Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session Q26: Quantum Error Correction and Dynamical Decoupling |
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Sponsoring Units: GQI Chair: Dave Bacon, University of Washington Room: D136 |
Wednesday, March 17, 2010 11:15AM - 11:27AM |
Q26.00001: Error threshold for topological color codes on Union Jack lattices Helmut G. Katzgraber, Ruben S. Andrist, Hector Bombin, Miguel Angel Martin-Delgado Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for very small proof of principle devices. Topologically-protected quantum computing aimes to solve this problem by encoding quantum bits and gates in topological properties of the hardware medium that are immune to noise that does not impact the entire medium at once. There are different approaches to achieve topological protection. While traditional approaches use quasiparticle braidings, topological color codes use string-net condensates in 3-colexes. We study the error threshold of topological color codes on Union Jack lattices that allow for the implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random 3-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Our results show that topological color codes on Union Jack lattices have similar error stability than color codes on triangular lattices, as well as the Kitaev toric code. [Preview Abstract] |
Wednesday, March 17, 2010 11:27AM - 11:39AM |
Q26.00002: Error threshold of topological color codes and random three-dimensional color gauge models Miguel A. Martin-Delgado, Ruben S. Andrist, Helmut G. Katzgraber, Hector Bombin Sensitivity to noise makes most of the current quantum computing schemes prone to error and non-scalable. Topologically-protected quantum computing solves this problem and prevents decoherence effects at the hardware level by encoding quantum states and gates in topological properties of the hardware medium. Recently, a braid-less implementation using brane-net condensates in 3-colexes has been proposed that allows for the implementation of a universal set of quantum gates. The latter is an active scheme for error correction. In this work, we compute the error threshold for a topologically-protected quantum color code in two space dimensions. By mapping the problem onto a new triangular/hexagonal lattice gauge theory with Ising spins and gauge degrees of freedom, we compute the stability of the proposal by randomly perturbing the plaquette interactions between the gauge spins and verifying the existence of a stable broken symmetry phase using Wilson loops. [Preview Abstract] |
Wednesday, March 17, 2010 11:39AM - 11:51AM |
Q26.00003: Computing error thresholds in topological quantum-computing models using exact zero-temperature algorithms Creighton K. Thomas, Helmut G. Katzgraber, Hector Bombin, Miguel Angel Martin-Delgado Efficient error correction in quantum computing devices may be achieved by using topological codes that encode information in the hardware of the medium. Topological color codes allow for a braid-less implementation of the whole Clifford group. It is therefore of interest to understand the error stability of these proposals. In two space dimensions, the topological error correction process is mapped onto a 3-body Ising model on a two-dimensional triangular lattice. Errors correspond to local sign changes of the plaquette interactions, thus introducing disorder and frustration between the spins. Finite-temperature simulations are difficult. Furthermore, it is unclear if the phase diagram exhibits reentrance, where the critical error concentration decreases as the temperature is lowered from the tricritical point. To address these issues, we have developed an exact ground state algorithm to find the error threshold of this model at zero temperature. Numerical results on the triangular lattice are presented and compared to finite-temperature Monte Carlo simulations. [Preview Abstract] |
Wednesday, March 17, 2010 11:51AM - 12:03PM |
Q26.00004: A Self-Correcting Quantum Memory in a Thermal Environment Beat R\"othlisberger, Stefano Chesi, Daniel Loss Self-correcting quantum memories, analogously to classical memories, provide robust storage of quantum information without the need of active error correction. While systems with topological ground states have been considered to be promising candidates for the realization of such passive memories, a large class of them was recently proven unstable against thermal fluctuations. We propose here new two-dimensional (2D) spin models unaffected by this result. Specifically, we introduce repulsive long-range interactions in the toric code and establish a memory lifetime polynomially increasing with the system size. We study the dynamics of the quantum memory in terms of diffusing anyons and support our analytical results with extensive numerical simulations. The scaling of the memory lifetime is especially favorable in the presence of a super-ohmic thermal environment. Our findings demonstrate that self-correcting quantum memories can exist in 2D at finite temperatures. [Preview Abstract] |
