Efficient tomography of a quantum many-body system

TL;DR

This paper introduces an efficient Matrix Product State tomography method for accurately estimating the states of large quantum many-body systems, demonstrated on a 14-qubit trapped-ion simulator, surpassing traditional quantum state tomography.

Contribution

The paper presents a theoretically proven MPS tomography technique that efficiently reconstructs states of 1D quantum systems, including out-of-equilibrium states, and applies it to large-scale quantum simulators.

Findings

Successfully reconstructed the dynamical state of a 14-qubit system

Revealed growth of entanglement during a quantum quench

Demonstrated efficiency over traditional quantum state tomography

Abstract

Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes impractical as the effort required grows exponentially in the number of constituents. Developing more efficient techniques is particularly pressing as precisely-controllable quantum systems that are well beyond the reach of QST are emerging in laboratories. Motivated by this, there is a considerable ongoing effort to develop new characterisation tools for quantum many-body systems. Here we demonstrate Matrix Product State (MPS) tomography, which is theoretically proven to allow the states of a broad class of quantum systems to be accurately estimated with an effort that increases efficiently with constituent number. We first prove that this broad class includes the out-of-equilbrium states produced by 1D systems with finite-range interactions, up to any fixed point in time. We then use the technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled spins (qubits): a size far beyond the reach of QST. Our results reveal the dynamical growth of entanglement and description complexity as correlations spread out during a quench: a necessary condition for future beyond-classical performance. MPS tomography should find widespread use to study large quantum many-body systems and to benchmark and verify quantum simulators and computers.