Practical variational tomography for critical 1D systems

TL;DR

This paper enhances a quantum state reconstruction method for critical 1D systems by optimizing measurement selection, significantly reducing experimental effort, and providing a certification bound for the reconstructed state’s accuracy.

Contribution

It introduces a numerically optimized measurement scheme for MERA tomography, reducing the number of measurements needed for critical 1D systems and providing a certifiable accuracy bound.

Findings

MERA tomography on 16-24 qubits requires similar effort as brute-force on 8 qubits.

Optimized measurement selection maximizes information extraction.

A computable bound certifies the distance between experimental and reconstructed states.

Abstract

We improve upon a recently introduced efficient quantum state reconstruction procedure targeted to states well-approximated by the multi-scale entanglement renormalization ansatz (MERA), e.g., ground states of critical models. We show how to numerically select a subset of experimentally accessible measurements which maximizes information extraction about renormalized particles, thus dramatically reducing the required number of physical measurements. We numerically estimate the number of measurements required to characterize the ground state of the critical 1D Ising (resp. XX) model and find that MERA tomography on 16-qubit (resp. 24-qubit) systems requires the same experimental effort than brute-force tomography on 8 qubits. We derive a bound computable from experimental data which certifies the distance between the experimental and reconstructed states.