Wednesday, March 17, 2010 12:03PM - 12:15PM |
Q26.00005: Analyses of Volume Thresholds in Quantum Fault Tolerance Gerald Gilbert, Yaakov Weinstein, Robert Calderbank, Vaneet Aggarwal Operator theoretic techniques and methods were recently used to successfully determine the optimal constraints needed to achieve fault tolerance for identity gates in quantum computing. Fault tolerance constraints were expressed in terms of volume thresholds in the complete error manifold associated to the practical implementation of a quantum computer. We extend the use of these methods to more general qubit transformations. [Preview Abstract] |
Wednesday, March 17, 2010 12:15PM - 12:27PM |
Q26.00006: Uncorrectable Errors in a Quantum Error Correction Code: The Limits of Resilient Quantum Computation in Correlated Environment E. Novais, E. R. Mucciolo, Harold U. Baranger In general, Quantum Error Correction (QEC) cannot perfectly protect quantum information. Errors that keep the logical qubit inside the logical Hilbert space lead to ``uncorrectable errors''; indeed, in most physical systems, this situation is the rule rather than the exception. We show that such uncorrectable errors change the conditions required for resilient quantum computation in correlated environments. Although QEC effectively reduces the coupling constant between the quantum computer and the environment, there are two distinct behaviors for the effect of noise in the long-time limit: (i) If the qubits are separated by a certain minimum distance, QEC changes the infrared behavior of the noise in favor of resilience [as derived in PRL 98, 040501 (2007) and PRA 78, 012314 (2008)]. (ii) If the qubits are not separated by that minimum distance, then the noise at low frequencies and long wave lengths reduces the time evolution of the computer to that of the bare system (i.e., without QEC). In this case, QEC provides no real advantage. We illustrate this point by calculating the entropy produced by uncorrectable errors, and then provide an upper bound on how long a quantum computation can be performed with a relatively high chance of success. [Preview Abstract] |
Wednesday, March 17, 2010 12:27PM - 12:39PM |
Q26.00007: Channel Optimized Quantum Error Correction Soraya Taghavi, Robert Kosut, Daniel Lidar We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate via numerical examples that our optimized QEC procedures always achieve a higher channel fidelity than the standard error correction method, which is agnostic about the specifics of the channel. This demonstrates the importance of channel characterization before QEC procedures are applied. Our main novel finding is that in the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction. We show this using a general rank minimization heuristic and supporting numerical calculations. Therefore, one can further improve the fidelity by utilizing all the available ancillas in the encoding block. [Preview Abstract] |
Wednesday, March 17, 2010 12:39PM - 12:51PM |
Q26.00008: Concatenated logical cluster state for measurement-based quantum computation Jaewoo Joo The highly entangled quantum states known as cluster states constitute a universal resource for measurement-based quantum computing (MBQC). How to construct a fault-tolerant protocol for MBQC is still an open question, however. We show how to build concatenated cluster states for MBQC using the five-qubit quantum error-correcting code. These states can be built by a series of single-qubit Hadamard and two-qubit controlled-phase gates. The number of operations is significantly reduced through the use of local complementation graph operations. Error thresholds are investigated and compared with current experimental capabilities. [Preview Abstract] |
Wednesday, March 17, 2010 12:51PM - 1:03PM |
Q26.00009: Non-Markovian errors and the cluster state machine gun Terry Rudolph, Netanel Lindner The hyperfine interaction between an electron and a nuclear spin bath is one of the more significant non-Markovian decoherence mechanisms affecting spin qubits in quantum dots. For the purposes of quantum error correction typically Markovian noise models are assumed. We show here that a recent proposal for a quantum dot based photon source Phys. Rev. Lett. 103, 113602 (2009) is not deleteriously affected by the non-Markovian noise because the noise can actually be, in some sense, bounded by a Markovian noise model. This allows for standard quantum fault tolerance results to go trough and shows that the device could be useful for scalable quantum computation. The technique we introduce for simplifying the analysis of the non Markovian noise will be of generic use in other architectures affected by similar decoherence mechanisms. [Preview Abstract] |
Wednesday, March 17, 2010 1:03PM - 1:15PM |
