiment as well as other single- and multi-qubit quantum enhanced metrology experiments. While these architectures were initially conceived in the context of large-scale QIP and quantum simulation, we face similar technical challenges in developing deployable ion trap based quantum sensors. This provides further impetus for developing relevant enabling technologies with both long- and short-term applications.

Quantum signatures of chaos in quantum tomography.

Vaibhav Madhok, CQUIC, University of New Mexico

We study the connection between quantum chaos and information gain in the time series of a measurement record used for quantum tomography. The record that is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on a large ensemble of identical systems. We find that, in the limit of vanishing noise, the fidelities of reconstruction are independent of the underlying chaos of the Floquet map. In the presence of noise, however, the fidelities on an average increase with the chaoticity of the map. Moreover, the number of time steps required to achieve a given fidelity decreases with the increase in the chaoticity, suggesting a connection between the rate of information gain and classical Lyapunov exponents.

Magic-state distillation with the four-qubit code

Adam Meier, National Institute of Standards and Technology

Universal quantum computation requires the ability to apply any unitary gate with an arbitrarily small error rate. The distillation of magic states is an often-cited technique for enabling universal quantum computation once the error rate for Clifford gates (a finite subset of unitary gates) has been made negligible by other methods. I present a routine for magic-state distillation that reduces the required overhead for a range of parameters of practical interest. Each iteration of the routine uses a four-qubit error-detecting code to distill eigenstates of the Hadamard gate, or H-states, at a cost of ten input states per two improved output states. Chaining this routine with the H-state distillation routine described by Bravyi and Kitaev allows for further improvements in overhead. Collaborators: B. Eastin and E. Knill

Optimized design of a polarization spectroscopy experiment to measure spin projection noise

Pascal Mickelson, University of Arizona

We optimize the design of an experiment to measure the projection noise associated with the collective spin of an atomic ensemble. In this setup, a weak probe laser will interact with a cold, trapped atomic sample of cesium atoms with high optical depth, leading to Faraday rotation of the probe light proportional to the atomic magnetization. If the atom-light coupling is strong enough, polarimetry of the probe light provides a measurement of the magnetization with resolution better than the spin projection noise, at which point measurement back-action becomes significant and can be used for quantum control of the spin. Here, we present two aspects of the experimental design: first, the "mode-matching" between the incident probe laser and the probe light scattered by the atoms, and second, the choice of trapping laser and geometry for creating the optically thick atomic samples needed for strong atom-light coupling. Our modeling indicates that the probe laser radius and the aspect ratio of the atomic cloud are the most important parameters for good mode-matching.

Ultrafast Control of Spin and Motion of Trapped Atomic Qubits

Jonathan Mizrahi, University of Maryland

J. Mizrahi, W. Campbell, C. Senko, and C. Monroe Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742 USA We experimentally demonstrate ultrafast spin flips of a trapped ion, using individual picosecond pulses from a mode-locked laser to drive Raman transitions between hyperfine qubit levels.[1] The large bandwidth and intensity of each pulse allow an individual pulse to coherently transfer more than 50% population in a time on the order of 10 ps. Furthermore, the large intensity of each pulse allows us to be far detuned (33 THz) from resonance, which makes decoherence due to spontaneous emission and AC Stark shift negligible. Complete control over the quantum state can be accomplished by splitting the pulse into two halves and varying the relative delay, resulting in single qubit rotation times on the order of 50 ps. By setting the delay to zero and arranging the two pulse halves in a counterpropagating configuration, an optical standing wave is applied to the ion for 10 ps. Sequences of these optical standing waves, spaced appropriately, should combine to produce a fast spin-dependent momentum kick. We plan to use this to implement proposals for motional gates which can be performed much faster than the oscillation period of the trap.[2,3] This research was supported by IARPA through ARO contract, the DARPA OLE program under ARO contract, the ARO MURI program, the NSF PIF Program, the AQUTE program, and the NSF Physics Frontier Center at JQI. [1] Campbell et al., PRL 105, 090502 (2010). [2] Garcia-Ripoll et al., PRL 91, 157901 (2003). [3] Duan, PRL 93, 100502 (2004).

