Probing quantum phase transitions via short depth quantum circuits for estimating quantum coherence and discrete Berry phases

Abstract Classical techniques for the simulation of complex many-body systems can be severely limited by the exponentially increasing dimensions of quantum systems, and prior assumptions are often required to efficiently extract information about non-local quantum properties. Short depth quantum algorithms are proposed that efficiently estimate non-local quantum properties such as the quantum coherence and discrete Berry phases to probe the quantum phase transitions in many body systems. The gate complexities of these algorithms scale linearly while the depth complexity scale logarithmically with system size. These algorithms are applied to probe the well-known Haldane to quantum paramagnetic phase transitions in spin-1 Heisenberg antiferromagnetic chains, which are topological phase transitions that cannot be identified via local order parameters. The algorithms are shown to be able to extract non-local information about the system give the correct signatures of topological phase transitions near critical points.