Certification of quantum states with hidden structure of their bitstrings

TL;DR

This paper introduces a computationally efficient method for characterizing and certifying large-scale many-body quantum states using simple measurements and dissimilarity analysis, applicable to states with various entanglement structures.

Contribution

It presents a novel, low-cost procedure for quantum state characterization based on projective measurements and bit-string dissimilarities, enabling certification without full tomography.

Findings

Effective in distinguishing states with different entanglement structures

Capable of detecting phase transitions in quantum magnetic systems

Correlates dissimilarity measures with quantum correlations

Abstract

The rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozen of qubits. This success poses a strong demand on efficient and reliable methods for characterization and verification of large-scale many-body quantum states. Traditional methods, such as quantum tomography, which require storing and operating wave functions on classical computers, become problematic to use in the regime of large number of degrees of freedom. In this paper, we propose a numerically cheap procedure to describe and distinguish quantum states which is based on a limited number of simple projective measurements in at least two different bases and computing inter-scale dissimilarities of the resulting bit-string patterns via coarse-graining. The information one obtains through this procedure can be viewed as a "hash function" of quantum state -- a simple set of numbers which is specific for a concrete many-body wave function and can be used for certification. By studying a number of archetypal examples, we show that it is enough to characterize quantum states with different structure of entanglement, including the chaotic quantum states. The connection of the dissimilarity to standard measures of quantum correlations such as von Neumann entropy is discussed. We also demonstrate that our approach can be employed to detect phase transitions of different nature in many-body quantum magnetic systems.