Efficient and feasible state tomography of quantum many-body systems

TL;DR

This paper introduces a new method for quantum state tomography in many-body lattice systems that leverages random circuits and existing experimental techniques to enable efficient, assumption-free, and scalable reconstruction of quantum states.

Contribution

It proposes a novel approach combining random circuits and quantum compressed sensing for scalable quantum state tomography in lattice systems, applicable with current experimental tools.

Findings

Allows assumption-free tomography with existing optical lattice techniques

Achieves constant effort in system size for certain states

Enables large-scale quantum state reconstruction in experiments

Abstract

We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for measuring a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary 2-designs, i.e., certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established techniques like optical super-lattices, laser speckles, and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. Combining our approach with tensor network methods - in particular the theory of matrix-product states - we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing in principle to perform tomography on large-scale systems readily available in present experiments.