Quantum state tomography and purity measurement of a multiqubit system with random single-pulse rotations

Abstract

Quantum state tomography and other measures of the global properties of a quantum state are indispensable tools in understanding many body physics through quantum simulators. Unfortunately, the number of experimental measurements of the system required to estimate these global quantities scales exponentially with system size. Here, we consider the use of random-axis measurements for quantum state tomography and state purity estimation. We perform a general analysis of the statistical deviation in such methods for any given algorithm. We then propose a simple protocol which relies on single-pulse X/Y rotations only. We find that it reduces the basis of the exponential growth, calculating the statistical variance to scale as a,b |∆ρ ab | 2 ∼ 5 N /Ntot for full tomography, and (∆µ) 2 ∼ 7 N /N 2 tot for purity estimation, for N qubits and Ntot measurements performed.