Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session F35: Focus Session: Quantum Computing Architectures and Algorithms: Quantum Control |
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Sponsoring Units: GQI Room: 702 |
Tuesday, March 4, 2014 8:00AM - 8:12AM |
F35.00001: A Fault-Tolerant Scheme of Holonomic Quantum Computation on Stabilizer Codes with Robustness to Low-weight Thermal Noise Yicong Zheng, Todd Brun We show an equivalence relation between fault-tolerant circuits for a stabilizer code and fault-tolerant adiabatic processes for holonomic quantum computation (HQC), in the case where quantum information is encoded in the degenerated ground space of the system Hamiltonian. By this equivalence, we can systematically construct a fault-tolerant HQC scheme, which can geometrically implement a universal set of encoded quantum gates by adiabatically deforming the system Hamiltonian. During this process, quantum information is protected from thermal excitation by an energy gap that does not change with the problem size. [Preview Abstract] |
Tuesday, March 4, 2014 8:12AM - 8:24AM |
F35.00002: Martin-Siggia-Rose approach to quantum error correction in the presence of time-dependent noise Rafael Hipolito, Paul Goldbart We consider the basic task of obtaining a target unitary operation (quantum gate) via external control fields coupled to a quantum system, while compensating for time-dependent noise. We address this problem by means of a formulation rooted in the MSR approach to noisy, classical, nonequilibrium systems. We express the noisy control problem as a path integral, and integrate out the noise to arrive at an effective noise-free description. To illustrate the approach, we consider a single spin-$s$ degree of freedom (with $s$ arbitrary) in the presence of Gaussian time-dependent noise, though our approach can be generalized to more complicated systems and noise distributions. Success is characterized via a ``fidelity,'' measuring the overlap between the ideal noise-free evolution and the noisy one. To make connection with MSR, we reformulate the fidelity in terms of a Schwinger-Keldysh path integral, with an added twist: ``forward'' and ``backward'' branches of the contour are inequivalent with respect to noise. We explore the effective description, and show how to evaluate the path integral to arbitrary order in noise strength. Our approach naturally treats the problem for arbitrary $s$ under a unified protocol, valid from the qbit limit ($s=1/2$) to the classical limit ($s \to \infty$). [Preview Abstract] |
Tuesday, March 4, 2014 8:24AM - 8:36AM |
F35.00003: A recursive construction of noiseless subsystem for qudits Utkan G\"ung\"ord\"u, Chi-Kwong Li, Mikio Nakahara, Yiu-Tung Poon, Nung-Sing Sze The noiseless subsystem is a method of using the inherent permutation symmetry of the noise to protect a subsystem against errors. Its construction becomes a formidable task with the growing number of qudits. In this work, we describe a recursive way of constructing noiseless subsystem for qudits, that is robust against collective noise of the form $W^{\otimes n}$, where $n$ is the number of qudits and $W$ is the Kraus operator acting on a single site. This kind of error appears when the wavelength of an environmental disturbance is much larger than the size of the quantum system, which makes it natural to assume all the qubits in the register suffer from the same error operator. The presented recursive scheme is a direct generalization of the recursive scheme described in \emph{Phys. Rev. A, {\bf 84}, (2011) 044301} for qubits. We show that the quantum error correction rate, i.e., the ratio of correctable qudits and the number of transmitted qudits, approaches $1/d$ as $n$ goes to infinity in this recursive scheme. [Preview Abstract] |
Tuesday, March 4, 2014 8:36AM - 9:12AM |
F35.00004: Gap protection and dynamical decoupling for reliable multi-qubit gates Invited Speaker: Wayne Witzel We propose a scheme for producing multi-qubit gates by adiabatically shuttling an electron between donors in silicon to produce operations that are diagonal in the computational basis. Exploiting the commutation of these diagonal operations, we can use single-qubit refocusing gates to cancel the sensitivity to low-frequency noise and details of the shuttling. This strategy of cancelling unwanted portions of an adiabatic process to build up robust multi-qubit operations could be applied to other systems. [Preview Abstract] |
Tuesday, March 4, 2014 9:12AM - 9:24AM |
