Efficient quantum state tomography

TL;DR

This paper introduces two efficient methods for quantum state tomography in one-dimensional systems, significantly reducing measurement and computational complexity for states approximated by matrix product states, with certified accuracy.

Contribution

The paper presents two novel schemes for quantum state tomography that are more efficient and scalable than traditional methods, applicable to a broad class of quantum states.

Findings

Both schemes require only a linear number of experimental operations.

The methods are polynomial in classical postprocessing complexity.

The reconstructed states' accuracy can be rigorously certified.

Abstract

Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.