Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session B37: Focus Session: Quantum Error Correction I 
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Sponsoring Units: GQI Chair: Francesco Petruccione, University of KwaZuluNatal Room: 212A 
Monday, March 2, 2015 11:15AM  11:27AM 
B37.00001: Overcoming erasure errors in quantum memories with multilevel systems Sreraman Muralidharan, Jianming Wen, Linshu Li, Liang Jiang We propose the usage of highly efficient error correcting codes of multilevel systems to encode quantum memories that suffer from erasure errors and introduce efficient hardware to repetitively correct these errors. Our scheme makes use of quantum polynomial codes to encode a quantum memory and generalized onebit teleportation circuits for multilevel systems to repetitively correct photon erasure errors and operation errors in a faulttolerant manner. We compare our scheme with earlier known schemes to encode quantum memories that use quantum parity codes and surface codes respectively and discuss the application of our encoded quantum memories for oneway quantum repeaters and show that they achieve a superior performance. [Preview Abstract] 
Monday, March 2, 2015 11:27AM  11:39AM 
B37.00002: Preserving flying qubit in singlemode fiber with Knill Dynamical Decoupling (KDD) Manish Gupta, Erik Navarro, Todd Moulder, Jason Mueller, Ashkan Balouchi, Katherine Brown, Hwang Lee, Jonathan Dowling The implementation of informationtheoreticcrypto protocol is limited by decoherence caused by the birefringence of a singlemode fiber. We propose the Knill dynamical decoupling scheme, implemented using halfwave plates, to minimize decoherence and show that a fidelity greater than 96{\%} can be achieved even in presence of rotation error. [Preview Abstract] 
Monday, March 2, 2015 11:39AM  11:51AM 
B37.00003: Multipulse dynamical decouplinglike protocol for controlling the light emission line of a twolevel system Herbert F. Fotso, Adrian Feiguin, Viatcheslav Dobrovitski Emission lines of quantum systems in solids, such as quantum dots or color centers, are often significantly affected by the coupling to the solidstate environment, so that the frequency of the emitted light slowly but uncontrollably fluctuates over time [1,2]. These fluctuations impede the photonbased quantum information processing schemes (e.g. the twophoton interference, where the frequencies of the photons should stay close), and impair the protocols using the stationarytoflying qubit conversion. We present a possible solution for this problem, which employs optical pulses applied to the emitting system, which stabilize the position of the emission line at the desired location. Modeling the emitter as a twolevel system, we analyze performance of the scheme both analytically and numerically. We show that already a few pulses, with rather large interpulse delay, can stabilize the emission line. We discuss application of the proposed scheme for stabilization of the zerophonon emission line of the NV centers in diamond, and the possible use of this scheme for facilitating the longdistance entanglement between the NV centers [3]. [1] K.M. Fu et al, PRL 103, 256404 (2009). [2] V. M. Acosta et al, PRL 108, 206401 (2012). [3] W. Pfaff et al, Science 345 6196, 532 (2014). [Preview Abstract] 
Monday, March 2, 2015 11:51AM  12:03PM 
B37.00004: Irreducible normalizer operators and thresholds for degenerate quantum codes with sublinear distances Leonid P. Pryadko, Ilya Dumer, Alexey A. Kovalev We construct a lower (existence) bound for the threshold of scalable quantum computation which is applicable to all stabilizer codes, including degenerate quantum codes with sublinear distance scaling. The threshold is based on enumerating irreducible operators in the normalizer of the code, i.e., those that cannot be decomposed into a product of two such operators with nonoverlapping support. For quantum LDPC codes with logarithmic or powerlaw distances, we get threshold values which are parametrically better than the existing analytical bound [1] based on percolation. The new bound also gives a finite threshold when applied to other families of degenerate quantum codes, e.g., the concatenated codes. [1] A. A. Kovalev and L. P. Pryadko, PRA \textbf{87}, 020304(R) (2013). [Preview Abstract] 
Monday, March 2, 2015 12:03PM  12:15PM 
B37.00005: Leakage Suppression in the Toric Code Martin Suchara, Andrew Cross, Jay Gambetta Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, these gadgets reduce the threshold and increase experimental complexity, and the costs have not been thoroughly understood. We explore a variety of techniques for leakage resilience in topological codes. Our contributions are threefold. First, we develop a leakage model that differs in critical details from earlier models. Second, we use MonteCarlo simulations to survey several syndrome extraction circuits. Third, given the capability to perform 3outcome measurements, we present a dramatically improved syndrome processing algorithm. Our simulations show that simple circuits with one extra CNOT per qubit reduce the accuracy threshold by less than a factor of 4 when leakage and depolarizing noise rates are comparable. This becomes a factor of 2 when the decoder uses 3outcome measurements. Finally, when the physical error rate is less than $2\times 10^{4}$, placing LRUs after every gate may achieve the lowest logical error rate. We expect that the ideas may generalize to other topological codes. [Preview Abstract] 
