Computing Canonical Averages with Quantum and Classical Optimizers: Thermodynamic Reweighting for QUBO Models of Physical Systems

• URL: http://arxiv.org/abs/2504.07094v1
• Date: Wed, 09 Apr 2025 17:59:32 GMT
• Title: Computing Canonical Averages with Quantum and Classical Optimizers: Thermodynamic Reweighting for QUBO Models of Physical Systems
• Authors: Francesco Slongo, Cristian Micheletti,
• Abstract summary: We introduce a histogram reweighting scheme applicable to QUBO-based sampling constrained to specific intervals of an order parameter, e.g., physical energy.<n>We demonstrate that the scheme can accurately recover the density of states, which in turn allows for calculating expectation values in the conjugate ensemble.<n>The method can thus be used to advance the state-of-the-art characterization of physical systems that admit a QUBO-based representation and that are otherwise intractable with real-space sampling methods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a general method to compute canonical averages for physical models sampled via quantum or classical quadratic unconstrained binary optimization (QUBO). First, we introduce a histogram reweighting scheme applicable to QUBO-based sampling constrained to specific intervals of an order parameter, e.g., physical energy. Next, we demonstrate that the scheme can accurately recover the density of states, which in turn allows for calculating expectation values in the conjugate ensemble, e.g., at a fixed temperature. The method can thus be used to advance the state-of-the-art characterization of physical systems that admit a QUBO-based representation and that are otherwise intractable with real-space sampling methods. A case in point are space-filling melts of lattice ring polymers, recently mapped in QUBO form, for which our method reveals that the ring catenation probability is non-monotonic with the bending rigidity.

Related papers

• Classical Estimation of the Free Energy and Quantum Gibbs Sampling from the Markov Entropy Decomposition [8.0411799613087]
  We revisit the Markov Entropy Decomposition to approximate the free energy in quantum spin lattices. We prove that this condition is satisfied for systems in 1D at any temperature as well as in the high-temperature regime under certain commutativity. We then use this fact to devise a rounding scheme that maps the solution of the convex relaxation to a global state and show that the scheme can be efficiently implemented on a quantum computer.
  arXiv  Detail & Related papers  (2025-04-24T09:53:53Z)
• Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts [64.34482582690927]
  We provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality.
  arXiv  Detail & Related papers  (2025-03-04T17:46:51Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Equivalence of dynamics of disordered quantum ensembles and semi-infinite lattices [44.99833362998488]
  We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice. This mapping provides a geometric interpretation on the loss of coherence when averaging over the ensemble and allows computation of the exact dynamics of the entire disordered ensemble in a single simulation.
  arXiv  Detail & Related papers  (2024-06-25T18:13:38Z)
• A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrodinger Equation [8.648660469053342]
  A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material.<n>We propose a solution via an ansatz which is cheap to sample from, yet satisfies the requisite quantum mechanical properties.
  arXiv  Detail & Related papers  (2024-05-28T15:42:15Z)
• MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimation [4.014524824655106]
  MESSY estimation is a Maximum-Entropy based Gradient and Symbolic densitY estimation method. We construct a gradient-based drift-diffusion process that connects samples of the unknown distribution function to a guess symbolic expression. We find that the addition of a symbolic search for basis functions improves the accuracy of the estimation at a reasonable additional computational cost.
  arXiv  Detail & Related papers  (2023-06-07T03:28:47Z)
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model [0.8258451067861933]
  We show that the effect of a Bosonic environment linearly coupled to a quantum system can be simulated by a Gaussian Lindblad master equation. For a subset of rational spectral densities, all parameters are explicitly specified without the need of any fitting procedure.
  arXiv  Detail & Related papers  (2023-01-18T14:17:17Z)
• Counting Phases and Faces Using Bayesian Thermodynamic Integration [77.34726150561087]
  We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP.
  arXiv  Detail & Related papers  (2022-05-18T17:11:23Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)
• 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)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Random Phase Product Sate for Canonical Ensemble [0.0]
  The RPPS method is an extension of the method of random phase state for full Hilbert space representation. The validity of the method is confirmed by comparing the average energy of N-site antiferromagnetic spin-1/2 Heisenberg chain model with open boundary conditions.
  arXiv  Detail & Related papers  (2020-06-25T14:53:48Z)

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.