The optimal reordering of measurements for photonic quantum tomography

TL;DR

This paper introduces an optimized measurement ordering strategy for photonic quantum tomography, significantly reducing the procedure time by solving a traveling salesman problem instance, verified experimentally for systems up to six qubits.

Contribution

It presents a novel method to optimally arrange measurements in quantum tomography, achieving substantial speedups without simplifying the system.

Findings

Tomography time can be halved for systems of three or more qubits.

Experimental verification up to six qubits confirms the speedup.

Method applies to quantum state and process characterization, as well as optical device testing.

Abstract

Quantum tomography is an essential method of the photonic technology toolbox and is routinely used for evaluation of experimentally prepared states of light and characterization of devices transforming such states. The tomography procedure consists of many different sequentially performed measurements. We present considerable tomography speedup by optimally arranging the individual constituent measurements, which is equivalent to solving an instance of the traveling salesman problem. As an example, we obtain solutions for photonic systems of up to five qubits, and conclude that already for systems of three or more qubits, the total duration of the tomography procedure can be halved. The reported speedup has been verified experimentally for quantum state tomography and also for full quantum process characterization up to six qubits, without resorting to any complexity reduction or simplification of the system of interest. Our approach is versatile and reduces the time of an input-output characterization of optical devices and various scattering processes as well.