Monday, March 2, 2015 12:15PM  12:27PM 
B37.00006: Autonomous quantum error correction with superconducting qubits Yao Lu, Eliot Kapit, Samuel Saskin, Nelson Leung, Nathan Earnest, David Mckay, Jens Koch, David Schuster Quantum error correction is of vital importance for the successful performance of quantum information tasks. Based on recent work [1], we propose a superconducting circuit with fluxdriven Josephson qubits capable of autonomously protecting manybody states against bitflip errors. Unlike the traditional error correction schemes where feedback operations are applied conditioned on the measurements, in our circuit, error correction is achieved by tailoring interactions between lowQ resonators (the ``shadow lattice'') and sinusoidally fluxdriven qubits. An energetic resonance condition minimizes errors generated by the resonator coupling itself while still allowing for rapid error correction. In this talk, I will introduce our autonomous quantum error correction scheme, and present our fabricated superconducting circuit. I will also discuss preliminary results obtained from our experiments. \\[4pt] [1] Phys. Rev. X 4, 031039 (2014) [Preview Abstract] 
Monday, March 2, 2015 12:27PM  12:39PM 
B37.00007: Soft decoding of a qubit readout apparatus Benjamin D'Anjou, William A. Coish Qubit readout is commonly performed by thresholding a collection of analog detector signals to obtain a sequence of singleshot bit values. The intrinsic irreversibility of the mapping from analog to digital signals discards soft information associated with an \emph{a posteriori} confidence that can be assigned to each bit value when a detector is wellcharacterized. Accounting for soft information, we show significant improvements in enhanced state detection with the quantum repetition code as well as quantum state/parameter estimation. These advantages persist in spite of nonGaussian features of realistic readout models, experimentally relevant small numbers of qubits, and finite encoding errors. These results show useful and achievable advantages for a wide range of current experiments on quantum state tomography, parameter estimation, and qubit readout. [Preview Abstract] 
Monday, March 2, 2015 12:39PM  12:51PM 
B37.00008: Faulttolerant Holonomic Quantum Computation in Surface Codes Yicong Zheng, Todd Brun We show that universal holonomic quantum computation (HQC) can be achieved by adiabatically deforming the gapped stabilizer Hamiltonian of the surface code, where quantum information is encoded in the degenerate ground space of the system Hamiltonian. We explicitly propose procedures to perform each logical operation, including logical state initialization, logical state measurement, logical CNOT, state injection and distillation,etc. In particular, adiabatic braiding of different types of holes on the surface leads to a topologically protected, nonAbelian geometric logical CNOT. Throughout the computation, quantum information is protected from both small perturbations and low weight thermal excitations by a constant energy gap, and is independent of the system size. Also the Hamiltonian terms have weight at most four during the whole process. The effect of thermal error propagation is considered during the adiabatic code deformation. With the help of active error correction, this scheme is faulttolerant, in the sense that the computation time can be arbitrarily long for large enough lattice size. It is shown that the frequency of error correction and the physical resources needed can be greatly reduced by the constant energy gap. [Preview Abstract] 
Monday, March 2, 2015 12:51PM  1:03PM 
B37.00009: Quantum error suppression with commuting Hamiltonians: Twolocal is too local Iman Marvian, Daniel Lidar We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the 2local case. By making the favorable assumption that the gap is infinite we show that singlesite perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonians which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the nohiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems, and should be of independent interest. The main reason that 2local commuting Hamiltonians cannot be used for quantum error suppression is [Preview Abstract] 
Monday, March 2, 2015 1:03PM  1:15PM 
