Phase transitions in parametrized quantum circuits

TL;DR

This paper constructs a class of parameterized quantum circuits that exhibit phase transitions and non-analytic behavior, providing insights into quantum critical phenomena and potential routes to quantum advantage.

Contribution

It introduces a mechanism for generating intrinsic non-analyticities in PQCs and demonstrates phase transitions within these circuits, linking them to quantum advantage.

Findings

PQC expectation values are non-analytic functions of parameters at phase transition points.

Classical simulation efficiency decreases near the phase transition, indicating quantum advantage potential.

Distinct behaviors of entanglement and order parameters reveal a phase diagram of the PQC states.

Abstract

Phase transitions are among the most intriguing phenomena in physical systems, yet their behavior near criticality remain challenging to study using classical algorithms. Parameterized quantum circuits (PQCs) offer a promising approach to investigating such regimes on practical quantum computers. However, in order to use it to probe critical behavior, a PQC itself should be non-trivial and exhibit a phase transition and non-analyticity -- a property that has not yet been clearly identified. In this work, we identify a mechanism for generating non-analyticities intrinsically in PQCs. As a concrete realization, we construct a class of sequential PQCs whose observable expectation value is a non-analytic function of the circuit parameter in the infinite volume limit, showing that the prepared PQC states undergo a phase transition at the non-analytic points. The entanglement and the identified order parameter have distinct behaviors in different phases, revealing a phase diagram of the PQC state. We show that classical simulation of this PQC based on tensor networks and Pauli propagation gets less efficient in the vicinity of the phase transition point, indicating a physically motivated route towards practical quantum advantage using PQCs with phase transitions.