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arXiv:1909.10727 · Physical Review Research

Dynamically corrected gates suppressing spatiotemporal error correlations as measured by randomized benchmarking

Claire Edmunds, Cornelius Hempel, R. J. Harris, Virginia Frey, Thomas M. Stace, Michael J. Biercuk

Published Feb 13, 2020• 28 citations
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Abstract

This work introduces a method to measure error correlations in quantum circuits, both temporally between gates and spatially between qubits. The authors demonstrate that using appropriately tailored dynamically corrected gates can not only reduce the likelihood of errors, but also correlations between them, and can hence be used to precondition a circuit for quantum error correction.

DOI
10.1103/physrevresearch.2.013156

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This work introduces a method to measure error correlations in quantum circuits, both temporally between gates and spatially between qubits. The authors demonstrate that using appropriately tailored dynamically corrected gates can not only reduce the likelihood of errors, but also correlations between them, and can hence be used to precondition a circuit for quantum error correction.
Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of independent errors in quantum logic operations is at odds with realistic environments where error-sources may exhibit strong temporal correlations. We present experiments enabling the identification of error correlations between operations in quantum circuits, using only projective measurements at the end of the circuit. Using a single trapped ion qubit and engineered noise with tunable temporal correlations, we identify a clear signature of error correlations between sequential gates in randomly composed quantum circuits, and extract quantitative measures linked to the underlying noise correlation length. By replacing all gates in these circuits with "virtual" dynamically corrected gates (DCGs), we demonstrate that even in the presence of strongly correlated noise the signatures of error correlations between sequential gates appear similar to standard gates exposed to uncorrelated noise. A theoretical model applied to our experiments reveals that common DCGs suppress the correlated error component by over 270×270\times270× with 95%95\%95% confidence. Using block-correlated noise, we explore the scaling of the effective error correlation length at the virtual level, and show that DCGs exhibit error correlations indistinguishable from those arising from uncorrelated noise.
As quantum circuits become more integrated and complex, additional error sources that were previously insignificant start to emerge. Consequently, the fidelity of quantum gates benchmarked under pristine conditions falls short of predicting their performance in realistic circuits. To overcome this problem, we must improve their robustness against pertinent error models besides isolated fidelity. Here, we report the experimental realization of robust quantum gates in superconducting quantum circuits based on a geometric framework for diagnosing and correcting various gate errors. Using quantum process tomography and randomized benchmarking, we demonstrate robust single-qubit gates against quasistatic noise and spatially correlated noise in a broad range of strengths, which are common sources of coherent errors in large-scale quantum circuits. We also apply our method to nonstatic noises and to realize robust two-qubit gates. Our Letter provides a versatile toolbox for achieving noise-resilient complex quantum circuits.
Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely used to filter environmental noise from signals, but their performance is limited by the spectral properties of the signal and noise at hand. Quantum error correction schemes have therefore emerged as a complementary technique without the same limitations. To date, however, they have failed to correct the dominant noise type in many quantum sensors, which couples to each qubit in a sensor in the same way as the signal. Here we show how quantum error correction can correct for such noise, which dynamical decoupling can only partially address. Whereas dynamical decoupling exploits temporal noise correlations in signal and noise, our scheme exploits spatial correlations. We give explicit examples in small quantum devices and demonstrate a method by which error-correcting codes can be tailored to their noise.
Coherent errors, and especially those that occur in correlation among a set of qubits, are detrimental for large-scale quantum computing. Correlations in noise can occur as a result of spatial and temporal configurations of instructions executing on the quantum processor. In this paper, we perform a detailed experimental characterization of many of these error sources, and theoretically connect them to the physics of superconducting qubits and gate operations. Equipped with this knowledge, we devise compiler strategies to suppress these errors using dynamical decoupling or error compensation into the rest of the circuit. Importantly, these strategies are successful when the context at each layer of computation is taken into account: how qubits are connected, what crosstalk terms exist on the device, and what gates or idle periods occur in that layer. Our context-aware compiler thus suppresses some dominant sources of error, making further error mitigation or error correction substantially less expensive. For example, our experiments show an increase of 18.5%\mathbf{1 8. 5 \%}18.5% in layer fidelity for a candidate 10 -qubit circuit layer compared to context-unaware suppression. Owing to the exponential nature of error mitigation, these improvements due to error suppression translate to several orders of magnitude reduction of sampling overhead for a circuit consisting of a moderate number of layers.
Abstract Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely used to filter environmental noise from signals, but their performance is limited by the spectral properties of the signal and noise at hand. Quantum error correction schemes have therefore emerged as a complementary technique without the same limitations. To date, however, they have failed to correct the dominant noise type in many quantum sensors, which couples to each qubit in a sensor in the same way as the signal. Here we show how quantum error correction can correct for such noise, which dynamical decoupling can only partially address. Whereas dynamical decoupling exploits temporal noise correlations in signal and noise, our scheme exploits spatial correlations. We give explicit examples in small quantum devices and demonstrate a method by which error-correcting codes can be tailored to their noise.
Dynamic quantum circuits integrate unitary evolution with mid-circuit measurement and feedforward, enabling conditional operations essential for efficient quantum algorithms and foundational for fault-tolerant quantum computation. However, such operations introduce measurement-induced errors and control constraints that are not addressed by conventional error-suppression techniques. Here, we introduce an empirical learning framework that optimizes dynamical decoupling (DD) sequences for dynamic circuits at the level of circuit subintervals and qubit subregisters. Applying empirically learned DD sequences, we achieve a three-fold reduction in average dynamic circuit error rates as measured via randomized benchmarking. We apply the learned strategies to the dynamic circuit implementation of the quantum Fourier transform with measurement (QFT+M), demonstrating nontrivial process fidelity on connected chains of up to 20 qubits. Applying the resulting enhancement, we perform a high signal-to-noise QFT immediately following the preparation of a 10-qubit entangled state. Our results demonstrate that empirically optimized DD systematically outperforms theoretically derived sequences for dynamic circuits, establishing it as an efficient approach for error suppression in dynamic quantum circuits, with direct relevance to applications requiring measurement and feedback such as quantum error correction.