Energy gap of quantum spin glasses: a projection quantum Monte Carlo study

• URL: http://arxiv.org/abs/2602.20108v1
• Date: Mon, 23 Feb 2026 18:26:59 GMT
• Title: Energy gap of quantum spin glasses: a projection quantum Monte Carlo study
• Authors: L. Brodoloni, G. E. Astrakharchik, S. Giorgini, S. Pilati,
• Abstract summary: We investigate the scaling of $$ with system size $N$ for two paradigmatic quantum spin-glass models.<n>We find that the inverse-gap distribution develops a fat tail with infinite variance as $N$ increases.<n>This finding provides a promising outlook for the potential efficiency of quantum annealers for optimization problems with dense connectivity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The performance of quantum annealing for combinatorial optimization is fundamentally limited by the minimum energy gap $Δ$ encountered at quantum phase transitions. We investigate the scaling of $Δ$ with system size $N$ for two paradigmatic quantum spin-glass models: the two-dimensional Edwards-Anderson (2D-EA) and the all-to-all Sherrington-Kirkpatrick (SK) models. Utilizing a newly proposed unbiased energy-gap estimator for continuous-time projection quantum Monte Carlo simulations, complemented by high-performance sparse eigenvalue solvers, we characterize the gap distributions across disorder realizations. It is found that, in the 2D-EA case, the inverse-gap distribution develops a fat tail with infinite variance as $N$ increases. This indicates that the unfavorable super-algebraic scaling of $Δ$, recently reported for binary couplings [Nature 631, 749 (2024)], persists for the Gaussian disorder considered here, pointing to a universal feature of 2D spin glasses. Conversely, the SK model retains a finite-variance distribution, with the disorder-averaged gap following a rather slow power law, close to $Δ\propto N^{-1/3}$. This finding provides a promising outlook for the potential efficiency of quantum annealers for optimization problems with dense connectivity.

Related papers

• Unsupervised Discovery of Intermediate Phase Order in the Frustrated $J_1$-$J_2$ Heisenberg Model via Prometheus Framework [0.0]
  We apply the Prometheus variational autoencoder framework to explore the $J_1$-$J$ phase diagram.<n>We identify the structure factor $S(,)$ and $S(,)$ as the dominant order parameters.<n>This work establishes a scalable pathway for applying machine learning to frustrated quantum systems.
  arXiv  Detail & Related papers  (2026-02-25T00:44:51Z)
• FFT-Accelerated Auxiliary Variable MCMC for Fermionic Lattice Models: A Determinant-Free Approach with $O(N\log N)$ Complexity [52.3171766248012]
  We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems.<n>We validate our algorithm on benchmark quantum physics problems, accurately reproducing known theoretical results.<n>Our work provides a powerful tool for large-scale probabilistic inference and opens avenues for physics-inspired generative models.
  arXiv  Detail & Related papers  (2025-10-13T07:57:21Z)
• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model [0.26107298043931204]
  We study the nontrivial renormalization-group scenario of fixed-point annihilation in spin-boson models. We find a tunable transition between two localized phases that can be continuous or strongly first-order. We also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent.
  arXiv  Detail & Related papers  (2024-03-04T19:00:07Z)
• Skew-Gaussian model of small-photon-number coherent Ising machines [0.0]
  A Gaussian quantum theory of bosonic modes has been widely used to describe quantum optical systems. We develop an extended Gaussian model including two third-order fluctuation products. This new model more precisely replicates the success probability predicted by the quantum master equation (QME)
  arXiv  Detail & Related papers  (2024-03-01T00:08:48Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Resummation-based Quantum Monte Carlo for Entanglement Entropy Computation [0.40964539027092917]
  We develop a new algorithm, dubbed ResumEE, to compute the entanglement entropy. Our ResumEE algorithm is efficient for precisely evaluating the entanglement entropy of SU($N$) spin models with continuous $N$.
  arXiv  Detail & Related papers  (2023-10-02T18:00:02Z)
• 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)
• SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality [0.582519087605215]
  We present high-accuracy quantum Monte Carlo results for the SU(2)-symmetric $S=1/2$ spin-boson (or Bose-Kondo) model. Using a detailed scaling analysis, we provide direct numerical evidence for the collision and annihilation of two RG fixed points at $sast = 0.6540(2)$.
  arXiv  Detail & Related papers  (2022-03-04T19:00:19Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.