Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
arXiv:1510.08057 · doi:10.1103/PhysRevLett.117.180402
Abstract
The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is , where is the tunneling splitting. An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC, and achieve linear scaling in . We provide a physical understanding of these results and their range of applicability based on an instanton picture.
5 pages, 4 figures, 10 pages of supplemental material
References in corpus (14)
- What is the Computational Value of Finite Range Tunneling?
- Many-body mobility edge in a mean-field quantum spin glass
- Interplay of quantum and thermal fluctuations in a frustrated magnet
- The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
- Unexpectedly high pressure for molecular dissociation in liquid hydrogen by a reliable electronic simulation
- On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
- On quantum mean-field models and their quantum annealing
- Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs
- Quantum annealing: the fastest route to quantum computation?
- Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise
- Quantum Monte Carlo Simulations of Tunneling in Quantum Adiabatic Optimization
- Open system quantum annealing in mean field models with exponential degeneracy
- Simulated quantum annealing of double-well and multi-well potentials
- Anomalous behavior of the energy gap in the one-dimensional quantum XY model
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- Challenges of variational quantum optimization with measurement shot noise
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- Quantum annealing correction at finite temperature: ferromagnetic -spin models
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- Simulated quantum annealing as a simulator of non-equilibrium quantum dynamics
- Accelerated Quantum Monte Carlo with Probabilistic Computers
- Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet
- Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics
- Scaling Advantage in Approximate Optimization with Quantum Annealing
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- Assessment of Quantum Annealing for the Construction of Satisfiability Filters
- Understanding Quantum Tunneling using Diffusion Monte Carlo Simulations
- Quantum phase transition with inhomogeneous driving in the Lechner-Hauke-Zoller model
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- Phase transition of Frustrated Ising model via D-wave Quantum Annealing Machine
- On the dynamics of Simulated Quantum Annealing in random Ising chains
- Supervised learning of random quantum circuits via scalable neural networks
- Optimization by a quantum reinforcement algorithm
- From Ansätze to Z-gates: a NASA View of Quantum Computing
- Stoquasticity in circuit QED
- Dynamics of Order Parameters of Non-stoquastic Hamiltonians in the Adaptive Quantum Monte Carlo Method
- Tunneling in projective quantum Monte Carlo simulations with guiding wave functions
- Quantum optimization within lattice gauge theory model on a quantum simulator
- Sampling diverse near-optimal solutions via algorithmic quantum annealing
- GraphStateVis: Interactive Visual Analysis of Qubit Graph States and their Stabilizer Groups
- Theoretical survey of unconventional quantum annealing methods applied to adifficult trial problem
- Quantum Monte Carlo Annealing with Multi-Spin Dynamics
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- Noise-tolerant quantum speedups in quantum annealing without fine tuning
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- Improving nonstoquastic quantum annealing with spin-reversal transformations
- Polynomial Time Algorithms for Estimating Spectra of Adiabatic Hamiltonians
- Energy barriers between metastable states in first order quantum phase transitions
- Exact expression of the energy gap at first-order quantum phase transitions of a non-stoquastic Hamiltonian
- Entropy Computing, A Paradigm for Optimization in Open Photonic Systems
- Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
- Validating a Two Qubit Non-Stoquastic Hamiltonian in Quantum Annealing
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- Classical Simulated Annealing Using Quantum Analogues
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- Degeneracy Engineering for Classical and Quantum Annealing: A Case Study of Sparse Linear Regression in Collider Physics
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