Entangling ISWAP gate using frequency shifted anharmonic qubits

Felix Motzoi, University of Waterloo, Institute for Quantum Computing

We examine the coupling between frequency separated qubits, typical of superconducting implementations. We show how to correct for errors coming from finite turn-on time (corresponding to bringing the qubits into resonance) as well as leakage error (corresponding to exciting population out of the qubit manifold), namely by bringing the qubits in and out of resonance repeatedly to cancel out the unwanted parts of the Hamiltonian. The gates presented are smooth and robust and represent a whole class of analytic and numeric solutions for the evolution of the composite system.

Spin Squeezing and Metrology in an Ensemble of Spins Greater than 1/2

Leigh Norris, University of New Mexico

Spin squeezed states have generated great interest for their possible applications in metrology and quantum information processing. Substantial research has been directed both at producing spin squeezed states and understanding the properties of the states themselves. We explore this problem for an ensemble of alkali atomic spins interacting with a single spatial mode of the electromagnetic field through the Faraday effect, a system that has previously been used for spin squeezing protocols. In our setup, the amplified projection noise of spin-f qudits leads to enhanced entangling interactions due to increased measurement backaction on the atoms. The entanglement generated can then be converted into meaningful spin squeezing through local unitary control. We also investigate whether these control techniques can be adapted to create other metrologically useful states, such as the "phase squeezed states" defined by Combes and Wiseman (2004).

A Miniature Ion-Trap Frequency Standard

Heather Partner, Sandia National Labs / University of New Mexico

We are developing a highly miniaturized atomic clock to probe the 12.6 GHz hyper fine transition in 171Yb ions. Ultimately, we intend to produce a clock that is less than 5 cm^3 in size, consumes <50 mW of power, and has a long-term frequency stability of 10^-14 at one month. Our approach incorporates an integrated vacuum package using buffer-gas cooled trapped ions and microfabricated oscillator and light sources. We have designed and built several vacuum packages with different levels of integration for testing and characterization of their ion trapping and clock performance capabilities. We report on results from these packages and their contribution to our future plans for the project. Peter Schwindt, Yuan-Yu Jau, Heather Partner, Lu Fang, Adrian Casias, Ken Wojciechowski, Roy Olsson, Darwin Serkland, Ron Manginell, Robert Boye, John Prestage, Nan Yu

Quantum Compiling

Paul Pham, University of Washington

Quantum compilers will be needed to implement algorithms on a proposed 40-qubit quantum computer in the next several years as part of the MUSIQC Project. Quantum compilation is the approximation of a high-level algorithm using an efficient, hardware-dependent, universal instruction set. In theory, the Solovay-Kitaev procedure shows us how to do this compiling in poly-logarithmic time on a classical computer, but with a large preprocessing step and no parallelism to reduce circuit depth. The lesser-known procedure by Kitaev, Vyalyi, and Shen offers a potential solution to both of these problems by trading space for time: namely, adding ancillary qubits and a run-time quantum gate simulation applying phase estimation on magic states. We present an open source code implementing both the Solovay-Kitaev and KSV algorithms for single-, two-qubit, and Toffoli gates necessary for most quantum algorithms--ready to be used for the quantum computers of tomorrow--and compare the final resources needed between these algorithms.

Adiabatic Shelving and State Detection for Barium Ion Qubit

Paul Pham, University of Washington

Ion trap experiments now commonly use a field-programmable gate array (FPGA) with direct digital synthesis (DDS) to synchronize operations for state preparation and state detection using an integrated pulse programmer. New operations can be supported in FPGA source code using a high-level language like VHDL without redesigning hardware and using open source designs, reducing cost and labor while increasing flexibility. We report on the successful use of such an open source pulse programmer to perform adiabatic shelving of Barium-137 from the hyperfine levels of the 6S1/2 ground state to the 5D5/2 state to perform state-dependent fluorescence. The programmable, phase-continuous frequency sweep of DDS allows investigation of the Landau-Zener curve by varying the sweep range and resolution. In addition, our pulse programmer is capable of counting input TTL pulses from a photomultiplier tube (PMT), storing these counts into memory for data acquisition, and branching to different pulse sequences based on comparing these counts to a threshold value. Together, these features will allow for future state detection and form the foundation for quantum error correction. Source code, documentation, and hardware designs are available online from http://pulse-programmer.org.

