Accelerated spin-adapted ground state preparation with non-variational quantum algorithms

• URL: http://arxiv.org/abs/2506.04663v1
• Date: Thu, 05 Jun 2025 06:16:17 GMT
• Title: Accelerated spin-adapted ground state preparation with non-variational quantum algorithms
• Abstract summary: The spin-adapted ground state is the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-$z$ component.<n>This paper proposes a new procedure based on non-variational quantum algorithms to obtain the spin-adapted ground state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Various methods have been explored to prepare the spin-adapted ground state, the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-$z$ component. In such problem settings, variational and non-variational methods commonly incorporate penalty terms into the original Hamiltonian to enforce the desired constraints. While in variational approaches, only $O(n_{\textrm{spin}}^2)$ measurements are required for the calculation of the penalty terms for the total spin magnitude, non-variational approaches, such as probabilistic imaginary-time evolution or adiabatic time evolution, are expected to be more computationally intensive, requiring $O(n_{\textrm{spin}}^4)$ gates naively. This paper proposes a new procedure based on non-variational quantum algorithms to obtain the spin-adapted ground state. The proposed method consists of two steps: the first step is to prepare a spin-magnitude adapted state and the second step is post-processing for the desired $S_z$. By separating into two steps, the procedure achieves the desired spin-adapted ground state while reducing the number of penalty terms from $O(n_{\textrm{spin}}^4)$ to $O(n_{\textrm{spin}}^2)$. We conducted numerical experiments for spin-1/2 Heisenberg ring models and manganese trimer systems. The results confirmed the effectiveness of our method, demonstrating a significant reduction in gate complexity and validating its practical usefulness.

Related papers

• Kibble-Zurek Dynamics in Two-dimensional Frustrated Systems with a Neural Foundation-state Subspace Method [0.6524460254566904]
  We introduce a Neural Foundation-state Subspace (NFS) method for near-adiabatic dynamics.<n>A foundation neural-network quantum state represents the ground-state manifold along the driving path.<n>We validate the method on the two-dimensional transverse-field Ising model.
  arXiv  Detail & Related papers  (2026-09-03T16:58:54Z)
• Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
  We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
  arXiv  Detail & Related papers  (2026-07-28T09:29:37Z)
• Anisotropic Quantum Annealing vs Trit Annealing [0.0]
  We show that for a suitable range of the anisotropy strength $D$, the spin-$1$ annealer reaches the ground state with higher fidelity.<n>These findings suggest that higher spin annealers offer intrinsic advantages for robust and flexible quantum optimization.
  arXiv  Detail & Related papers  (2025-12-29T13:53:15Z)
• Phase Transitions in Open Dicke Model: a degenerate perturbation theory approach [0.0]
  We study the steady-state behavior of the open Dicke model, which describes the collective interaction of $N$ spin-$1/2$ particles with a lossy, quantized cavity mode.<n>While the standard model conserves total spin, Kirton and Keeling citePhysRevLett.118.123602 demonstrated that even infinitesimal homogeneous local dephasing destroys this phase transition.<n>We analyze this interplay using perturbation theory across subspaces of fixed total spin, $S$.
  arXiv  Detail & Related papers  (2025-05-19T04:33:30Z)
• Beyond Boson Sampling: Higher Spin Sampling as a Practical Path to Quantum Supremacy [0.0]
  We introduce spin sampling for arbitrary spin-$S$ states as a practical path to quantum supremacy.<n>We identify a quasi-linear scaling relation between the number of sites $m$ and the number of spins $n$ as $msim n1+epsilon$.<n>This suggests that, within a spin system, an equivalent Fock-state boson sampling task in the linear mode region is experimentally feasible with reduced resource requirements.
  arXiv  Detail & Related papers  (2025-05-12T07:57:21Z)
• 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)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Efficiently Escaping Saddle Points for Policy Optimization [43.636107996849375]
  Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance.<n>We propose a variance-reduced second-order method that uses second-order information in the form of Hessian vector products (HVP) and converges to an approximate second-order stationary point (SOSP) with sample complexity of $tildeO(epsilon-3)$.
  arXiv  Detail & Related papers  (2023-11-15T12:36:45Z)
• 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)
• Achieving quantum metrological performance and exact Heisenberg limit precision through superposition of $s$-spin coherent states [0.0]
  This study delves into quantum phase estimation using $s$-spin coherent states superposition. We analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit.
  arXiv  Detail & Related papers  (2023-08-18T21:46:26Z)
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls [77.34726150561087]
  The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. We adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem.
  arXiv  Detail & Related papers  (2023-07-17T13:37:18Z)
• A hybrid quantum algorithm to detect conical intersections [39.58317527488534]
  We show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule.
  arXiv  Detail & Related papers  (2023-04-12T18:00:01Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• Beyond one-axis twisting: Simultaneous spin-momentum squeezing [0.0]
  We introduce a novel method to generate entanglement across two distinct degrees of freedom. This leads to three axes undergoing twisting due to the two degrees of freedom and their entanglement, with the resulting potential for a more rich context of quantum entanglement.
  arXiv  Detail & Related papers  (2022-06-24T21:08:24Z)
• Momentum-Based Policy Gradient with Second-Order Information [40.51117836892182]
  We propose a variance-reduced policy-gradient method, called SHARP, which incorporates second-order information into gradient descent. Unlike most previous work, our proposed algorithm does not require importance sampling which can compromise the advantage of variance reduction process. Our extensive experimental evaluations show the effectiveness of the proposed algorithm on various control tasks and its advantage over the state of the art in practice.
  arXiv  Detail & Related papers  (2022-05-17T11:56:50Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Adiabatic ground state preparation in an expanding lattice [0.0]
  We implement and characterize a numerical algorithm inspired by the $s$-source framework [Phys. Rev.B 93, 045127] for building a quantum many-body ground state wavefunction on a lattice of size $2L$. We find that the construction works particularly well when the gap is large and, interestingly, at scale in critical points.
  arXiv  Detail & Related papers  (2020-02-22T01:18:48Z)

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.