Permutation Matrix Representation Quantum Monte Carlo
arXiv:1908.03740 · doi:10.1088/1742-5468/ab9e64
Abstract
We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its off-diagonal terms and is both parameter-free and Trotter error-free. In our approach, the quantum dimension consists of products of elements of a permutation group. As such, it allows for the study of a very wide variety of models on an equal footing. To demonstrate the utility of our technique, we use it to clarify the emergence of the sign problem in the simulations of non-stoquastic physical models. We showcase the flexibility of our algorithm and the advantages it offers over existing state-of-the-art by simulating transverse-field Ising model Hamiltonians and comparing the performance of our technique against that of the stochastic series expansion algorithm. We also study a transverse-field Ising model augmented with randomly chosen two-body transverse-field interactions.
15 pages, 6 figures
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- Determining QMC simulability with geometric phases
- A quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs
- Specialising Neural-network Quantum States for the Bose Hubbard Model
- A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians
- A universal black-box quantum Monte Carlo approach to quantum phase transitions
- Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
- Path Integral Monte Carlo in the Angular Momentum Basis for a Chain of Planar Rotors
- Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach
- A simple quantum simulation algorithm with near-optimal precision scaling
- A quantum Monte Carlo algorithm for arbitrary high-spin Hamiltonians