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 KwaZulu-Natal 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 one-bit teleportation circuits for multilevel systems to repetitively correct photon erasure errors and operation errors in a fault-tolerant 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 one-way 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 single-mode 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 information-theoretic-crypto protocol is limited by decoherence caused by the birefringence of a single-mode fiber. We propose the Knill dynamical decoupling scheme, implemented using half-wave 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 decoupling-like protocol for controlling the light emission line of a two-level 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 solid-state environment, so that the frequency of the emitted light slowly but uncontrollably fluctuates over time [1,2]. These fluctuations impede the photon-based quantum information processing schemes (e.g. the two-photon interference, where the frequencies of the photons should stay close), and impair the protocols using the stationary-to-flying 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 two-level system, we analyze performance of the scheme both analytically and numerically. We show that already a few pulses, with rather large inter-pulse delay, can stabilize the emission line. We discuss application of the proposed scheme for stabilization of the zero-phonon emission line of the NV centers in diamond, and the possible use of this scheme for facilitating the long-distance 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 non-overlapping support. For quantum LDPC codes with logarithmic or power-law 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 Monte-Carlo simulations to survey several syndrome extraction circuits. Third, given the capability to perform 3-outcome 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 3-outcome 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 flux-driven Josephson qubits capable of autonomously protecting many-body states against bit-flip errors. Unlike the traditional error correction schemes where feed-back operations are applied conditioned on the measurements, in our circuit, error correction is achieved by tailoring interactions between low-Q resonators (the ``shadow lattice'') and sinusoidally flux-driven 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 single-shot 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 well-characterized. 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 non-Gaussian 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: Fault-tolerant 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, non-Abelian 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 fault-tolerant, 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: Two-local 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 2-local case. By making the favorable assumption that the gap is infinite we show that single-site 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 no-hiding 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 2-local 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 D-Wave quantum annealer. Using a combination of optimized encoding and decoding techniques, our scheme enables the D-Wave device to solve minor embedded hard instances at least as well as it would on a native implementation. Our work is a proof-of-concept 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 D-Wave 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 low-weight 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 quaternion-based path-integral 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 path-integral 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 quaternion-based 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: Phase-modulated decoupling and error suppression in qubit-oscillator systems Todd Green, Michael Biercuk A key requirement for scalable QIP is the ability to controllably produce high-fidelity multi-particle 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 qubit-oscillator entanglement at the conclusion of an interaction period. We demonstrate how the exclusive use of discrete phase shifts in the field moderating the qubit-oscillator 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 Molmer-Sorensen 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] |
Monday, March 2, 2015 2:03PM - 2:15PM |
B37.00015: ABSTRACT WITHDRAWN |
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