Monte Carlo sampling from the quantum state space. II

TL;DR

This paper adapts Hamiltonian Monte Carlo methods to efficiently generate high-quality random samples of quantum states within the physical state space, improving sampling reliability for quantum information tasks.

Contribution

It introduces a novel application of Hamiltonian Monte Carlo to quantum state sampling, ensuring samples stay within physical constraints and reducing correlations.

Findings

Effective sampling within quantum state space demonstrated with qubit examples

Hamiltonian Monte Carlo reduces correlations and increases sampling efficiency

Method applicable when an efficient parameterization of the quantum state space is available

Abstract

High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local maxima or evaluating an integral over a region in the quantum state space are but two exemplary applications of many. These tasks can only be performed reliably and efficiently with Monte Carlo methods, which involve good samplings of the parameter space in accordance with the relevant target distribution. We show how the Markov-chain Monte Carlo method known as Hamiltonian Monte Carlo, or hybrid Monte Carlo, can be adapted to this context. It is applicable when an efficient parameterization of the state space is available. The resulting random walk is entirely inside the physical parameter space, and the Hamiltonian dynamics enable us to take big steps, thereby avoiding strong correlations between successive sample points while enjoying a high acceptance rate. We use examples of single and double qubit measurements for illustration.