Understanding Quantum Tunneling using Diffusion Monte Carlo Simulations

Abstract

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as $1/{\Delta }^2$, where $\Delta$ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests there is no quantum advantage in using QAs w.r.t. quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model, where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving the door open for potential quantum speedup, even for stoquastic models. In this work, we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as $1/\Delta$, i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain points at an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.

arXiv comment9 pages, 7 figures

References in corpus (31)

• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• Quantum annealing with more than one hundred qubits
• Theory of Quantum Annealing of an Ising Spin Glass
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Defining and detecting quantum speedup
• Mathematical Foundation of Quantum Annealing
• Experimental signature of programmable quantum annealing
• Quantum versus Classical Annealing of Ising Spin Glasses
• Quantum Monte Carlo Calculations of Neutron Matter
• Ground state of a homogeneous Bose gas: a diffusion Monte Carlo calculation
• Green Function Monte Carlo with Stochastic Reconfiguration: an effective remedy for the sign problem disease
• Optimization by Quantum Annealing: Lessons from hard 3-SAT cases
• Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
• Reexamining classical and quantum models for the D-Wave One processor
• Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass
• A Coherent Quantum Annealer with Rydberg Atoms
• Path Integral Ground State with a Fourth-Order Propagator: Application to Condensed Helium
• Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stochastic Hamiltonians
• Optimization by Quantum Annealing: Lessons from Simple Cases
• Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
• Scaling analysis and instantons for thermally-assisted tunneling and Quantum Monte Carlo simulations
• Adiabatic optimization versus diffusion Monte Carlo
• Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing
• Bosonic superfluid-insulator transition in continuous space
• Polynomial-time classical simulation of quantum ferromagnets
• Quantum Monte Carlo Simulations of Tunneling in Quantum Adiabatic Optimization
• Simulated quantum annealing of double-well and multi-well potentials
• Monte Carlo studies of quantum and classical annealing on a double-well
• Quantum annealing of an Ising spin-glass by Green's function Monte Carlo
• Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

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