Boltzmann Sampling of Frustrated J1 - J2 Ising Models with Programmable Quantum Annealers

One of the surprising, and potentially very useful, capabilities of analog quantum computers, such as D-Wave quantum annealers, is sampling from the Boltzmann, or Gibbs, distribution defined by a classical Hamiltonian. In this study, we thoroughly examine the ability of D-Wave quantum annealers to sample from the Boltzmann distribution defined of a canonical type of competing magnetic frustration $J_1$-$J_2$ model; the ANNNI (axial next-nearest-neighbor Ising) model. Boltzmann sampling error rate is quantified for standard linear-ramp anneals ranging from $5$ nanosecond annealing times up to $2000$ microseconds on two different D-Wave quantum annealing processors. Interestingly, we find some analog hardware parameters which result in a very high accuracy (down to a TVD of $0.0003$) and low temperature sampling (down to $\beta =32.2$) in a frustrated region of the ANNNI model magnetic phase diagram. This bolsters the viability of current analog quantum computers for thermodynamic sampling applications of highly frustrated magnetic spin systems.