Quantum Markov Chain Monte Carlo for Cosmological Functions

Abstract

We present an implementation of Quantum Computing for a Markov Chain Monte Carlo method with an application to cosmological functions, to derive posterior distributions from cosmological probes. The algorithm proposes new steps in the parameter space via a quantum circuit whose resulting statevector provides the components of the shift vector. The proposed point is accepted or rejected via the classical Metropolis-Hastings acceptance method. The advantage of this hybrid quantum approach is that the step size and direction change in a way independent of the evolution of the chain, thus ideally avoiding the presence of local minima. The results are consistent with analyses performed with classical methods, both for a test function and real cosmological data. The final goal is to generalize this algorithm to test its application to complex cosmological computations.