Q26.00010: Maximal Success Probabilities of Linear-Optical Quantum Gates Amos Matthew Smith, Dmitry Uskov, Lev Kaplan We apply numerical optimization techniques to obtain optimal implementations of generic linear-optical KLM-type two-qubit entangling gates, and we extend our techniques to the three-qubit Toffoli gate. We find that direct implementations of generic two-qubit gates and of the Toffoli gate have higher success rates and require lower ancilla resources than the conventional schemes of decomposing the gates into universal gates such as CNOT. A generic two-qubit gate constructed using three CNOT gates has a maximum success rate of $S\approx 0.0004$. We find a lower bound for the success of any generic two-qubit gate implemented directly with perfect fidelity to be $S>0.0063$, an improvement of an order of magnitude. At the same time, our implementation uses only half the resources of the CNOT decomposition. We then examine the Toffoli gate, and again find a direct implementation that has a higher success rate while requiring fewer ancilla resources than the previous best known implementation. [Preview Abstract] |
Wednesday, March 17, 2010 1:15PM - 1:27PM |
Q26.00011: Dynamical Decoupling with Imperfect Pulses in P Doped Silicon Z. Wang, W. Zhang, V. V. Dobrovitski, A. M. Tyryshkin, S. A. Lyon, J. Ager Dynamical decoupling (DD) is an important tool for prolonging coherence in solid-state spin systems. For advanced DD protocols comprising many pulses, the accumulation of pulse errors may become devastating. We studied DD of the electron spins of P donors in silicon with pulsed ESR [1]. Two-axis periodic pulse sequences, and their concatenated and symmetrized versions, have been investigated experimentally and theoretically. The impact of pulse errors has been analyzed for different initial states of the P spins. Depending on the sequence, some spin components decay after only 3 periods (12 pulses), while other components exhibit artificial freezing [2] at long times. We give a theoretical description for these effects, showing that their origin is the accumulation of pulse errors. We identify promising sequences where the impact of errors is minimized. [1] A. M. Tyryshkin et al., J. Phys. Cond. Mat. 18, S783 (2006) [2] W. Zhang et al., Phys. Rev. B 77, 125336 (2008) [Preview Abstract] |
Wednesday, March 17, 2010 1:27PM - 1:39PM |
Q26.00012: Combining Dynamical Decoupling with Robust Optimal Control for Improved Quantum Information Processing Matthew D. Grace, Wayne M. Witzel, Malcolm S. Carroll Constructing high-fidelity control pulses that are robust to control and system/environment fluctuations is a crucial objective for quantum information processing (QIP). We combine dynamical decoupling (DD) with optimal control (OC) to identify control pulses that achieve this objective numerically. Previous DD work has shown that general errors up to (but not including) third order can be removed from $\pi$- and $\pi/2$-pulses without concatenation. By systematically integrating DD and OC, we are able to increase pulse fidelity beyond this limit. Our hybrid method of quantum control incorporates a newly-developed algorithm for robust OC, providing a nested DD-OC approach to generate robust controls. Motivated by solid-state QIP, we also incorporate relevant experimental constraints into this DD-OC formalism. To demonstrate the advantage of our approach, the resulting quantum controls are compared to previous DD results in open and uncertain model systems. This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000. [Preview Abstract] |
Wednesday, March 17, 2010 1:39PM - 1:51PM |
Q26.00013: Some general results on dynamical decoupling Zhen-Yu Wang, Ren-Bao Liu We analyze the efficacy of dynamical decoupling in suppressing decoherence using the time-expansion of the noise correlations. We prove that when the time-expansion of the noise correlations has odd power terms, the dynamical decoupling cannot eliminate the decoherence to an arbitrary order of the short time. And we also show that for noise without hard high-frequency cut-off, the Carr-Purcell-Meiboom-Gill sequences are the optimal solution in the short-time limit. [Preview Abstract] |
Wednesday, March 17, 2010 1:51PM - 2:03PM |
Q26.00014: Comparing different dynamical decoupling schemes in prolonging qubit Hu Jianliang, Liu Renbao In dynamical decoupling (DD), spins are flipped by a sequence of $\pi$-rotation pulses to average the coupling to the environment down to zero. Such schemes are important for protecting quantum coherence in quantum computing and in high-precision magnetic resonance spectroscopy. We carried out theoretical study of the performance of three DD schemes, namely, the Uhrig DD, the periodical DD and the concatenated DD, in prolonging the qubit coherence time in a quantum spin bath. We also studied how different DD schemes perform against certain errors in spin-flip controls such as the rotation-angle and timing errors. Using an exactly solvable model -- the 1D XY model, we show that all the three DD schemes prolong the coherence time linearly with the number of spin-flip pulses, and the coherence reduction due to the control errors also increases linearly. [Preview Abstract] |
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