Quantum computing for classical problems: Variational Quantum Eigensolver for activated processes

• URL: http://arxiv.org/abs/2107.13025v1
• Date: Tue, 27 Jul 2021 18:16:16 GMT
• Title: Quantum computing for classical problems: Variational Quantum Eigensolver for activated processes
• Authors: Pierpaolo Pravatto, Davide Castaldo, Federico Gallina, Barbara Fresch, Stefano Corni, Giorgio J. Moro
• Abstract summary: This paper reports the development and implementation of a Variational Quantum Eigensolver procedure to solve the Fokker-Planck-Smoluchowski eigenvalue problem. We show that such an algorithm, typically adopted to address quantum chemistry problems, can be applied effectively to classical systems paving the way to new applications of quantum computers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The theory of stochastic processes impacts both physical and social sciences. At the molecular scale, stochastic dynamics is ubiquitous because of thermal fluctuations. The Fokker-Plank-Smoluchowski equation models the time evolution of the probability density of selected degrees of freedom in the diffusive regime and it is therefore a workhorse of physical chemistry. In this paper we report the development and implementation of a Variational Quantum Eigensolver procedure to solve the Fokker-Planck-Smoluchowski eigenvalue problem. We show that such an algorithm, typically adopted to address quantum chemistry problems, can be applied effectively to classical systems paving the way to new applications of quantum computers. We compute the conformational transition rate in a linear chain of rotors experiencing nearest-neighbour interaction. We provide a method to encode on the quantum computer the probability distribution for a given conformation of the chain and assess its scalability in terms of operations. Performance analysis on noisy quantum emulators and quantum devices (IBMQ Santiago) is provided for a small chain showing results in good agreement with the classical benchmark without further addition of any error mitigation technique.

Related papers

• Modeling Stochastic Chemical Kinetics on Quantum Computers [0.0]
  We show how quantum algorithms can be employed to model chemical kinetics using the Schl"ogl Model of a trimolecular reaction network. Our quantum computed results from both noisy and noiseless quantum simulations agree within a few percent with the classically computed eigenvalues and zeromode.
  arXiv  Detail & Related papers  (2024-04-12T18:53:38Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning [5.630204194930539]
  We present a novel method that employs parametric Gaussian process regression (GPR) within an active learning framework to mitigate noise in quantum computations. We demonstrate the effectiveness of our method on a 2-site Anderson impurity model and a 8-site Heisenberg model, using the IBM open-source quantum computing framework, Qiskit.
  arXiv  Detail & Related papers  (2021-11-16T22:29:43Z)
• Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers [0.0]
  We show how to tackle the problem using a suitably quantum computer. We propose a hybrid quantum-classical sampling scheme to escape local minima.
  arXiv  Detail & Related papers  (2021-08-25T18:04:52Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
  We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
  arXiv  Detail & Related papers  (2021-03-04T18:21:00Z)
• Quantum simulation of open quantum systems in heavy-ion collisions [0.0]
  We present a framework to simulate the dynamics of hard probes such as heavy quarks or jets in a hot, strongly-coupled quark-gluon plasma (QGP) on a quantum computer. Our work demonstrates the feasibility of simulating open quantum systems on current and near-term quantum devices.
  arXiv  Detail & Related papers  (2020-10-07T18:00:02Z)
• Considerations for evaluating thermodynamic properties with hybrid quantum-classical computing work-flows [0.0]
  Quantum chemistry applications on quantum computers currently rely heavily on the variational quantum eigensolver algorithm. We present a summary of the hybrid quantum-classical work-flow to compute thermodynamic properties. We show that through careful selection of work-flow options, nearly order-of-magnitude increases in accuracy are possible at equivalent computing time.
  arXiv  Detail & Related papers  (2020-03-04T19:32:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.