F35.00005: Robustness of composite pulse sequences to time- dependent noise Chingiz Kabytayev, Todd J. Green, Kaveh Khodjasteh, Lorenza Viola, Michael J. Biercuk, Kenneth R. Brown Quantum control protocols can minimize the effect of noise sources that reduce the quality of quantum operations. Originally developed for NMR, composite pulse sequences correct for unknown static control errors \footnote{True J. Merrill and Kenneth R. Brown. arXiv:1203.6392v1. In press Adv. Chem. Phys. (2013)}. We study these compensating pulses in the general case of time-varying Gaussian control noise using a filter-function approach \footnote{T. J. Green et al. New J. Phys. 15 095004 (2013)} and detailed numerics. Three different noise models were considered in this work: amplitude noise, detuning noise and simultaneous presence of both noises. Pulse sequences are shown to be robust to noise up to frequencies as high as $\sim$10\% of the Rabi frequency. Robustness of pulses designed for amplitude noise is explained using a geometric picture that naturally follows from filter function. We also discuss future directions including new pulses correcting for noise of certain frequency. [Preview Abstract] |
Tuesday, March 4, 2014 9:24AM - 9:36AM |
F35.00006: Optimal arbitrarily accurate composite pulse sequences Guang Hao Low, Theodore Yoder Implementing a single qubit unitary is often hampered by imperfect control. Systematic amplitude errors $\epsilon$, caused by incorrect duration or strength of a pulse, are an especially common problem. But a sequence of imperfect pulses can provide a better implementation of a desired operation, as compared to a single primitive pulse. We find optimal pulse sequences consisting of $L$ primitive $\pi$ or $2\pi$ rotations that suppress such errors to arbitrary order $\mathcal{O}(\epsilon^{n})$ on arbitrary initial states. Optimality is demonstrated by proving an $L=\mathcal{O}(n)$ lower bound and saturating it with $L=2n$ solutions. Closed-form solutions for arbitrary rotation angles are given for $n=1,2,3,4$. Perturbative solutions for any $n$ are proven for small angles, while arbitrary angle solutions are obtained by analytic continuation up to $n=12$. The derivation proceeds by a novel algebraic and non-recursive approach, in which finding amplitude error correcting sequences can be reduced to solving polynomial equations. [Preview Abstract] |
Tuesday, March 4, 2014 9:36AM - 9:48AM |
F35.00007: Dynamically Corrected Gates for Qubits with Always-on Ising Interactions: Error model and fault-tolerance Amrit De, Leonid Pryadko We prescribe a method to implement a universal set of dynamically-corrected quantum gates on any qubit network that forms a sparse bipartite graph using sequences of decoupling pulses. The qubit networks have Ising interactions that are always turned on and our method works to selectively decouple the interactions even when they differ. We study the error operators associated with the constructed gates for small qubit clusters and give bounds on high-order errors. We find that the present gate set can be used to achieve fault-tolerance with a concatenated code by choosing a suitable qubit network. [Preview Abstract] |
Tuesday, March 4, 2014 9:48AM - 10:00AM |
F35.00008: Qubits with always-on couplings and gates based on decoupling pulse sequences: fault tolerance with quantum LDPC codes Kathleen Hamilton, Alexey Kovalev, Amrit De, Leonid Pryadko Universal gate sets based on decoupling pulse sequences can be efficiently constructed to a given order of the Magnus series by working with small qubit clusters. However, the most likely systematic errors of such gates typically involve few qubits, with a possibility of run-away large error cluster formation when scaled to large systems. We analyze the existence of a fault-tolerant decoding threshold when such gate sets are used with a quantum low-density parity check (LDPC) code. In particular, we show that the existence of such a threshold when the code is used for quantum memory can be related to the existence of a finite percolation transition between random clusters on a graph associated with the code. The results also apply to other systems where gates are constructed perturbatively, e.g., by tuning qubits in and out of resonance. [Preview Abstract] |
Tuesday, March 4, 2014 10:00AM - 10:12AM |
F35.00009: Precision Quantum Control with Trapped $^{171}$Yb$^{+}$ Ions Alexander Soare, David Hayes, James McLoughlin, Xinglong Zhen, Michael Lee, M.C. Jarrat, Harrison Ball, Todd Green, Michael Biercuk We present our recent work in developing and characterizing novel methods for quantum error suppression using trapped~$^{171}$Yb$^{+}$~ions as a model experimental platform. A flexible, robust microwave system allows us to access the 12.6 GHz, hyperfine qubit manifold in trapped~$^{171}$Yb$^{+}$. The ultra low phase noise characteristics of our source allow the realization of free-evolution coherence times in excess of three seconds, and operational fidelities F\textgreater 99.99{\%}, characterized by randomized benchmarking. Starting from this baseline, we leverage high-bandwidth vector modulation capabilities to experimentally validate our recent theoretical work developing Walsh-modulated control operations for error-resilient single-qubit control in the presence of synthesized noise. ~This theory is based on a generalized filter-transfer-function formalism useful for predicting the fidelity of arbitrary operations in the presence of general Gaussian noise. We provide the first experimental validation of this formalism, showing good agreement between experimental measurements and theoretical predictions with no free parameters. ~These demonstrations support the notion of physical-layer error evasion as an efficient means to realize high-fidelity quantum control across a wide range of quantum technologies. [Preview Abstract] |
