Quantum Benchmarking via Random Dynamical Quantum Maps

TL;DR

This paper introduces a benchmarking protocol for quantum computers using random dynamical quantum maps, enabling a comprehensive error assessment without full tomography, validated through simulations and IBM Quantum experiments.

Contribution

It proposes a novel benchmarking method based on random quantum circuits and steady-state analysis, capturing system-wide errors including gate and measurement inaccuracies.

Findings

The protocol effectively characterizes error sources through steady-state distributions.

Numerical simulations show the relationship between errors and final state distributions.

Experimental implementation on IBM Quantum devices validates the approach.

Abstract

We present a benchmarking protocol for universal quantum computers, achieved through the simulation of random dynamical quantum maps. This protocol provides a holistic assessment of system-wide error rates, encapsulating both gate inaccuracies and the errors associated with mid-circuit qubit measurements and resets. By employing random quantum circuits and segmenting mid-circuit qubit measurement and reset in a repeated fashion, we steer the system of qubits to an ensemble of steady-states. These steady-states are described by random Wishart matrices, and align with the steady-state characteristics previously identified in random Lindbladian dynamics, including the universality property. The protocol assesses the resulting ensemble probability distribution measured in the computational basis, effectively avoiding a tomographic reconstruction. Our various numerical simulations demonstrate the relationship between the final distribution and different error sources. Additionally, we implement the protocol on state-of-the-art transmon qubits provided by IBM Quantum, drawing comparisons between empirical results, theoretical expectations, and simulations derived from a fitted noise model of the device.