Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization

• URL: http://arxiv.org/abs/2604.01555v1
• Date: Thu, 02 Apr 2026 03:00:01 GMT
• Title: Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization
• Abstract summary: A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems.<n>In this article, we demonstrate that leveraging the inherent structures of the system can significantly mitigate these scalability challenges.
• Score: 3.4234084547821477
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over the possible states expressible by this ansatz, one can alternatively formulate the problem as a noncommutative polynomial optimization problem. This optimization problem can then be addressed using a hierarchy of semidefinite programming relaxations. In contrast to variational calculations, the semidefinite program can provide lower bounds for ground state energies and upper and lower bounds on observable expectation values. However, this approach typically suffers from severe scalability issues, limiting its applicability to small-to-medium-scale systems. In this article, we demonstrate that leveraging the inherent structures of the system can significantly mitigate these scalability challenges and thus allows us to compute meaningful bounds for quantum spin systems on up to $16\times16$ square lattices.

Related papers

• A Quantum Spectral Framework for Solving PDEs [0.0]
  Partial differential equations (PDEs) are fundamental across numerous scientific fields.<n>Attempts to solve this problem typically rely on either classical sparsity and low-rank decompositions.<n>Quantum Computing offers a promising alternative, as it allows us to operate in significantly larger spaces.
  arXiv  Detail & Related papers  (2026-04-28T16:33:59Z)
• SpinGQE: A Generative Quantum Eigensolver for Spin Hamiltonians [42.007194397302825]
  Ground state search is central to quantum computing.<n>We present SpinGQE, an extension of the Generative Quantum Eigensolver framework to spin Hamiltonians.<n>We employ a transformer-based decoder to learn over quantum circuits that produce low-energy states.
  arXiv  Detail & Related papers  (2026-03-25T13:38:15Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Non-commutative optimization problems with differential constraints [0.0]
  Non-commutative optimization (NPO) problems seek to minimize the state average of a quench of some operator variables.<n>We consider a variant of NPO problems where a subset of the operator variables satisfies a system of ordinary differential equations.<n>We find that, under mild conditions of operator boundedness, for every such problem one can construct a standard NPO problem with the same solution.
  arXiv  Detail & Related papers  (2024-08-05T15:46:57Z)
• Warm-Start Variational Quantum Policy Iteration [39.04157716488156]
  Reinforcement learning is a powerful framework aiming to determine optimal behavior in highly complex decision-making scenarios. We propose the variational quantum policy iteration (VarQPI) algorithm, realizing this step with a NISQ-compatible quantum-enhanced subroutine. Its scalability is supported by an analysis of the structure of generic reinforcement learning environments.
  arXiv  Detail & Related papers  (2024-04-16T13:16:19Z)
• Optimal compression of constrained quantum time evolution [0.0]
  Time evolution of quantum many-body systems is one of the most promising applications for near-term quantum computers. In this work, we demonstrate a simplification of the variational optimization of circuits implementing the time evolution operator of local Hamiltonians. Our results show that the encoding of constraints allows a reduction of optimization cost by more than one order of magnitude and scalability to arbitrary large system sizes.
  arXiv  Detail & Related papers  (2023-11-10T19:00:02Z)
• Circumventing superexponential runtimes for hard instances of quantum adiabatic optimization [0.0]
  We present a general construction of instances of the problem for which the minimum gap decays superexponentially with system size. The small gap arises from locally independent choices, which cause the system to initially evolve and localize into a configuration far from the solution. We show that quantum quenches in these models can exhibit signatures of quantum many-body scars, which in turn, can circumvent the superexponential gaps.
  arXiv  Detail & Related papers  (2023-06-22T18:00:02Z)
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states [0.0]
  We consider energy problems for quantum many-body systems with extensive Hamiltonians and finite-range interactions.<n>We prove that variational optimization problems for matrix product states, tree tensor networks, and the multiscale entanglement renormalization ansatz are free of barren plateaus.
  arXiv  Detail & Related papers  (2023-03-31T22:49:49Z)
• Multiobjective variational quantum optimization for constrained problems: an application to Cash Management [45.82374977939355]
  We introduce a new method for solving optimization problems with challenging constraints using variational quantum algorithms. We test our proposal on a real-world problem with great relevance in finance: the Cash Management problem. Our empirical results show a significant improvement in terms of the cost of the achieved solutions, but especially in the avoidance of local minima.
  arXiv  Detail & Related papers  (2023-02-08T17:09:20Z)
• Analyzing Prospects for Quantum Advantage in Topological Data Analysis [35.423446067065576]
  We analyze and optimize an improved quantum algorithm for topological data analysis. We show that super-quadratic quantum speedups are only possible when targeting a multiplicative error approximation. We argue that quantum circuits with tens of billions of Toffoli can solve seemingly classically intractable instances.
  arXiv  Detail & Related papers  (2022-09-27T17:56:15Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation [101.22379613810881]
  We consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive process. We propose a tractable approximation that allows us to scale our method to high-capacity neural network models.
  arXiv  Detail & Related papers  (2021-02-16T06:04:27Z)

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.