The Role of Initial Entanglement in Adaptive Gibbs State Preparation on Quantum Computers

Sampling from distributions is an important capability for a range of tasks in science and engineering, including in machine learning applications. Quantum computers hold promise for the capability of sampling from distributions that are hard to sample from with usual (classical) computers. We have recently introduced an adaptive quantum variational algorithm for Gibbs state preparation, a state that can be sampled to yield a thermal (or Gibbs) distribution. This has applications in statistical physics, stochastic processes, and optimization. Here we explore the role of the initial quantum correlations (i.e., entanglement) built into the ‘data’ quantum bits (those that will be sampled) and the ancilla quantum bits (those that assist in preparing the Gibbs state) in the run-time of the adaptive state-preparation algorithm. Based on our simulations, we conclude that certain types of entangled states perform better for Ising Hamiltonians, while others are more appropriate for XY Hamiltonians. We also show that both perform well if multiple operators are added at each iteration through the ‘TETRIS-ADAPT’ technique.