Reconstructing complex states of a 20-qubit quantum simulator

TL;DR

This paper presents an efficient variational tomography method for reconstructing highly entangled 20-qubit quantum states using minimal measurement bases, outperforming neural network approaches.

Contribution

Introduces a variational matrix product state approach for quantum state tomography that is efficient for large multi-qubit systems, reducing measurement resources.

Findings

Achieved high-quality state reconstruction with only 27 measurement bases.

Demonstrated faster convergence than neural network-based methods.

Validated the approach on a 20-qubit trapped-ion quantum simulator.

Abstract

A prerequisite to the successful development of quantum computers and simulators is precise understanding of physical processes occurring therein, which can be achieved by measuring the quantum states they produce. However, the resources required for traditional quantum-state estimation scale exponentially with the system size, highlighting the need for alternative approaches. Here we demonstrate an efficient method for reconstruction of significantly entangled multi-qubit quantum states. Using a variational version of the matrix product state ansatz, we perform the tomography (in the pure-state approximation) of quantum states produced in a 20-qubit trapped-ion Ising-type quantum simulator, using the data acquired in only 27 bases with 1000 measurements in each basis. We observe superior state reconstruction quality and faster convergence compared to the methods based on neural network quantum state representations: restricted Boltzmann machines and feedforward neural networks with autoregressive architecture. Our results pave the way towards efficient experimental characterization of complex states produced by the quench dynamics of many-body quantum systems.