B37.00010: Quantum Error Correction for Minor Embedded Quantum Annealing Walter Vinci, Gerardo Paz Silva, Anurag Mishra, Tameem Albash, Daniel Lidar While quantum annealing can take advantage of the intrinsic robustness of adiabatic dynamics, some form of quantum error correction (QEC) is necessary in order to preserve its advantages over classical computation. Moreover, realistic quantum annealers are subject to a restricted connectivity between qubits. Minor embedding techniques use several physical qubits to represent a single logical qubit with a larger set of interactions, but necessarily introduce new types of errors (whenever the physical qubits corresponding to the same logical qubit disagree). We present a QEC scheme where a minor embedding is used to generate a $8\times8\times2$ cubic connectivity out of the native one and perform experiments on a DWave quantum annealer. Using a combination of optimized encoding and decoding techniques, our scheme enables the DWave device to solve minor embedded hard instances at least as well as it would on a native implementation. Our work is a proofofconcept that minor embedding can be advantageously implemented in order to increase both the robustness and the connectivity of a programmable quantum annealer. Applied in conjunction with decoding techniques, this paves the way toward scalable quantum annealing with applications to hard optimization problems. [Preview Abstract] 
Monday, March 2, 2015 1:15PM  1:27PM 
B37.00011: Comparing codes for error corrected quantum annealing Anurag Mishra, Tameem Albash, Gerardo Paz, Daniel Lidar Previous work on the DWave Two (DW2) device has demonstrated the effectiveness of using error correction and suppression for quantum annealers. As the size of a quantum annealer increases, error correction becomes crucial for improved performance. We introduce a new type of code for error correction tailored to the hardware graph of the DW2, discuss the result of benchmarking this code on qubit chains, discuss various new decoding methods, and compare the performance to previous quantum annealing correction schemes. [Preview Abstract] 
Monday, March 2, 2015 1:27PM  1:39PM 
B37.00012: Parafermion stabilizer codes Utkan Gungordu, Rabindra Nepal, Alexey Kovalev We define and study parafermion stabilizer codes [Phys. Rev. A 90, 042326 (2014)] which can be viewed as generalizations of Kitaev's one dimensional model of unpaired Majorana fermions. Parafermion stabilizer codes can protect against lowweight errors acting on a small subset of parafermion modes in analogy to qudit stabilizer codes. Examples of several smallest parafermion stabilizer codes are given. Our results show that parafermions can achieve a better encoding rate than Majorana fermions. A locality preserving embedding of qudit operators into parafermion operators is established which allows one to map known qudit stabilizer codes to parafermion codes. We also present a local 2D parafermion construction that combines topological protection of Kitaev's toric code with additional protection relying on parity conservation. [Preview Abstract] 
Monday, March 2, 2015 1:39PM  1:51PM 
B37.00013: Error mitigation in the control of quantum spin systems subject to environmental noise: A quaternionbased pathintegral formulation Rafael Hipolito, Paul Goldbart We address the task of controlling a quantum system, i.e., giving it a predetermined unitary evolution via control fields that are subject to limitations. This task is complicated by the challenge of truly isolating a quantum system from environmental effects; hence, the need to mitigate the impact of noise. We consider the case of a spin system coupled to an environment that is not necessarily in equilibrium. We develop a pathintegral formulation based on an action that features degrees of freedom expressed in terms of quaternions and effective interactions determined by correlators that characterize the environment. We compare this quaternionbased description with more conventional approaches, and show that quaternions yield distinct, not solely {\ae}sthetic, advantages. For example, the quaternion formulation does not suffer from the phenomenon of `gimbal lock\rlap', a phenomenon that can create difficulties for numerical schemes. [Preview Abstract] 
Monday, March 2, 2015 1:51PM  2:03PM 
B37.00014: Phasemodulated decoupling and error suppression in qubitoscillator systems Todd Green, Michael Biercuk A key requirement for scalable QIP is the ability to controllably produce highfidelity multiparticle entanglement on demand. This is accomplished in experimental systems using a variety of techniques, but a prominent approach relies on the realization of an indirect interaction between basic quantum systems mediated by bosonic oscillator modes. A significant source of infidelity in these experiments is the presence of residual qubitoscillator entanglement at the conclusion of an interaction period. We demonstrate how the exclusive use of discrete phase shifts in the field moderating the qubitoscillator interaction  easily implemented with modern synthesizers  is sufficient to both ensure multiple oscillator modes are decoupled and to suppress the effects of fluctuations in the driving field. We present detailed example protocols tailored to the execution of MolmerSorensen entangling gates in trapped ion systems and demonstrate that our approach allows multiqubit gate implementation with a significant reduction in technical complexity relative to previously deomstrated protocols. [Preview Abstract] 

B37.00015: ABSTRACT WITHDRAWN 
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