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arXiv:2303.17565 · Physical Review Research

Context-aware fidelity estimation

Dripto M. Debroy, Élie Genois, Jonathan A. Gross, Wojciech Mruczkiewicz, Kenny Lee, Sabrina Hong, Zijun Chen, Vadim Smelyanskiy, Jiang Zhang

Published Dec 5, 2023• 5 citations
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Abstract

We present context-aware fidelity estimation (CAFE), a framework for benchmarking quantum operations that offers several practical advantages over existing methods such as randomized benchmarking (RB) and cross-entropy benchmarking. In CAFE, a gate or a subcircuit from some target experiment is repeated $n$ times before being measured. By using a subcircuit, we account for effects from the spatial and temporal circuit context. Since coherent errors accumulate quadratically while incoherent errors grow linearly, we can separate them by fitting the measured fidelity as a function of $n$. One can additionally interleave the subcircuit with dynamical decoupling sequences to remove certain coherent error sources from the characterization when desired. We have used CAFE to experimentally validate our single- and two-qubit unitary characterizations by measuring fidelity against estimated unitaries. In numerical simulations, we find that CAFE produces fidelity estimates at least as accurate as interleaved RB while using significantly fewer resources. We also introduce a compact formulation for preparing an arbitrary two-qubit state with a single entangling operation and use it to present a concrete example using CAFE to study controlled-$Z$ gates in parallel on a Sycamore processor.

