Finite-depth scaling of infinite quantum circuits for quantum critical points

TL;DR

This paper demonstrates how finite-depth quantum circuits on NISQ devices can effectively model and analyze critical quantum systems, revealing universal scaling relations and extracting critical properties.

Contribution

It introduces universal finite-depth scaling relations for quantum circuits representing critical states and verifies them numerically at two distinct critical points.

Findings

Universal finite-depth scaling relations are established.

Numerical verification at critical Ising and XXZ models.

Quantum circuits can capture critical properties on NISQ devices.

Abstract

The scaling of the entanglement entropy at a quantum critical point allows us to extract universal properties of the state, e.g., the central charge of a conformal field theory. With the rapid improvement of noisy intermediate-scale quantum (NISQ) devices, these quantum computers present themselves as a powerful tool to study critical many-body systems. We use finite-depth quantum circuits suitable for NISQ devices as a variational ansatz to represent ground states of critical, infinite systems. We find universal finite-depth scaling relations for these circuits and verify them numerically at two different critical points, i.e., the critical Ising model with an additional symmetry-preserving term and the critical XXZ model.