Probing quantum phase transitions via short-depth quantum circuits for estimating quantum coherence and discrete Berry phases
Phys. Rev. B 112, 014108 – Published 17 July, 2025
DOI: https://doi.org/10.1103/gydb-9jt2
Abstract
Classical techniques for the simulation of complex many-body systems are often constrained by the exponential growth of the dimensions of quantum systems, requiring prior assumptions to efficiently extract nonlocal quantum properties. To address this limitation, we propose efficient short-depth quantum algorithms for estimating nonlocal quantum properties, such as quantum coherence and discrete Berry phases, to probe quantum phase transitions in many-body systems. The gate complexities of the quantum circuits scale linearly while the depth complexity scales logarithmically with system size. We demonstrate the applicability of these algorithms by investigating the well-known Haldane-to-quantum-paramagnetic phase transitions in spin-1 Heisenberg antiferromagnetic chains. These transitions, being topological in nature, cannot be identified using local order parameters, necessitating the measurement of nonlocal quantum properties. Our results show that the algorithms successfully extract nonlocal information and provide accurate signatures of topological phase transitions near critical points.