DOI
10.1103/physrevresearch.5.043202

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We present context-aware fidelity estimation (CAFE), a framework for benchmarking quantum operations that offers several practical advantages over existing methods such as randomized benchmarking (RB) and cross-entropy benchmarking. In CAFE, a gate or a subcircuit from some target experiment is repeated nnn times before being measured. By using a subcircuit, we account for effects from the spatial and temporal circuit context. Since coherent errors accumulate quadratically while incoherent errors grow linearly, we can separate them by fitting the measured fidelity as a function of nnn. One can additionally interleave the subcircuit with dynamical decoupling sequences to remove certain coherent error sources from the characterization when desired. We have used CAFE to experimentally validate our single- and two-qubit unitary characterizations by measuring fidelity against estimated unitaries. In numerical simulations, we find that CAFE produces fidelity estimates at least as accurate as interleaved RB while using significantly fewer resources. We also introduce a compact formulation for preparing an arbitrary two-qubit state with a single entangling operation and use it to present a concrete example using CAFE to study controlled-ZZZ gates in parallel on a Sycamore processor.
Abstract There is currently a significant need for robust and efficient methods for characterizing quantum devices. While there has been significant progress in this direction, there remains a crucial need to precisely determine the strength and type of errors on individual gate operations, in order to assess and improve control as well as reliably bound the total error in a quantum circuit given some partial information about the errors on the components. In this work, we first provide an optimal bound on the total fidelity of a circuit in terms of component fidelities, which can be efficiently experimentally estimated via randomized benchmarking (RB). We then derive a tighter bound that applies under additional information about the coherence of the error, namely, the unitarity, which can also be estimated via a related experimental protocol. This improved bound smoothly interpolates between the worst-case quadratic and best-case linear scaling for composite error channels. As an application we show how our analysis substantially improves the achievable precision on estimates of the infidelities of individual gates under interleaved RB, enabling greater precision for current experimental methods to assess and tune-up control over quantum gate operations.
Cross-entropy benchmarking (XEB) with single-qubit reference sequences is widely used to characterize multi-qubit gates in large-scale quantum processors, despite the lack of a rigorous theoretical justification. Here we show that the commonly employed additive single-qubit errors approximation underlying this approach breaks down and leads to a systematic overestimation of gate fidelities. We derive an analytical expression for the joint decay of simultaneous single-qubit reference sequences, identify when interleaved circuits generate sufficient randomization for the standard depolarizing approximation, and obtain a refined expression for the interleaved gate fidelity estimation. Experiments on a superconducting quantum processor validate the theory and demonstrate that fidelities obtained using XEB with single-qubit references agree with those extracted from standard interleaved randomized benchmarking (IRB), while achieving higher precision due to reduced reference-sequence errors. Our results establish theoretical foundation for interleaved benchmarking protocols employing single-qubit reference sequences and show that, with appropriate post-processing, they provide a simple and accurate alternative to multi-qubit Clifford reference circuits.
Randomized benchmarking (RB) protocols have become an essential tool for providing a meaningful partial characterization of experimental quantum operations. While the RB decay rate is known to enable estimates of the average fidelity of those operations under gate-independent Markovian noise, under gate-dependent noise this rate is more difficult to interpret rigorously. In this paper, we prove that single-qubit RB experiments provide direct estimates of the gateset circuit fidelity, a novel figure of merit which characterizes the expected average fidelity over arbitrary circuits of operations from the gateset. We also prove that, in the limit of high-fidelity single-qubit experiments, the difficulty introduced by gate-dependence reduces to a basis mismatch between the gates and the state-preparation and measurement procedures, that is, to a unitary degree of freedom in labeling the Pauli matrices. Based on numerical evidence and physically motivated arguments, we conjecture that these result hold for higher dimensions.
Fidelity estimation is a fundamental tool for assessing quantum resource states across quantum information science. For small infidelity εεε, tomography and direct fidelity estimation (DFE) have worst-case sample complexity O(1/ε2)O(1/ε^2)O(1/ε2) at fixed relative accuracy and confidence. Direct target projections achieve O(1/ε)O(1/ε)O(1/ε) but generally require non-Clifford operations whose reliability depends on the resource states that are typically the target of benchmarking. Here, we introduce the Bell--coherence fidelity estimation (BCFE) with optimal sample complexity Θ(1/ε)Θ(1/ε)Θ(1/ε) using only Clifford gates and Pauli measurements. We prove that BCFE is applicable to arbitrary pure targets, possibly multi-qubit, with the statistical error of the single-copy coherence part explicitly controlled. To evaluate BCFE in a practical setting, we apply BCFE to analog rotation resource states in the candidate early-FTQC architecture called the Space-Time Efficient Analog Rotations (STAR) architecture. In the simulations using surface codes, BCFE is estimated to require up to approximately 272727 times fewer resource states than DFE for the same standard error in the infidelity estimate, while its estimates remain close to reference values despite circuit-level noise in the additional Bell measurement operations. These results support efficient resource benchmarking within fault-tolerant quantum computing.
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.
With the continued scaling of quantum processors, holistic benchmarks are essential for extensively evaluating device performance. Layer fidelity is a benchmark well-suited to assessing processor performance at scale. Key advantages of this benchmark include its natural alignment with randomized benchmarking (RB) procedures, crosstalk awareness, fast measurements over large numbers of qubits, high signal-to-noise ratio, and fine-grained information [1]. In this work, we extend the analysis of the original layer fidelity manuscript to optimize parameters of the benchmark and extract deeper insights of its application. We present a robust protocol for identifying optimal qubit chains of arbitrary lengthNNN, demonstrating that our method yields error per layered gate (EPLG) values40%−70%40 \% - 70 \%40%−70%lower than randomly selected chains forN=100N=100N=100qubits. We further establish layer fidelity as an effective performance monitoring tool, capturing both edge-localized and device-wide degradation by tracking optimal chains of length 50 and 100, and fixed chains of length 100. Additionally, we refine error analysis by proposing parameter bounds on the number of randomizations and Clifford lengths used in direct RB fits, minimizing fit uncertainties. Finally, we use layer fidelity to analyze the impact of varying gate durations on layered two-qubit (2Q) errors, showing that prolonged gate times leading to idling times significantly increase these quantities. These findings extend the applicability of the layer fidelity benchmark and provide practical guidelines for optimizing quantum processor evaluations.