Optimizing Circuit Reusing and its Application in Randomized Benchmarking

Zhuo Chen; Guoding Liu; Xiongfeng Ma

doi:10.22331/q-2025-01-23-1606

Optimizing Circuit Reusing and its Application in Randomized Benchmarking

Zhuo Chen, Guoding Liu, and Xiongfeng Ma

Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084 China

Published:	2025-01-23, volume 9, page 1606
Editor:	Pei Zeng
Eprint:	arXiv:2407.15582v3
Doi:	https://doi.org/10.22331/q-2025-01-23-1606
Citation:	Quantum 9, 1606 (2025).

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Abstract

Quantum learning tasks often leverage randomly sampled quantum circuits to characterize unknown systems. An efficient approach known as ``circuit reusing,'' where each circuit is executed multiple times, reduces the cost compared to implementing new circuits. This work investigates the optimal reusing times that minimizes the variance of measurement outcomes for a given experimental cost. We establish a theoretical framework connecting the variance of experimental estimators with the reusing times $R$. An optimal $R$ is derived when the implemented circuits and their noise characteristics are known. Additionally, we introduce a near-optimal reusing strategy that is applicable even without prior knowledge of circuits or noise, achieving variances close to the theoretical minimum. To validate our framework, we apply it to randomized benchmarking and analyze the optimal $R$ for various typical noise channels. We further conduct experiments on a superconducting platform, revealing a non-linear relationship between $R$ and the cost, contradicting previous assumptions in the literature. Our theoretical framework successfully incorporates this non-linearity and accurately predicts the experimentally observed optimal $R$. These findings underscore the broad applicability of our approach to experimental realizations of quantum learning protocols.

Featured image: Process of quantum learning task with circuit reusing strategy.
1. Input the quantum learning objective and prior knowledge about the quantum device performance and implemented circuits into a classical computer for analysis. 2. Design the learning protocol by setting parameters such as the number of reuses $R$ and the number of unique circuits $N$, and generate the corresponding quantum circuits. 3. Execute quantum operations and measurements to gather data for estimating the target quantity. 4. Analyze the collected data using classical post-processing to derive the desired quantity.

Popular summary

To construct large-scale quantum computers, precise and efficient characterization of the target quantum systems in the laboratory—called "quantum learning"—is essential. A crucial strategy in quantum learning tasks is "randomization," which involves averaging outcomes from circuits sampled at random to obtain a desired quantity. To mitigate experimental costs in practice, the strategy of "circuit reusing" is usually accompanied by "randomization," which means repeatedly implementing each circuit multiple times. In practice, reusing the same circuit generally entails a lower cost than initializing new circuits, while from a theoretical standpoint, sampling more circuits can enhance randomness, in turn improving estimation precision. Determining the optimal number of reusing times, especially in a realistic noisy case, is essential for the practical implementation of various quantum learning tasks.

In this work, we analyze the relationship between the fluctuation level of measurement results, the number of different sampled circuits, and the reusing times for each circuit. We solve the optimal reusing number of times that achieves minimal variance for measurement results given a fixed cost. We further propose a near-optimal solution that is derived without prior task knowledge, offering more convenience. Both solutions apply to various quantum learning tasks. As an application of our theories, we experimentally execute the "standard RB" protocol on a superconducting platform. Our experimental results validate our theoretical model, confirming the consistency between the experimentally determined optimal reusing times $R$ and those predicted theoretically. We anticipate our results will be broadly applied in experiments across various quantum learning tasks.

► BibTeX data

@article{Chen2025optimizingcircuit,
  doi = {10.22331/q-2025-01-23-1606},
  url = {https://doi.org/10.22331/q-2025-01-23-1606},
  title = {Optimizing {C}ircuit {R}eusing and its {A}pplication in {R}andomized {B}enchmarking},
  author = {Chen, Zhuo and Liu, Guoding and Ma, Xiongfeng},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1606},
  month = jan,
  year = {2025}
}

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