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- W2512312062 abstract "Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between ${L}_{1}$ and ${L}_{2}$ normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-$k$-SAT at $k=2,3,4$." @default.
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- W2512312062 date "2016-10-13" @default.
- W2512312062 modified "2023-09-23" @default.
- W2512312062 title "Adiabatic optimization versus diffusion Monte Carlo methods" @default.
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- W2512312062 doi "https://doi.org/10.1103/physreva.94.042318" @default.
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