VQE as Initial State Preparation for QPE on Heisenberg Spin-Glass Hamiltonians

• URL: http://arxiv.org/abs/2606.15061v1
• Date: Sat, 13 Jun 2026 02:35:48 GMT
• Title: VQE as Initial State Preparation for QPE on Heisenberg Spin-Glass Hamiltonians
• Abstract summary: Ground state energy calculation of physical systems is perhaps the most promising use case for quantum computing.<n>We study whether the NISQ-era algorithm VQE could be used to efficiently prepare high-overlap states of disordered fully-connected anisotropic Heisenberg spin glass quantum Hamiltonians.
• Score: 3.953304476953445
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum Phase Estimation (QPE) is the quantum algorithmic workhorse for computing ground state energies of quantum Hamiltonians with quantum computers. Ground state energy calculation of physical systems is perhaps the most promising use case for quantum computing in terms of scientific and commercial value with a plausible path to outperformance of classical alternatives. This path, however, hinges on the availability of initial states for QPE with significant overlap with the true ground state. Using extensive (classical) numerical computations, we study whether the NISQ-era algorithm VQE (Variational Quantum Eigensolver) could be used to efficiently prepare high-overlap states of disordered fully-connected anisotropic Heisenberg spin glass quantum Hamiltonians with up to $15$ qubits. We find that (i) -- consistent with widely held, but rarely numerically illustrated beliefs -- VQE is generally unable to efficiently converge to the ground state for our Hamiltonians, which is a well-known issue with VQE due to a variety of factors including vanishing gradients and local minima; (ii) low energy states do not necessarily have large ground-state overlap, but there is typically a correlation between the two measures; (iii) adding more than three layers to the VQE ansatz neither improves overlap nor the energies found; and (iv) the best-found overlap scaling as a function of the Hamiltonian system size is not strongly exponentially decreasing, suggesting potential for VQE to be a heuristic state preparation algorithm for QPE.

Related papers

• Hybrid Quantum Algorithms for Computational Chemistry: Application to the Pyridine-Li ion Complex [0.0]
  Three quantum algorithms are investigated for capturing electron correlation in large-scale molecular systems.<n>Results show how new generations of hybrid quantum-classical frameworks overcome the scalability and noise sensitivity that constrain conventional VQE approaches.<n>Both SQD and HI-VQE exhibit robustness against hardware noise, a critical improvement over earlier approaches.
  arXiv  Detail & Related papers  (2026-01-15T02:23:09Z)
• Quantum Simulation and Energy Estimation for Discretized Anharmonic oscillator [1.0079626733116613]
  A quantum circuit with a filter-based design and Toffoli gates is constructed to track quantum state evolution.<n>For energy estimation, the Variational Quantum Eigensolver (VQE) with a TwoLocal ansatz and variational Quantum Deflation (VQD) are used.
  arXiv  Detail & Related papers  (2025-09-25T08:49:09Z)
• Extending Quantum Perceptrons: Rydberg Devices, Multi-Class Classification, and Error Tolerance [67.77677387243135]
  Quantum Neuromorphic Computing (QNC) merges quantum computation with neural computation to create scalable, noise-resilient algorithms for quantum machine learning (QML) At the core of QNC is the quantum perceptron (QP), which leverages the analog dynamics of interacting qubits to enable universal quantum computation.
  arXiv  Detail & Related papers  (2024-11-13T23:56:20Z)
• Non-unitary Coupled Cluster Enabled by Mid-circuit Measurements on Quantum Computers [37.69303106863453]
  We propose a state preparation method based on coupled cluster (CC) theory, which is a pillar of quantum chemistry on classical computers. Our approach leads to a reduction of the classical computation overhead, and the number of CNOT and T gates by 28% and 57% on average.
  arXiv  Detail & Related papers  (2024-06-17T14:10:10Z)
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation [39.20075231137991]
  We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems.<n> scaling these methods to larger system sizes reveals three key challenges: the smoothness of the CDF for large supports, the lack of tight lower bounds on the overlap with the true ground state, and the difficulty of preparing high-quality initial states.
  arXiv  Detail & Related papers  (2024-05-06T18:00:03Z)
• On the feasibility of performing quantum chemistry calculations on quantum computers [0.0]
  We propose two criteria for evaluating two leading quantum approaches for finding the ground state of molecules. The first criterion applies to the variational quantum eigensolver (VQE) algorithm. The second criterion applies to the quantum phase estimation (QPE) algorithm.
  arXiv  Detail & Related papers  (2023-06-05T06:41:22Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Quantum Davidson Algorithm for Excited States [42.666709382892265]
  We introduce the quantum Krylov subspace (QKS) method to address both ground and excited states. By using the residues of eigenstates to expand the Krylov subspace, we formulate a compact subspace that aligns closely with the exact solutions. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems.
  arXiv  Detail & Related papers  (2022-04-22T15:03:03Z)
• Improved variational quantum eigensolver via quasi-dynamical evolution [0.0]
  The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. There are problems with VQE that forbid a favourable scaling towards quantum advantage. We propose and extensively test a quantum annealing inspired algorithm that supplements VQE. The improved VQE avoids barren plateaus, exits local minima, and works with low-depth circuits.
  arXiv  Detail & Related papers  (2022-02-21T11:21:44Z)
• On exploring the potential of quantum auto-encoder for learning quantum systems [60.909817434753315]
  We devise three effective QAE-based learning protocols to address three classically computational hard learning problems. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
  arXiv  Detail & Related papers  (2021-06-29T14:01:40Z)
• Classically-Boosted Variational Quantum Eigensolver [0.0]
  Near-term quantum computers can represent classically-intractable quantum states. The sensitivity to sampling error and device noise approaches zero in the limit where the classically tractable states are able to describe an eigenstate.
  arXiv  Detail & Related papers  (2021-06-09T00:56:50Z)
• Quantum circuit architecture search for variational quantum algorithms [88.71725630554758]
  We propose a resource and runtime efficient scheme termed quantum architecture search (QAS) QAS automatically seeks a near-optimal ansatz to balance benefits and side-effects brought by adding more noisy quantum gates. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks.
  arXiv  Detail & Related papers  (2020-10-20T12:06:27Z)

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.