Software Verification via Quantum Learning and Testing

Kristen Pudenz, University of Southern California

We attack the exponentially difficult problem of verification of classical software using a novel quantum approach. This approach is based on training and using a classifier whose job it is to identify software bugs. Such an approach has two complementary quantum aspects. The first is to formulate the training problem as a quantum one. The second is to apply the trained classifier in quantum-parallel on the space of all paired input and output vectors which may be generated by the software under test. We present a practical algorithm for attacking both problems with limited available qubits, along with selected simulation results for the proposed algorithm.

Nested Uhrig Dynamical Decoupling with Non-Uniform Error Suppression

Gregory Quiroz, University of Southern California

Here the performance of Nested Uhrig Dynamical Decoupling (NUDD) for qubit systems is analyzed when error suppression is non-uniform. The error suppression provided by NUDD is controlled by the sequence order of each nested sequence. The properties of the error suppression are characterized with respect to varying sequence order to verify the expected error suppression scaling of UDD, order N+1 error suppression with respect to the total time of evolution for an Nth order sequence. The system operators present in the system-environment evolution are isolated and used to quantify the order of error suppression associated with each system error operator. Using this as a measurement, error suppression is examined with respect to the strength of system-environment interaction, as well as the pure bath strength. In the case of single-qubit NUDD, known as Quadratic Dynamical Decoupling (QDD), the results show that the error suppression provided by the inner sequence scales exactly with that of UDD, while the outer sequence dynamics leads to error suppression greater than or equal to that expected from UDD. These results can be extended to multi-qubit systems where the error suppression scaling for the inner sequence applied to each qubit follows that of UDD and the outer sequence applied to each qubit gives an error suppression greater than or equal to N+1.

Optimized Dynamical Decoupling Using Genetic Algorithms

Gregory Quiroz, University of Southern California

Using a combination of Genetic Algorithm and Simulated Annealing techniques, it is shown that optimal Dynamical Decoupling sequences can be found for a fixed number of pi-pulses. Considering a single qubit system, the Pauli operators are chosen to be the set of possible pi-pulse rotations to be implemented on the system. Fixing the free evolution period between successive pulses, sequences containing up to 256 pulses are constructed. In addition to locating optimal sequences, this method allows for the characterization of sequence lengths with respect to the order of error suppression. From this analysis, the minimum sequence length required for a particular order of error suppression is readily located. The performance of the optimized sequences is compared to known deterministic sequence structures such as Concatenated Dynamical Decoupling (CDD) and Quadratic Dynamical Decoupling (QDD).

Symmetric and monolithic microfabricated ion trap

Fayaz Shaikh, Georgia Institute of Technology

In the effort to miniaturize the ion traps and scale up the number of ions for Quantum Information Processing (QIP) several trap designs have been explored. Many of these designs are planar and consist of the segmented surface electrodes. Although promising scalability, these designs suffer from the challenges of shallower trap depths, radial asymmetry, and the charging due to laser interactions with dielectric surfaces. In this poster, we present a monolithic, symmetric two-level ion trap design and the associated micro-fabrication processes. This trap produces a deep (~1 eV for Yb+ ion), radially symmetric RF confinement field. The trap has an angled through-chip slot which allows backside ion loading and through laser access while avoiding surface light scattering and dielectric charging that can corrupt the design control electrode compensating potentials. The geometrical trap features and dimensions are optimized for trapping long linear ion chains for the quantum simulation and computation architectures. This research is funded by DARPA/DSO.

