Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers
arXiv:2108.11410 · doi:10.1103/PhysRevA.104.022431
Abstract
The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of thermally activated rare-event processes between long-lived metastable states, such as protein folding, is still elusive. In this case, one needs both the finite-temperature canonical distribution function and the reaction current between the reactant and product states, to completely characterize the dynamic. Here we show how to tackle this problem using a quantum computer. We use the connection between a classical stochastic dynamics and the Schroedinger equation, also known as stochastic quantization, to variationally prepare quantum states allowing us to unbiasedly sample from a Boltzmann distribution. Similarly, reaction rate constants can be computed as ground state energies of suitably transformed operators, following the supersymmetric extension of the formalism. Finally, we propose a hybrid quantum-classical sampling scheme to escape local minima, and explore the configuration space in both real-space and spin hamiltonians. We indicate how to realize the quantum algorithms constructively, without assuming the existence of oracles, or quantum walk operators. The quantum advantage concerning the above applications is discussed.
arXiv commentOriginal submission date to the journal 12 April 2021
References in corpus (40)
- Escaping free-energy minima
- A variational eigenvalue solver on a quantum processor
- Quantum Algorithms Revisited
- Parallel Tempering: Theory, Applications, and New Perspectives
- Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations
- A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
- Towards Practical Quantum Variational Algorithms
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Variational ansatz-based quantum simulation of imaginary time evolution
- Quantum measurements and the Abelian Stabilizer Problem
- Quantum Natural Gradient
- Semiclassical Fourier Transform for Quantum Computation
- Polynomial-time quantum algorithm for the simulation of chemical dynamics
- Efficient Simulation of Quantum Systems by Quantum Computers
- Quantum speedup of Monte Carlo methods
- Variational quantum algorithms for nonlinear problems
- Quantum Metropolis Sampling
- Quantum Risk Analysis
- Creating superpositions that correspond to efficiently integrable probability distributions
- Quantum Simulations of Classical Annealing Processes
- Evidence for supercritical behavior of high-pressure liquid hydrogen
- Dominant Pathways in Protein Folding
- A Quantum-Quantum Metropolis Algorithm
- Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation
- Simulations of Many-Body Quantum Systems by a Quantum Computer
- Electron-Phonon Systems on a Universal Quantum Computer
- Speed-up via Quantum Sampling
- A Threshold for Quantum Advantage in Derivative Pricing
- Quantum simulation of the single-particle Schrodinger equation
- Non-adiabatic molecular quantum dynamics with quantum computers
- Quantum speedup of classical mixing processes
- Precise measurement of quantum observables with neural-network estimators
- Efficient Quantum Walk Circuits for Metropolis-Hastings Algorithm
- Efficient State Preparation for Quantum Amplitude Estimation
- Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing
- Quantum Sampling Algorithms for Near-Term Devices
- Quantum algorithms for classical lattice models
- Metastable states, transitions, basins and borders at finite temperatures
- Dominant Reaction Pathways by Quantum Computing
- Fluctuations in the Ensemble of Reaction Pathways
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- Accelerating equilibrium spin-glass simulations using quantum annealers via generative deep learning
- Quantum computing for genomics: conceptual challenges and practical perspectives
- From quantum-enhanced to quantum-inspired Monte Carlo
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- Computing Canonical Averages with Quantum and Classical Optimizers: Thermodynamic Reweighting for QUBO Models of Physical Systems
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