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arXiv:1205.2725 · Physical Review A

High-fidelity adiabatic quantum computation via dynamical decoupling

Gregory Quiroz, Daniel A. Lidar

Published Oct 24, 2012• 31 citations
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Abstract

We introduce high-order dynamical decoupling strategies for open-system adiabatic quantum computation. Our numerical results for the random-unitary map model demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding which allows computation to proceed alongside decoupling, can dramatically enhance the fidelity of adiabatic quantum computation in spite of decoherence.

DOI
10.1103/physreva.86.042333

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We introduce high-order dynamical decoupling strategies for open-system adiabatic quantum computation. Our numerical results for the random-unitary map model demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding which allows computation to proceed alongside decoupling, can dramatically enhance the fidelity of adiabatic quantum computation in spite of decoherence.
Quantum computation (QC) relies on the ability to implement high-fidelity quantum gate operations and successfully preserve quantum state coherence. One of the most challenging obstacles for reliable QC is overcoming the inevitable interaction between a quantum system and its environment. Unwanted interactions result in decoherence processes that cause quantum states to deviate from a desired evolution, consequently leading to computational errors and loss of coherence. Dynamical decoupling (DD) is one such method, which seeks to attenuate the effects of decoherence by applying strong and expeditious control pulses solely to the system. Provided the pulses are applied over a time duration sufficiently shorter than the correlation time associated with the environment dynamics, DD effectively averages out undesirable interactions and preserves quantum states with a low probability of error, or fidelity loss. In this study various aspects of this approach are studied from sequence construction to applications of DD to protecting QC. First, a comprehensive examination of the error suppression properties of a near-optimal DD approach is given to understand the relationship between error suppression capabilities and the number of required DD control pulses in the case of ideal, instantaneous pulses. While such considerations are instructive for examining DD efficiency, i.e., performance vs the number of control pulses, high-fidelity DD in realizable systems is difficult to achieve due to intrinsic pulse imperfections which further contribute to decoherence. As a second consideration, it is shown how one can overcome this hurdle and achieve robustness and recover high-fidelity DD in the presence of faulty control pulses using Genetic Algorithm optimization and sequence symmetrization. Thirdly, to illustrate the implementation of DD in conjunction with QC, the utilization of DD and quantum error correction codes (QECCs) as a protection method for adiabatic quantum computing (AQC) is discussed. A performance comparison between two deterministic DD schemes is given, where preference towards one particular method is found due to sequence structure and procedure from which higher accuracy sequences are generated.
Quantum information processing requires overcoming decoherence—the loss of ‘quantumness’ due to the inevitable interaction between the quantum system and its environment. One approach towards a solution is quantum dynamical decoupling—a method employing strong and frequent pulses applied to the qubits. Here we report on the first experimental test of the concatenated dynamical decoupling (CDD) scheme, which invokes recursively constructed pulse sequences. Using nuclear magnetic resonance, we demonstrate a near order of magnitude improvement in the decay time of stored quantum states. In conjunction with recent results on high fidelity quantum gates using CDD, our results suggest that quantum dynamical decoupling should be used as a first layer of defense against decoherence in quantum information processing implementations, and can be a stand-alone solution in the right parameter regime.
Dynamical decoupling (DD) and Decoherence free subspace (DFS) are powerful techniques in quantum computing aimed at enhancing fidelity by mitigating the detrimental effects of noise and environmental interactions. In quantum systems, noise and decoherence can degrade the coherence of quantum states, leading to errors and reduced computational accuracy. DD employs carefully designed sequences of control pulses to periodically intervene and counteract these undesired interactions, while DFS utilizes subspace encoding techniques to protect quantum information from decoherence. To evaluate and compare the fidelity achieved by DD and DFS, this paper presents a series of experiments considering the effect of time and the number of qubits. The experiments provide valuable insights into the performance of both methods under different conditions. By systematically examining the fidelity results, the impact of time and the scaling behavior with increasing qubits can be assessed. The experimental findings showcase the effectiveness of DD in reducing the impact of noise and extending the coherence time of quantum states. By strategically manipulating the quantum system, DD minimizes error accumulation and preserves the integrity of fragile quantum information. It is observed that the decrease in fidelity with increasing t is relatively small and gradual. Despite being outperformed by DD, the DFS method exhibits robustness and maintains a high degree of fidelity even in the presence of extended time durations.
The main obstacles to the realization of high-fidelity quantum gates are the control errors arising from inaccurate manipulation of a quantum system and the decoherence caused by the interaction between the quantum system and its environment. Nonadiabatic holonomic quantum computation allows for high-speed implementation of whole-geometric quantum gates, making quantum computation robust against control errors. Dynamical decoupling provides an effective method to protect quantum gates against environment-induced decoherence, regardless of collective decoherence or independent decoherence. In this paper, we put forward a protocol of nonadiabatic holonomic quantum computation protected by dynamical decoupling. Due to the combination of nonadiabatic holonomic quantum computation and dynamical decoupling, our protocol not only possesses the intrinsic robustness against control errors but also protects quantum gates against environment-induced decoherence.
In the closed system setting I will show how to obtain extremely accurate adiabatic QC by proper choice of the interpolation between the initial and final Hamiltonians. Namely, given an analytic interpolation whose first N initial and final time derivatives vanish, the error can be made to be smaller than 1/N^N, with an evolution time which scales as N and the square of the norm of the time-derivative of the Hamiltonian, divided by the cube of the gap (joint work with Ali Rezakhani and Alioscia Hamma). In the open system setting I will describe a method for protecting adiabatic QC by use of a hybrid encoding-dynamical decoupling scheme. This strategy can be used to protect spin-based universal adiabatic QC against arbitrary 1-local noise using only global magnetic fields. By combining error bounds for the closed and open system settings, I will show that in principle the method is scalable to arbitrarily large computations.