A microfabricated surface ion trap on a high finesse optical mirror

Molu Shi, Massachusetts Institute of Technology

A single trapped ion in a high finesse optical cavity offers a strong experimental platform in the pursuit of efficient light matter interfaces, which holds a great potential for large scale quantum information processing. Efforts towards realizing such interfaces are however, faced with three major challenges, currently impeding the advancement of the field: (i) the trapping potential can be perturbed in the presence of dielectric mirrors, which affect both the trap rf-fields and allows build-up of stray charges on the substrates via light-induced charging; (ii) when close to material surfaces, anomalous heating of ions may lead to rapid decoherence of their motional states; (iii) the need for scalable trap technology imposes severe design and fabrication constraints on the experiment. Here we present a new approach to integrate an optical cavity into an ion trap, in which a linear surface electrode Paul trap is microfabricated directly on a high finesse mirror. A circular aperture located in the central trap electrode allows the ion to interact with the cavity mirror. Single to a few 88Sr+ ions have been stably trapped for hours 170 mirons above the surface of this trap, and the measured heating rate is only 0.1 quanta/ms. Furthermore, the additional optical loss introduced by the fabrication process has been evaluated using cavity ring-down spectroscopy, and found to be as low as 80ppm, without any post-fabrication cleaning. This validates the scalability of our fabrication procedure to integrate an ion trap with a high finesse mirror. Combining the system with a concave mirror (ROC = 1mm) with commercially available coatings for light at 408 nm (45ppm transmission + 25ppm loss), one can form a near-confocal cavity, with finesse of over 20,000. For the 88Sr+ 5 2S1/2 to 5 2P3/2 transition(408 nm) in particular, this implies a cooperativity of C = 9, which allows for the mapping of quantum states between ions and photons with high efficiency.

Dimensionality and spatial entanglement in Bose-Einstein condensates

Alexandre Tacla, University of New Mexico

We investigate the effects of the emergence of three-dimensional behavior on a quasi-one-dimensional Bose-Einstein condensate (BEC) trapped by a highly elongated potential. By analytically performing the Schmidt decomposition of the condensate wave function in the perturbative regime, we derive corrections to the 1D approximation due to the reshaping of the BEC in the tightly confined direction with increasing nonlinearity strength. This approach provides a straightforward way to redefine the transverse and longitudinal wave functions as well as to calculate the amount of entanglement that arises between the two spatial directions. Numerical integration of the three-dimensional Gross-Pitaevskii (GP) equation for different trapping potentials and experimentally accessible parameters reveals good agreement with our analytical model even for relatively high nonlinearities. In particular, we show that even for such stronger nonlinearities the entanglement remains remarkably small, which allows the condensate to be well described by a separable wave function that corresponds to a single Schmidt term.

Quantum Computing at Lockheed Martin

Greg Tallant, Lockheed Martin

Poster presentation outlining recent Lockheed Martin initiatives to leverage quantum computing technologies and capabilities to solve key industry problems, including software verification and validation.

On-site interactions as a resource for universal quantum computation

Michael Underwood, Institute for Quantum Information Science at the University of Calgary

We present a novel scheme for universal quantum computation based on spinless bosons hopping on a two-dimensional lattice with on-site interactions. Our setup is comprised of a 2×n lattice for an n-qubit system; the two rows correspond to the computational basis states, and a boson in each column encodes a qubit. The system is initialized with n bosons occupying the n sites of the |0⟩ row, and the lattice deep enough to prevent tunneling. Arbitrary single-qubit X rotations are implemented by tuning the tunneling strength between the |0⟩ and |1⟩ sites of the appropriate column, and Z rotations by applying a local potential to the |1⟩ site. Entanglement is generated by hopping between the |1⟩ sites of adjacent qubits; by tuning the on-site interaction strength of the bosons, a non-trivialcontrolled phase is acquired if these two qubits are in the state |11⟩.Because the quantum information is encoded entirely in the lattice positions of the bosons, the encoded qubits are inherently robust against decoherence. An implementation in terms of ultracold atoms in optical lattices is suggested.

