Parallelized Sequential Monte Carlo Sampling for Quantum State Tomography

This talk will look at the Bayesian inference algorithm Sequential Monte Carlo Sampling (SMC) as a way to efficiently sample from high-dimensional probability distributions found in quantum systems when performing Quantum State Tomography (QST). QST refers to any method that can characterize a quantum state given projections on that state. However, QST is notoriously challenging for all but the smallest quantum systems as the computational cost of simulating multiple qubits scales exponentially with the size of the Hilbert Space of the system. Although this is the main source of the computational power of quantum information processing, still, efficient QST algorithms are needed to help understand the nature of new quantum machines. Here, we use SMC to implement a parallelizable Bayesian tomography method. Our SMC algorithm combines established Bayesian tomography methods MCMC methods like preconditioned Crank-Nicholson Sampling, importance sampling, and particle filters to make an efficient and parallelizable method for QST. By finding a parallelizable Bayesian inference method, we can keep the statistical rigor of Bayesian methods, like natural error bars, and decrease some of the computational cost on each core that is notorious with Bayesian methods. Using SMC, we were able to demonstrate scaling of accuracy with increased core numbers, which was more evident with larger Hilbert Space systems, and we were able to get results obtained by non-parallel methods in a fraction of the time using this new QST method.