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arXiv:1303.2045 · Physical Review A

Dynamic decoupling in the presence of colored control noise

Ido Almog, Gil Loewenthal, Jonathan Coslovsky, Yoav Sagi, Nir Davidson

Published Oct 12, 2016• 9 citations
arXivHTMLPDF

Abstract

An optimal dynamic decoupling of a quantum system coupled to a noisy environment must take into account also the imperfections of the control pulses. We present a formalism which describes, in a closed-form expression, the evolution of the system, including the spectral function of both the environment and control noise. We show that by measuring these spectral functions, our expression can be used to optimize the decoupling pulse sequence. We demonstrate this approach with an ensemble of optically trapped ultracold rubidium atoms, and use quantum process tomography to identify the effect of the environment and control noise. Our approach is applicable and important for any realistic implementation of quantum information processing.

DOI
10.1103/physreva.94.042317

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An optimal dynamic decoupling of a quantum system coupled to a noisy environment must take into account also the imperfections of the control pulses. We present a formalism which describes, in a closed-form expression, the evolution of the system, including the spectral function of both the environment and control noise. We show that by measuring these spectral functions, our expression can be used to optimize the decoupling pulse sequence. We demonstrate this approach with an ensemble of optically trapped ultracold rubidium atoms, and use quantum process tomography to identify the effect of the environment and control noise. Our approach is applicable and important for any realistic implementation of quantum information processing.
Decoherence is one of the most important obstacles that must be overcome in quantum information processing. It depends on the qubit-environment coupling strength, but also on the spectral composition of the noise generated by the environment. If the spectral density is known, fighting the effect of decoherence can be made more effective. Applying sequences of inversion pulses to the qubit system, we developed a method for dynamical decoupling noise spectroscopy. We generate effective filter functions that probe the environmental spectral density without requiring assumptions about its shape. Comparing different pulse sequences, we recover the complete spectral density function and distinguish different contributions to the overall decoherence.
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.
Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here we revisit the question of its efficacy in the presence of noisy pulses in scenarios important for quantum devices today: pulses with gate control errors, and the computational setting where DD is used to reduce noise in every computational gate. We focus on the well-known schemes of periodic (or universal) DD and its extension, concatenated DD, for scaling up its power. The qualitative conclusions from our analysis of these two schemes nevertheless apply to other DD approaches. In the presence of noisy pulses, DD does not always mitigate errors. It does so only when the added noise from the imperfect DD pulses does not outweigh the increased ability in averaging away the original background noise. We present break-even conditions that delineate when DD is useful, and further find that there is a limit in the performance of concatenated DD, specifically in how far one can concatenate the DD pulse sequences before the added noise no longer offers any further benefit in error mitigation.
The dynamical decoupling (DD) method is widely adopted to preserve coherence in different quantum systems. In the case of ideal pulses, its effects on the suppression of noise can be analytically described by the mathematical form of filter function. However, in practical experiments, the unavoidable pulse errors limit the efficiency of DD. In this paper, we study the effects of imperfect pulses on DD efficiency based on quantum trajectories. By directly generating a pseudo noise sequence correlated in time, we can explore the performance of DD with different pulse errors in the typical noise environment. It shows that, for the typical 1/ f noise environment, the phase error of operational pulses severely affects the performance of noise suppression, while the detuning and intensity errors have less influence. Also, we get the thresholds of these errors for efficient DD under the given experimental conditions. Our method can be widely applied to guide practical DD experimental implementation.
The dynamics of quantum systems are unavoidably influenced by their environment, but in turn observing a quantum system (probe) can allow one to measure its environment: Measurements and controlled manipulation of the probe such as dynamical decoupling sequences as an extension of the Ramsey interference measurement allow to spectrally resolve a noise field coupled to the probe. Here, we introduce fast and robust estimation strategies for the characterization of the spectral properties of classical and quantum dephasing environments. These strategies are based on filter function orthogonalization, optimal control filters maximizing the relevant Fisher Information and multi-qubit entanglement. We investigate and quantify the robustness of the schemes under different types of noise such as finite-precision measurements, dephasing of the probe, spectral leakage and slow temporal fluctuations of the spectrum.