Average-case quantum complexity from glassiness

• URL: http://arxiv.org/abs/2510.08497v1
• Date: Thu, 09 Oct 2025 17:37:33 GMT
• Title: Average-case quantum complexity from glassiness
• Authors: Alexander Zlokapa, Bobak T. Kiani, Eric R. Anschuetz,
• Abstract summary: Glassiness -- a phenomenon in physics characterized by a rough free-energy landscape -- implies hardness for stable classical algorithms.<n>We prove that the standard notion of quantum glassiness based on replica symmetry breaking obstructs stable quantum algorithms for Gibbs sampling.
• Score: 45.57609001239456
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Glassiness -- a phenomenon in physics characterized by a rough free-energy landscape -- implies hardness for stable classical algorithms. For example, it can obstruct constant-time Langevin dynamics and message-passing in random $k$-SAT and max-cut instances. We provide an analogous framework for average-case quantum complexity showing that a natural family of quantum algorithms (e.g., Lindbladian evolution) fails for natural Hamiltonian ensembles (e.g., random 3-local Hamiltonians). Specifically, we prove that the standard notion of quantum glassiness based on replica symmetry breaking obstructs stable quantum algorithms for Gibbs sampling, which we define by a Lipschitz temperature dependence in quantum Wasserstein complexity. Our proof relies on showing that such algorithms fail to capture a structural phase transition in the Gibbs state, where glassiness causes the Gibbs state to decompose into clusters extensively separated in quantum Wasserstein distance. This yields average-case lower bounds for constant-time local Lindbladian evolution and shallow variational circuits. Unlike mixing time lower bounds, our results hold even when dynamics are initialized from the maximally mixed state. We apply these lower bounds to non-commuting, non-stoquastic Hamiltonians by showing a glass transition via the replica trick. We find that the ensemble of all 3-local Pauli strings with independent Gaussian coefficients is average-case hard, while providing analytical evidence that the general $p$-local Pauli ensemble is non-glassy for sufficiently large constant $p$, in contrast to its classical (Ising $p$-spin, always glassy) and fermionic (SYK, never glassy) counterparts.

Related papers

• Polynomial Time Quantum Gibbs Sampling for Fermi-Hubbard Model at any Temperature [9.62464358196899]
  We prove a constant gap of the perturbed Lindbladian corresponding to interacting fermions up to some maximal coupling strength.<n>This is achieved by using theorems about stability of the gap for lattice fermions.<n>As an application, we explain how to calculate partition functions for the considered systems.
  arXiv  Detail & Related papers  (2025-01-02T18:56:02Z)
• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma.<n>This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles.<n>We show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• 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)
• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem.<n>We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions.<n>We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Quantum Non-Identical Mean Estimation: Efficient Algorithms and Fundamental Limits [15.89518426969296]
  We investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples from different bounded or sub-Gaussian random variables. On the other hand, we prove that, in general, it is impossible for any quantum algorithm to achieve quadratic speed-up over the number of classical samples needed.
  arXiv  Detail & Related papers  (2024-05-21T14:42:39Z)
• An efficient and exact noncommutative quantum Gibbs sampler [0.0]
  We construct the first efficiently implementable and exactly detailed-balanced Lindbladian for Gibbs states of arbitrary noncommutative Hamiltonians. Our construction can also be regarded as a continuous-time quantum analog of the Metropolis-Hastings algorithm.
  arXiv  Detail & Related papers  (2023-11-15T18:51:24Z)
• Hilbert Space Fragmentation in Open Quantum Systems [0.7412445894287709]
  We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum systems. We find that it can stabilize highly entangled steady states.
  arXiv  Detail & Related papers  (2023-05-05T18:00:06Z)
• Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture [0.0]
  We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem. These problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We show that guidable local Hamiltonian problems for both classes of guiding states are $mathsfQCMA$-complete in the inverse-polynomial precision setting.
  arXiv  Detail & Related papers  (2023-02-22T19:00:00Z)
• The principle of majorization: application to random quantum circuits [68.8204255655161]
  Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. We verified that all the families of circuits satisfy on average the principle of majorization. Clear differences appear in the fluctuations of the Lorenz curves associated to states.
  arXiv  Detail & Related papers  (2021-02-19T16:07:09Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.