Scalable Randomized Benchmarking of Quantum Computers Using Mirror Circuits

Timothy Proctor, Stefan Seritan, Kenneth Rudinger, Erik Nielsen, Robin Blume-Kohout, and Kevin Young

Phys. Rev. Lett. 129, 150502 – Published 6 October 2022

Abstract

The performance of quantum gates is often assessed using some form of randomized benchmarking. However, the existing methods become infeasible for more than approximately five qubits. Here we show how to use a simple and customizable class of circuits—randomized mirror circuits—to perform scalable, robust, and flexible randomized benchmarking of Clifford gates. We show that this technique approximately estimates the infidelity of an average many-qubit logic layer, and we use simulations of up to 225 qubits with physically realistic error rates in the range 0.1%–1% to demonstrate its scalability. We then use up to 16 physical qubits of a cloud quantum computing platform to demonstrate that our technique can reveal and quantify crosstalk errors in many-qubit circuits.

Received 22 December 2021
Revised 22 July 2022
Accepted 7 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.150502

Physics Subject Headings (PhySH)

Quantum benchmarking Quantum computation

Superconducting qubits

Quantum Information, Science & Technology

Authors & Affiliations

Timothy Proctor ^1,2, Stefan Seritan ^1,2, Kenneth Rudinger^1,2, Erik Nielsen^1,2, Robin Blume-Kohout^1,2, and Kevin Young^1,2

¹Quantum Performance Laboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
²Quantum Performance Laboratory, Sandia National Laboratories, Livermore, California 94550, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 129, Iss. 15 — 7 October 2022

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Scalable RB with mirror circuits. (a) Randomized mirror circuits over Clifford gates enable scalable RB. These circuits contain $d / 2$ pairs of layers consisting of a layer and its inverse (pink boxes) sampled from some set of $n$ -qubit Clifford layers, $d + 1$ layers of uniformly random Pauli gates (green boxes), and a layer of uniformly random one-qubit Clifford gates and this layer’s inverse (blue boxes). The number of “Pauli-dressed” layers (gray boxes) $d$ is the circuit’s benchmark depth. These circuits’ “effective polarization” $S$ , a quantity closely related to success probability, decays exponentially with $d$ . (b) Demonstrating our method on 1, 2, 4, 8, and 16 qubit subsets of IBM Q Rueschlikon. Points (violin plots) are the means (distributions) of $S$ versus $d$ , and the curves are fits to $S = A p^{d}$ . Each $r$ is a rescaling of $p$ that approximates the infidelity of an average Pauli-dressed $n$ -qubit layer (uncertainties are $1 σ$ here and throughout).
Reuse & Permissions
Figure 2
Validating MRB with many-qubit simulations. Simulations of MRB on up to 225 qubits show that it reliably approximates the infidelity of $n$ -qubit layers, i.e., $r_{Ω} \approx ε_{Ω}$ . (a) $r_{Ω}$ versus $ε_{Ω}$ for randomly sampled error models. Each point was generated from an independent simulation (sampling an error model and circuits, simulating the circuits, and then applying the analysis to estimate $r_{Ω}$ ) for gates subject to stochastic Pauli errors. (b) $r_{Ω}$ and $ε_{Ω}$ versus $n$ for two illustrative error models, with (model 2) and without (model 1) long-range crosstalk. This demonstrates the power of MRB to highlight crosstalk errors.
Reuse & Permissions
Figure 3
Validating MRB using cloud access experiments. MRB, DRB, and standard RB on 1–5 qubits of IBM Q Quito. (a)–(c) The means (points) and distributions (violin plots) of the circuit polarizations versus benchmark depth ( $d$ ), and fits to an exponential $A p^{d}$ (curves). (d) Error rates ( $r$ ) obtained from the fit’s decay rate for DRB and MRB versus the number of qubits ( $n$ ), and the values predicted from calibration data. The DRB and MRB error rates are in close agreement, validating MRB against the reliable but unscalable DRB protocol. The measured $r$ diverges from the predictions of Quito’s calibration data as $n$ increases, indicating crosstalk. (e) The mean polarizations at $d = 0$ ( $S_{0}$ ) decrease rapidly with $n$ for DRB and standard RB [at best $\log (S_{0}) = 1 - O (n^{2} / \log n)$ ] making them infeasible beyond a few qubits, whereas $\log (S_{0}) = 1 - O (n)$ for MRB.
Reuse & Permissions
Figure 4
Mapping out the performance of a 16-qubit processor. MRB was used to probe the performance of $n$ -qubit regions of IBM Q Rueschlikon. (a) The measured error rate $(r_{Ω})$ for each qubit subset that was tested (black lines are $1 σ$ uncertainties) and (b) the overoptimistic predictions from calibration data. The horizontal axis is a device schematic (nodes are qubits and edges the available cnots).
Reuse & Permissions

Physical Review Letters