Mixed State Variational Quantum Eigensolver for the Estimation of Expectation Values at Finite Temperature

• URL: http://arxiv.org/abs/2401.17194v1
• Date: Tue, 30 Jan 2024 17:29:58 GMT
• Title: Mixed State Variational Quantum Eigensolver for the Estimation of Expectation Values at Finite Temperature
• Authors: Giuseppe Clemente
• Abstract summary: We introduce a novel hybrid quantum-classical algorithm for the near-term computation of expectation values in quantum systems at finite temperatures. This is based on two stages: on the first one, a mixed state approximating a fiducial truncated density matrix is prepared through Variational Quantum Eigensolving (VQE) techniques. This is then followed by a reweighting stage where the expectation values for observables of interest are computed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a novel hybrid quantum-classical algorithm for the near-term computation of expectation values in quantum systems at finite temperatures. This is based on two stages: on the first one, a mixed state approximating a fiducial truncated density matrix is prepared through Variational Quantum Eigensolving (VQE) techniques; this is then followed by a reweighting stage where the expectation values for observables of interest are computed. These two stages can then be iterated again with different hyperparameters to achieve arbitrary accuracy. Resource and time scalability of the algorithm is discussed with a near-term perspective.

Related papers

• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Calculating the expected value function of a two-stage stochastic optimization program with a quantum algorithm [0.0]
  Two-stage programming is a problem formulation for decision-making under uncertainty. This work uses a quantum algorithm to estimate the expected value function with a speedup.
  arXiv  Detail & Related papers  (2024-02-23T00:07:34Z)
• Algorithmic Cluster Expansions for Quantum Problems [0.0]
  We establish a general framework for developing approximation algorithms for a class of counting problems. We apply our framework to approximating probability amplitudes of a class of quantum circuits close to the identity. We show that our algorithmic condition is almost optimal for expectation values and optimal for thermal expectation values in the sense of zero freeness.
  arXiv  Detail & Related papers  (2023-06-15T09:11:48Z)
• Quantum Thermal State Preparation [39.91303506884272]
  We introduce simple continuous-time quantum Gibbs samplers for simulating quantum master equations. We construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states. Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time.
  arXiv  Detail & Related papers  (2023-03-31T17:29:56Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Phenomenological Theory of Variational Quantum Ground-State Preparation [0.0]
  The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a Hamiltonian exploiting parametrized quantum circuits. We show that the algorithm's success crucially depends on other parameters such as the learning rate. We propose a symmetry-enhanced simulation protocol that should be used if the gap closes.
  arXiv  Detail & Related papers  (2022-05-12T18:00:04Z)
• Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation [50.591267188664666]
  Quantum chemistry and materials is one of the most promising applications of quantum computing. Much work is still to be done in matching industry-relevant problems in these areas with quantum algorithms that can solve them.
  arXiv  Detail & Related papers  (2022-03-14T16:51:36Z)
• Dual-Frequency Quantum Phase Estimation Mitigates the Spectral Leakage of Quantum Algorithms [76.15799379604898]
  Quantum phase estimation suffers from spectral leakage when the reciprocal of the record length is not an integer multiple of the unknown phase. We propose a dual-frequency estimator, which approaches the Cramer-Rao bound, when multiple samples are available.
  arXiv  Detail & Related papers  (2022-01-23T17:20:34Z)
• Mitigating algorithmic errors in quantum optimization through energy extrapolation [4.426846282723645]
  We present a scalable extrapolation approach to mitigating a non-negligible error in estimates of the ground state energy. We have verified the validity of these approaches through both numerical simulation and experiments on an IBM quantum computer.
  arXiv  Detail & Related papers  (2021-09-16T17:39:11Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Variational Quantum Algorithms for Trace Distance and Fidelity Estimation [7.247285982078057]
  We introduce hybrid quantum-classical algorithms for two distance measures on near-term quantum devices. First, we introduce the Variational Trace Distance Estimation (VTDE) algorithm. Second, we introduce the Variational Fidelity Estimation (VFE) algorithm.
  arXiv  Detail & Related papers  (2020-12-10T15:56:58Z)

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.