Efficient Learning Implies Quantum Glassiness

• URL: http://arxiv.org/abs/2505.00087v1
• Date: Wed, 30 Apr 2025 18:00:29 GMT
• Title: Efficient Learning Implies Quantum Glassiness
• Authors: Eric R. Anschuetz,
• Abstract summary: We show a surprising relation between quantum learning theory and algorithmic hardness.<n>We show that finding near-ground states of certain sparse disordered quantum systems is average-case hard for "Lipschitz" quantum algorithms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show a surprising relation between quantum learning theory and algorithmic hardness. We demonstrate that finding near-ground states of certain sparse disordered quantum systems is average-case hard for "Lipschitz" quantum algorithms if there exists an efficient, local learning algorithm -- such as the classical shadows algorithm -- for estimating the energy of a state of the system. A corollary of our result is that many standard quantum algorithms fail to find near-ground states of these systems, including short-time Lindbladian dynamics, short-time quantum annealing, phase estimation, and shallow-depth variational quantum algorithms. To achieve this, we introduce a topological property of quantum systems that we call the quantum overlap gap property (QOGP). This property is only satisfied by systems with an efficient local learning algorithm for the energy. We prove that systems which exhibit this topological property in their low-energy space are intractable for quantum algorithms whose outputs are stable under perturbations to their inputs. We then prove that the QOGP is satisfied for a sparsified variant of the quantum $p$-spin model, giving the first known algorithmic hardness-of-approximation result for quantum algorithms in finding the ground state of a non-stoquastic, noncommuting quantum system. Our resulting lower bound for quantum algorithms optimizing this model using Lindbladian evolution matches the best-known time lower bound for classical Langevin dynamics optimizing classical $p$-spin models. For this reason we suspect that finding ground states of typical quantum $p$-spin models using quantum algorithms is, in practice, as intractable as the classical $p$-spin model is for classical algorithms. Inversely, we show that the Sachdev--Ye--Kitaev (SYK) model does not exhibit the QOGP, consistent with previous evidence that the model is rapidly mixing at low temperatures.

Related papers

• Quantum phase classification via quantum hypothesis testing [0.39102514525861415]
  We propose a classification algorithm based on the quantum Neyman-Pearson test, which is theoretically optimal for distinguishing between two quantum states. Our results show that the proposed method achieves lower classification error probabilities and significantly reduces the training cost. These findings highlight the potential of quantum hypothesis testing as a powerful tool for quantum phase classification.
  arXiv  Detail & Related papers  (2025-04-05T08:23:45Z)
• Accelerating Quantum Reinforcement Learning with a Quantum Natural Policy Gradient Based Approach [36.05085942729295]
  This paper introduces a Quantum Natural Policy Gradient (QNPG) algorithm, which replaces the random sampling used in classicalNPG estimators with a deterministic gradient estimation approach.<n>The proposed QNPG algorithm achieves a sample complexity of $tildemathcalO(epsilon-1.5)$ for queries to the quantum oracle, significantly improving the classical lower bound of $tildemathcalO(epsilon-2)$ for queries to the Markov Decision Process (MDP)
  arXiv  Detail & Related papers  (2025-01-27T17:38:30Z)
• Quantum Subroutines in Branch-Price-and-Cut for Vehicle Routing [0.0]
  We demonstrate in this work how quantums with limited resources can be integrated in large-scale exact optimization algorithms for NP-hard problems. A key feature of our algorithm is it not only from the best solution returned by the quantum but from all solutions below a certain cost threshold.
  arXiv  Detail & Related papers  (2024-12-20T08:27:23Z)
• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem. We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. 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)
• An Efficient Classical Algorithm for Simulating Short Time 2D Quantum Dynamics [2.891413712995642]
  We introduce an efficient classical algorithm for simulating short-time dynamics in 2D quantum systems.<n>Our results reveal the inherent simplicity in the complexity of short-time 2D quantum dynamics.<n>This work advances our understanding of the boundary between classical and quantum computation.
  arXiv  Detail & Related papers  (2024-09-06T09:59:12Z)
• Quantum quench dynamics as a shortcut to adiabaticity [31.114245664719455]
  We develop and test a quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. Our experiments show that this approach significantly outperforms the adiabatic algorithm.
  arXiv  Detail & Related papers  (2024-05-31T17:07:43Z)
• Rapidly Achieving Chemical Accuracy with Quantum Computing Enforced Language Model [22.163742052849432]
  QiankunNet-VQE is a transformer based language models enforced with quantum computing to learn and generate quantum states. It has been implemented using up to 12 qubits and attaining an accuracy level competitive with state-of-the-art classical methods.
  arXiv  Detail & Related papers  (2024-05-15T07:50:57Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• 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)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Classical simulation of short-time quantum dynamics [0.0]
  We present classical algorithms for approximating the dynamics of local observables and nonlocal quantities. We establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.
  arXiv  Detail & Related papers  (2022-10-20T18:00:04Z)
• Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization [0.0]
  Variational quantum-classical hybrid algorithms are seen as a promising strategy for solving practical problems on quantum computers in the near term. Here, we introduce the fast-and-slow algorithm, which uses gradients to identify a promising region in Bayesian space. Our results move variational quantum algorithms closer to their envisioned applications in quantum chemistry, optimization, and quantum simulation problems.
  arXiv  Detail & Related papers  (2022-03-04T17:48:57Z)
• 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)

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.