Spectra of noisy parameterized quantum circuits: Single-Ring universality

TL;DR

This paper investigates the spectral properties of noisy parameterized quantum circuits on NISQ devices, revealing a transition in spectral density that links quantum chaos, random matrix theory, and current quantum hardware limitations.

Contribution

It demonstrates how the spectral properties of noisy quantum circuits can be modeled and analyzed using non-Hermitian random matrix theory, establishing a connection to dissipative quantum chaos.

Findings

Spectral density transitions from annulus to disk with circuit depth

Spectral properties closely match those of a known ensemble of random maps

Establishes a link between NISQ noise effects and non-Hermitian random matrix theory

Abstract

Random unitaries are an important resource for quantum information processing. While their universal properties have been thoroughly analyzed, it is not known what happens to these properties when the unitaries are sampled on the present-day noisy intermediate-scale quantum (NISQ) computers. We implement parameterized circuits, which have been proposed as a means to generate random unitaries, on an IBM Quantum processor and model these implementations as quantum maps. To retrieve the maps, a machine-learning assisted tomography is used. We find the spectrum of a map to be either an annulus or a disk depending on the circuit depth and detect an annulus-disk transition. By their spectral properties, the retrieved maps appear to be very similar to a recently introduced ensemble of random maps, for which spectral densities can be analytically evaluated. Our results establish, via Dissipative Quantum Chaos theory, a connection between intrinsic properties of present-day noisy intermediate-scale quantum (NISQ) computing platforms and non-Hermitian random matrix theory.