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Physical Review A

Suppressing systematic control errors to high orders

Pavel Bažant, Holger Frydrych, G. Alber, Igor Jex

Published Aug 10, 2015• 2 citations
Publisher

Abstract

Dynamical decoupling is a powerful method for protecting quantum information against unwanted interactions with the help of open-loop control pulses. Realistic control pulses are not ideal and may introduce additional systematic errors. We introduce a class of self-stabilizing pulse sequences capable of suppressing such systematic control errors efficiently in qubit systems. Embedding already known decoupling sequences into these self-stabilizing sequences offers powerful means to achieve robustness against unwanted external perturbations and systematic control errors. As these self-stabilizing sequences are based on single-qubit operations, they offer interesting perspectives for future applications in quantum information processing.

DOI
10.1103/physreva.92.022325

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Dynamical decoupling is a powerful method for protecting quantum information against unwanted interactions with the help of open-loop control pulses. Realistic control pulses are not ideal and may introduce additional systematic errors. We introduce a class of self-stabilizing pulse sequences capable of suppressing such systematic control errors efficiently in qubit systems. Embedding already known decoupling sequences into these self-stabilizing sequences offers powerful means to achieve robustness against unwanted external perturbations and systematic control errors. As these self-stabilizing sequences are based on single-qubit operations, they offer interesting perspectives for future applications in quantum information processing.
Abstract Dynamical decoupling (DD), usually implemented by sophisticated sequences of instantaneous control pulses, is a well-established quantum control technique for quantum information and quantum sensing. In practice, the pulses are inevitably imperfect with many systematic errors that may influence the performances of DD. In particular, Rabi error and detuning are primary systemic errors arising from finite pulse duration, incorrect time control, and frequency instability. Here, we propose a phase-modulated DD with staggered global phases for the basic units of the pulse sequences to suppress these systemic errors. By varying the global phases appended to the pulses in the dynamical decoupling unit alternatively with 0 or π, our protocol can significantly reduce the influences of Rabi error and detuning. Our protocol is general and can be combined with the most existing DD sequences such as universal DD, knill DD, XY, etc. As an example, we further apply our method to quantum lock-in detection for measuring time-dependent alternating signals. Our study paves the way for a simple and feasible way to realize robust dynamical decoupling sequences, which can be applicable for various quantum sensing scenarios.
Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences can equally suppress its effect on the system. Under these conditions, the remaining decay of the qubits under DD allows us to compare very precisely the robustness of the different DD sequences with respect to imperfections of the control pulses.
Over the past decade we have seen an explosion of demonstrations of quantum coherence in atomic, optical, and condensed matter systems. These developments have placed a new emphasis on the production of robust and optimal quantum control techniques in the presence of environmental noise. We discuss the use of dynamical decoupling as a form of open-loop quantum control capable of suppressing the effects of dephasing in quantum coherent systems. We introduce the concept of dynamical decoupling pulse-sequence construction as a filter-design problem, making connections with filter design from control theory and electrical engineering in the analysis of pulse-sequence performance for the preservation of the phase degree of freedom in a quantum superposition. A detailed mathematical description of how dephasing and the suppression of dephasing can be reduced to a linear control problem is provided, and used as motivation and context for studies of the filtration properties of various dynamical decoupling sequences. Our work then takes this practical perspective in addressing both "standard" sequences derived from nuclear magnetic resonance and novel optimized sequences developed in the context of quantum information. Additionally, we review new techniques for the numerical construction of optimized pulse sequences using the filter-design perspective. We show how the filter-design perspective permits concise comparisons of the relative capabilities of these sequences and reveals the physics underlying their functionality. The use of this new analytical framework allows us to derive new insights into the performance of these sequences and reveals important limiting issues, such as the effect of digital clocking on optimized sequence performance.
Over the past decade we have seen an explosion of demonstrations of quantum coherence in atomic, optical, and condensed matter systems.These developments have placed a new emphasis on the production of robust and optimal quantum control techniques in the presence of environmental noise.We discuss the use of dynamical decoupling as a form of open-loop quantum control capable of suppressing the effects of dephasing in quantum coherent systems.We introduce the concept of dynamical decoupling pulse-sequence construction as a filter-design problem, making connections with filter design from control theory and electrical engineering in the analysis of pulse-sequence performance for the preservation of the phase degree of freedom in a quantum superposition.A detailed mathematical description of how dephasing and the suppression of dephasing can be reduced to a linear control problem is provided, and used as motivation and context for studies of the filtration properties of various dynamical decoupling sequences.Our work then takes this practical perspective in addressing both "standard" sequences derived from nuclear magnetic resonance and novel optimized sequences developed in the context of quantum information.Additionally, we review new techniques for the numerical construction of optimized pulse sequences using the filter-design perspective.We show how the filter-design perspective permits concise comparisons of the relative capabilities of these sequences and reveals the physics underlying their functionality.The use of this new analytical framework allows us to derive new insights into the performance of these sequences and reveals important limiting issues, such as the effect of digital clocking on optimized sequence performance.
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.
We describe experimental and theoretical studies of open-loop quantum control techniques known as dynamical decoupling (DD) for the suppression of decoherence-induced errors in quantum systems. Our experiments on trapped atomic ion qubits demonstrate that it is possible to optimize the construction of DD sequences for a given noise power spectral density. Studies of novel sequences derived analytically or through numerical optimization – while maintaining fixed control resources – demonstrate large gains in our ability to preserve quantum coherence in arbitrary noise environments.