Every Benchmark All at Once

TL;DR

The paper addresses the challenge of benchmarking noisy quantum devices by unifying randomized benchmarking (RB) techniques under the gate-set shadow protocol. It introduces a data-driven, PTM-based postprocessing pipeline that uses sequence correlation functions with a probe operator to extract multiple observables from a single dataset, and demonstrates applicability to standard RB, interleaved RB, simultaneous RB, correlated RB, and leakage RB across diverse gate-sets. Key contributions include explicit fitting models that yield decay parameters linked to fidelities, robust confidence-interval estimates via median-of-means and bootstrap methods, and reconstruction of unital marginals to diagnose crosstalk and correlated noise, as well as leakage metrics. The framework promises practical advantages, such as reduced gate-set size requirements, avoidance of SPAM biases, and flexible adaptation to various experimental setups, backed by open-source code for implementation.

Abstract

As quantum technology matures, the efficient benchmarking of quantum devices remains a key challenge. Although sample-efficient, information-theoretic benchmarking techniques have recently been proposed, there is still a gap in adapting these techniques to contemporary experiments. In this work, we re-formulate five of the most common randomized benchmarking techniques in the modern language of the gate-set shadow tomography. This reformulation brings along several concrete advantages over conventional formulations of randomized benchmarking. For standard and interleaved randomized benchmarking, we can reduce the required gate-set size and, using median-of-means estimators, also reduce the required experimental sample size. For simultaneous and correlated randomized benchmarking, we can additionally reconstruct the Pauli-terms of correlated noise channels using additional post-processing of only a single experimental dataset. We also present a minimal approach to extract leakage errors. Our work provides a clear avenue for comprehensive, reliable, and convenient benchmarking of quantum devices, with all methods formulated under a single umbrella technique that can be easily adapted to a range of experimental quantities and gate sets.

Figures (19)

• Figure 1: Overview of the the gate-set shadow protocol: data collection phase. (a) We start by selecting gates uniformly at random from a given gate-set $G$. (b) This creates a sequence of random gates that are then applied to the input state. The resulting outcome is measured in a computational basis. Iterating over this process allows us to create a data-set formed by the pairing of random sequences with the corresponding outcomes, $(x_i,\mathbf{g}_i)$
• Figure 2: Overview of the the gate-set shadow protocol: postprocessing phase. (c) For each data-set entry $(x_i,\mathbf{g}_i)$, we construct the sequence correlation function $f_A$. A typical choice for $A$ is to fix it as a subspace projector. Specific choices of subspace projectors are illustrated in the figure for the case of the two-qubit Clifford group($\mathbb{C}_2$) and the local Clifford group ($\mathbb{C}^{\times 2}_1$) as gate-sets. (d) Taking the mean (or median-of-means, MoM) of all the sequence correlation functions gives an estimate of the sequence function, $\hat{k}_A(m)$, which can then be fitted to an exponential decay model to extract targeted fidelities.
• Figure 3: Average sequence functions, $k_A(m)$, for different choices of gate-set and different choices of the random sequences. Recall that $m$ is the length of the sequences. The function $k_A(m)$ either emulates the sequence fidelity of standard (sta.) RB (random sequences) or interleaved (int.) RB (interleaved sequences). Panel a) makes use of the Clifford gate-set, while uses the $G(1)$ CNOT-Dihedral gate-set. Panel b) shows the sequence correlation function associated with the decay rate $\lambda_1$, and $\lambda_2$, respectively. These are required to estimate the average fidelity (see Eq.(\ref{['cdi_trace_formula']})). The estimated decay rates from the fit lead to average fidelities in Tab. \ref{['tab_fid_cnot']}. The noise model for the simulations is discussed in the main text. For panel b), only the decays obtained using the mean are showed, since in this case both estimators yield similar results.
• Figure 4: Coverage probability for different confidence intervals and different sample sizes. The results are obtained by simulating the gate-set shadow protocol 100 times, and recomputing the confidence intervals, using each of the listed methods in the main text. The two plots differ by the choice of estimator: mean (left) or median-of-means (right). In this case, the protocol uses the two-qubit Clifford group as gate-set and gate errors are simulated with a Pauli noise channel.
• Figure 5: Comparison of the decay curves of $\lambda_1$ and $\lambda_{1|2}$ for the gate error channel described in the main text. Each data point in the left panel results from the averaging of 1000 points, representing the different realizations of the random circuit at fixed circuit length $m$. The panel on the right shows the absolute difference between the estimated $\lambda_1$ and its ground truth value, based on the error model described in the main text. The estimates for the target parameters were obtained in both figures using the median-of-means (MoM).