Efficient Sympathetic Cooling

Grahame Vittorini, Georgia Institute of Technology

Grahame Vittorini, Craig Clark, Nathan Briggs and Kenneth Brown Schools of Chemistry and Biochemistry; Computational Science and Engineering; and Physics Georgia Institute of Technology A challenge of performing ion trap quantum computation with chains of ions is the heating of the trap vibrational modes. Trap heating can result in unwanted occupation of vibrational modes and a reduced fidelity for two ion gates. To combat this, specific ions within the chain can be tasked with cooling the entire chain via sympathetic cooling. The strength of the interaction between the cooling laser and cooling ions may have a significant effect on how efficiently the chain is sympathetically cooled. This interaction can be controlled via the intensity and detuning of the cooling beam as well as the time the cooling ions spend interacting with the cooling laser versus thermalizing with the ion chain. By using separate isotopes of Ca+, we can construct a chain of cooling and information ions with each isotope interacting with its resonant cooling laser independently. By adjusting the aforementioned interaction parameters and measuring the sideband spectrum of the information ions, we will be able to find the most efficient sympathetic cooling parameters. We will describe the experimental results so far as well as future related investigations.

The Hyperfine molecular Hubbard Hamiltonian

Michael Wall, Colorado School of Mines

We present the Hyperfine molecular Hubbard Hamiltonian, an effective low-energy Hamiltonian for an ultracold gas of heteronuclear alkali dimer molecules loaded into an optical lattice. The large permanent electric dipole moment of these molecules gives rise to long range dipole-dipole interactions in an electric field and allows for transitions between rotational states in an ac microwave field. Additionally, a strong magnetic field can be used to control the hyperfine degrees of freedom independently of the rotational degrees of freedom. Together these fields allow dynamical control over the number of internal states involved in the dynamics as well as the degree of correlation between the spatial and internal degrees of freedom. We discuss three of the Hamiltonian's experimental consequences:quantum dephasing, the dependence of the phase diagram on the molecular state, and tunable complexity, and provide characteristic entangled quantum dynamics simulations.

Microwave Near-Field Quantum Control of Trapped-Ion Qubits[*]

Ulrich Warring, National Institute of Standards and Technology

A major concern in the development of a future quantum processor is the scalability toward large numbers of qubits; its structure should enable one- and multi-qubit gates on arbitrarily selected qubits. As for a classical processor, micro fabrication leads to a promising route to build such a versatile ion-qubit quantum processor. Recent experiments with surface electrode ion traps have demonstrated the key ingredients for scalable ion loading, transporting, and trapping architecture. Here, we present an approach to incorporate ion-qubit manipulation into the surface-electrode structure which could enable its duplication along with the other infrastructure. In ongoing experiments we investigate the building block for a microwave near-field quantum control. It is based on an oscillating magnetic field generated by microwave currents in electrodes of a micro fabricated surface-electrode trap. The driving microwave frequency is tuned near resonant with a hyperfine transition in the Mg ion. The homogeneous field component is used to implement single-qubit gates, while the field gradient leads to a coupling of the ions internal and motional states. With further improvements, this coupling can be deployed to perform a multi-qubit operation. [* Supported by IARPA, NSA, DARPA, ONR and the NIST Quantum Information Program]

Speeding up Grover's algorithm by evolving via the nonlinear Schrödinger equation

Thomas Wong, University of California, San Diego

It is well-established that Grover's quantum search algorithm optimally searches an unordered database in O(N^(1/2)). While this algorithm can be understood in the digital circuit-based paradigm as a sequence of unitary transformations, it can also be understood in the analog paradigm as the Hamiltonian time-evolution of a system obeying the Schrödinger equation. Combining this analog paradigm of Grover's algorithm with the established fact that a nonlinear quantum theory results in further computational advantages, we show that Grover's algorithm, as governed by the nonlinear Schrödinger equation of the Gross-Pitaevskii type, searches an unordered database in O(N^(1/3)). Thus, we provide a tangible example of how a nonlinear quantum theory could be used to perform computation.