Tuesday, March 4, 2014 10:12AM - 10:24AM |
F35.00010: Improving Quantum Gate Performance using Optimal Control with Feedback Yuchen Peng, Frank Gaitan We present a procedure for improving the performance of a quantum gate based on optimal control theory with feedback. Starting with a quantum gate $U_{0} $ produced by a known control field ${\rm {\bf F}}_{0} (t)$ that provides a good approximation to a target gate $U_{t} $, we show how optimal control theory with feedback can be used to determine a modified control ${\rm {\bf F}}(t)={\rm {\bf F}}_{0} (t)+\Delta {\rm {\bf F}}(t)$ which yields a quantum gate $U$ that better approximates the target gate $U_{t} $. We illustrate the procedure by applying it to the gates in a universal set of quantum gates produced using non-adiabatic rapid passage [1]. We first examine the performance improvements produced with ideal controls, and then examine the robustness of these improvements in the presence of control field imperfections such as finite bandwidth, finite precision control parameters, and phase jitter. We find that this procedure reduces the gate error probability $P_{e} $ by 1-4 orders of magnitude even in the presence of control imperfections ($P_{e} \sim 10^{-4}$ improved to $10^{-8} < P_{e} < 10^{-5})$. \\[4pt] [1] R. Li and F. Gaitan, \textit{J. Mod. Opt.}~\textbf{58}, 1922 (2011). [Preview Abstract] |
Tuesday, March 4, 2014 10:24AM - 10:36AM |
F35.00011: Near-optimal measurement-based feedback control for a single qubit Ashkan Balouchi, Kurt Jacobs Feedback control of quantum systems via continuous measurements involves complex nonlinear dynamics. As a result, even for a single qubit the optimal measurement for feedback control is known only in very special cases. We show here that for a broad class of noise processes, a series of compelling arguments can be applied to greatly simplify the problem of steady-state preparation of the ground-state, while loosing little in the way of optimality. Using numerical optimization to solve this simplified control problem, we obtain for the first time a non-trivial feedback protocol valid for all feedback strengths in the regime of good control. The protocol can be described relatively simply, and contains a discontinuity as a function of feedback strength. [Preview Abstract] |
Tuesday, March 4, 2014 10:36AM - 10:48AM |
F35.00012: Quantum logic gates by Walsh modulation Harrison Ball, David Hayes, Michael J. Biercuk We study a new class of error suppressing protocols for nontrivial quantum logic gates robust against band-limited stochastic noise to high order. Our underlying mathematical framework is to generate an amplitude modulated control field via synthesis of Walsh functions (an orthonormal set of basis functions well-known in signal processing) resulting in a composite pulse sequence parameterized in the amplitudes of the Walsh spectral components. In this work we show how one Walsh amplitude may be constrained to generate a target Bloch rotation while the remainder may be fine-tuned to optimize the decoupling power of the sequence. We use the filter function formalism to quantify the decoupling power and to derive a decoupling condition which enables us to prescribe an optimization procedure, searching over Walsh spectral weights. With these insights we characterize the robustness of a generalized family of rotary spin echo sequences against both dephasing noise and relaxation noise coaxial with control. We further derive a family of nontrivial, bounded, amplitude modulated gates decoupled to first order against dephasing noise, and describe a method to discover similar families of higher order protocols intrinsically compatible with control hardware and digital control circuitry. [Preview Abstract] |
Tuesday, March 4, 2014 10:48AM - 11:00AM |
F35.00013: Robust quantum channel for optical coherent-state qubits under environment noise Shin-Tza Wu, Ming-Jay Yang We study the non-Markovian dynamics of optical qubits encoded via coherent states with opposite phases which are exposed to environment noises. Making use of a coherent-state path integral formulation, we are able to study non-perturbatively the dynamics of the coherent-state qubits under strong environment coupling. We apply this formulation to examine the time evolution of a noisy quantum channel formed by two coherent-state qubits that are subject to uncorrelated local environment noises. In particular, we examine the time evolution of entanglement and maximal teleportation fidelity of the noisy quantum channel and show that at strong coupling, due to large feedbacks from the environment noise, it is possible to maintain a robust quantum channel in the long-time limit if appropriate error-correcting code is applied. [Preview Abstract] |
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