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Physical Review A

Demonstration of the reduction of decoherent errors in a solid-state qubit using dynamic decoupling techniques

Sarah E. Beavan, E. Fraval, Matthew J. Sellars, Jevon J. Longdell

Published Sep 4, 2009• 25 citations
Publisher

Abstract

We experimentally demonstrate that decoherent errors for a qubit can be reduced using dynamic decoupling control. The quantum system in our experiment is a praseodymium ground-state hyperfine transition in ${\text{Pr}}^{3+}:{\text{Y}}_{2}{\text{SiO}}_{5}$. These experiments were undertaken using an ensemble, where care was taken to reduce incoherent errors resulting from inhomogeneity across the sample. The volume of the Bloch sphere after transformation by the applied pulse sequence was used as a measure of fidelity of the qubit. The strength of the qubit-environment coupling can be tuned by the application of a magnetic field, allowing for regimes of varying decoherence rates to be investigated. We show that the Bloch sphere volume, with the application of dynamic decoupling pulse sequences, decays at a slower rate than observed under free evolution.

DOI
10.1103/physreva.80.032308

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We experimentally demonstrate that decoherent errors for a qubit can be reduced using dynamic decoupling control. The quantum system in our experiment is a praseodymium ground-state hyperfine transition in Pr3+:Y2SiO5{\text{Pr}}^{3+}:{\text{Y}}_{2}{\text{SiO}}_{5}Pr3+:Y2​SiO5​. These experiments were undertaken using an ensemble, where care was taken to reduce incoherent errors resulting from inhomogeneity across the sample. The volume of the Bloch sphere after transformation by the applied pulse sequence was used as a measure of fidelity of the qubit. The strength of the qubit-environment coupling can be tuned by the application of a magnetic field, allowing for regimes of varying decoherence rates to be investigated. We show that the Bloch sphere volume, with the application of dynamic decoupling pulse sequences, decays at a slower rate than observed under free evolution.
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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.
Quantum computers must be able to function in the presence of decoherence. The simplest strategy for decoherence reduction is dynamical decoupling (DD), which requires no encoding overhead and works by converting quantum gates into decoupling pulses. Here, using the IBM and Rigetti platforms, we demonstrate that the DD method is suitable for implementation in today's relatively noisy and small-scale cloud-based quantum computers. Using DD, we achieve substantial fidelity gains relative to unprotected, free evolution of individual superconducting transmon qubits. To a lesser degree, DD is also capable of protecting entangled two-qubit states. We show that dephasing and spontaneous emission errors are dominant in these systems, and that different DD sequences are capable of mitigating both effects. Unlike previous work demonstrating the use of quantum error correcting codes on the same platforms, we make no use of postselection and hence report unconditional fidelity improvements against natural decoherence.
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.
One of the biggest challenges for implementing quantum devices is the requirement to perform accurate quantum gates. The destructive effects of interactions with the environment present some of the most difficult obstacles that must be overcome for precise quantum control. In this work we implement a proof of principle experiment of quantum gates protected against a fluctuating environment and control pulse errors using dynamical decoupling techniques. We show that decoherence can be reduced during the application of quantum gates. High-fidelity quantum gates can be achieved even if the gate time exceeds the free evolution decoherence time by one order of magnitude and for protected operations consisting of up to 330 individual control pulses.