Manipulations of the Ba-138+ Zeeman Qubit

John Wright, University of Washington

The ¹³⁸Ba⁺ ground state two level Zeeman system is an attractive qubit because of its simplicity, lifetime and easily accessible cooling and excited states. The 25 MHz Zeeman transition can be driven using a Stanford frequency generator applied directly to the trap electrodes. Readout is performed by excitation to the D_5/2 state with a 1762 nm fiber laser. Remote entanglement for modular quantum computer designs can be implemented using a Ti:saphire laser to drive a transition to P_1/2 from the higher ground state. The excited state spontaneously decays to the ground state with the entangled, emitted photon π-polarized in the case of decay to the +1/2 Zeeman state, and σ-polarized in the other case. A partial Bell measurement can then be used to project a pair of ions into an entangled basis. The proposed remote entanglement scheme can also be used to perform loophole-free verification of Bell's inequality.

Fast protocols for local implementation of nonlocal unitaries

Li Yu, Carnegie Mellon University

This work builds upon PRA 81, 062315(2010) in which we introduced new protocols to implement nonlocal unitaries by means of LOCC with the help of a maximally entangled state. We have designed improved protocols which need less time than the previous protocols for some unitaries. These "fast" protocols involve concurrent classical communication in two opposite directions, instead of back-and-forth communication. We also explored to some extent the restrictions on possible fast protocols.

Parametric processes in a cavity resonator terminated with a DC-SQUID

Eva Zakka Bajjani, National Institute of Standard and Technology

The coplanar waveguide resonators with SQUIDs have become common to several recent superconducting quantum information experiments. We will present some recent results which demonstrate the manipulation of the internal harmonic modes of a microwave cavity resonator using a flux-driven SQUID as a parametric mode mixing resource.

Computable and asymptotically optimal lower bounds on confidence for rejecting local realism given experimental data

Yanbao Zhang, University of Colorado at Boulder, and National Institute of Standards and Technology

As a test of quantum mechanics, high-confidence demonstrations of violations of local realism (LR) are highly desirable. We propose to lower-bound the rejection confidence by a quantitative, prediction-based ratio test. The test gives a rigorous lower bound without requiring stationarity and independence of the experiment. In particular, the prepared quantum state can vary and depend on previous experiments and their outcomes. The best LR prediction can also depend on experimental history. If the prepared state does not vary in time, the bound is asymptotically optimal. We compare different rejection-confidence calculations, based on experimental standard deviation (SD), martingale theory [R. Gill, arXiv: quant-ph/0301059], or our method. We find that the confidence estimated by comparing Bell-inequality violation to experimental SD is higher than can be justified, while the confidence obtained from martingale theory is pessimistic. Collaborators: E. Knill and S. Glancy

Geometric Unitary Gates in Cold Atom Ensembles on an Atom Chip

Yicong Zheng, University of Southern California

We propose a feasible scheme to achieve quantum computation based on geometric manipulation of ensembles of atoms, and analyze it for neutral rubidium atoms magnetically trapped in planoconcave microcavities on an atom chip. The geometric operations are accomplished by optical excitation of a single atom into a Rydberg state in a constant electric field. Strong dipole-dipole interactions and incident lasers drive the dark state of the atom ensembles to undergo some specified cyclic evolutions that realize a universal set of quantum gates. Such geometric manipulation turns out naturally to protect the qubits from the errors induced by non-uniform laser illumination as well as cavity loss. The gate performance and decoherence processes are analyzed by numerical simulation.

Engineering a Frequency-Unentangled Downconversion Source

Kevin Zielnicki, University of Illinois at Urbana-Champaign

Pairs of polarization-entangled photons are a critical resource for optical quantum information processing. However, using downconversion to produce photon pairs can easily generate undesired correlations in frequency and spatial mode. Typical sources achieve high purity using spectral filtering, but this significantly decreases source brightness. We are implementing a method which uses group-velocity matching and a broad bandwidth pump to achieve an indistinguishable source with much higher brightness than a typical spectrally filtered source. Such a source will be particularly useful for creating multi-photon states, where the production rate enhancement scales exponentially in the number of photons. We discuss the design of this scheme, as well methods for characterizing the joint spectral intensity.

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