Fault tolerant computation of the static structure factor and finite size effects

• URL: http://arxiv.org/abs/2606.27734v1
• Date: Fri, 26 Jun 2026 05:31:08 GMT
• Title: Fault tolerant computation of the static structure factor and finite size effects
• Abstract summary: We develop a quantum post-processing strategy for the leading two-body finite-size correction.<n>After one-body shell effects are reduced by twist averaging, the dominant residual error is controlled by long-wavelength density fluctuations.<n>We also introduce adaptive global and local binary search procedures for identifying the infrared fitting window used to reconstruct the two-body finite size error correction.
• Score: 43.936586633107396
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Fault-tolerant quantum algorithms offer a promising pathway for estimating the ground-state energies of periodic materials that are beyond the practical reach of classical electronic-structure methods. A remaining challenge is finite-size mitigation: quantum algorithms evaluate a finite supercell or finite Brillouin-zone mesh, while materials properties are defined in the thermodynamic limit. In this work we develop a quantum post-processing strategy for the leading two-body finite-size correction. After one-body shell effects are reduced by twist averaging, the dominant residual error is controlled by long-wavelength density fluctuations, which are encoded in the small-momentum static structure factor $S(q)$. We formulate the corresponding operator in a Bloch-orbital basis, construct its block encoding through the density operator, and estimate its ground-state expectation value using an amplified Hadamard test. We also introduce adaptive global and local binary search procedures for identifying the infrared fitting window used to reconstruct the two-body finite size error correction. The resulting cost remains subleading relative to the main ground-state energy estimation routine: the structure-factor correction has leading $\tilde{O}(N_bN_k)^3$ dependence on the Bloch-orbital basis size, avoids the large plane-wave prefactor of full Hamiltonian simulation, and requires only $\tilde{O}(N_bN_k)$ logical qubits. This provides a fault-tolerant alternative to down-sampling, replacing repeated energy calculations on larger cells with targeted measurements of the infrared density correlations that control the finite-size effects.

Related papers

• Logarithmic-scale variational quantum eigensolver for off-lattice protein structure prediction in continuous torsional angle space [0.0]
  We propose a logarithmic-scale variational quantum eigensolver (VQE) that reduces qubit requirements for N torsional degrees of freedom to O(log2N)<n>This introduces the first all-atom, continuous-space quantum algorithm for protein structure prediction (QPSP)<n>It proves high-resolution prediction is feasible with exponentially fewer qubits.
  arXiv  Detail & Related papers  (2026-09-02T05:05:46Z)
• Scalable Lindblad Noise Learning via Stochastic Tensor-Network Simulation [48.887627688666974]
  Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies.<n>Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a simulation method, the Jump Method (TJM)<n>We demonstrate the approach on two noise models in the Ising model, in which independent dissipation rates are learned for each site up to $N_mathrmsite=16$.<n>This combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices.
  arXiv  Detail & Related papers  (2026-08-25T15:07:11Z)
• Quantum Decision Theory for Displacement Detection with Finite-Energy GKP States [46.2474896050764]
  We develop a framework for detecting phase-space displacements with finite-energy, $d$-level Gottesman-Kitaev-Preskill (GKP) probes.<n>For single-mode and entanglement-assisted architectures, we derive the Bayesian minimum-error probability.<n>We benchmark the resulting protocols against coherent-state, direction-matched squeezed-vacuum, and twin-beam schemes.
  arXiv  Detail & Related papers  (2026-08-08T10:32:05Z)
• Spectral amplification for ground-state energy estimation of electronic structure in first quantization [0.38107692506263574]
  We demonstrate a gate complexity improvement in first-quantized ground-state energy estimation of electronic structure Hamiltonians in a plane wave basis.<n>The improvement relies on identifying a sum-of-squares representation of the Hamiltonian which provides a lower bound certificate and low cost block encoding that leads to a provably lower quantum phase estimation gate cost.<n>The reduction in block encoding normalization and similar block encoding costs to prior work is demonstrated to reduce resource estimates for materials and chemical systems by a factor of $2 - 44times$ corresponding to the lowest cost estimates for ab initio materials simulation.
  arXiv  Detail & Related papers  (2026-07-16T18:01:29Z)
• A Physics-Informed Neural Network with a Modified Lorentzian Activation for Nonlocal Gradient-Flow Equations in Dynamic Density Functional Theory [0.8602553195689513]
  We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations.<n>These equations involve nonlinearities, nonlocal interaction terms, and an underlying gradient-flow structure.<n>We adapt the PINN methodology to DDFT gradient-flow equations and introduce two computational components.
  arXiv  Detail & Related papers  (2026-06-24T22:01:13Z)
• Deforming the Trail: Baseline Quantum Circuitry for $\text{SU(2)}_k$ Lattice Gauge Theory [0.0]
  We provide a strategy of gauge-variant completions to extend unitarity to the entire computational Hilbert space.<n>We show that the physical Hilbert space dimension of the deformed plaquette operator scales equivalently to its non-deformed counterpart with a constant factor.<n>Q-deformation continues to pass scrutiny as a reliable truncation offering advantages in quantum circuit synthesis.
  arXiv  Detail & Related papers  (2026-05-14T17:01:35Z)
• Fault-tolerant simulation of the electronic structure using Projector Augmented-Waves and Bloch orbitals [43.936586633107396]
  We present the Bloch--UPAW framework that combines Bloch-orbital $k$-space structure with unitary projector-augmented-wave augmentation.<n>We derive a linear-combination-of-unitaries decomposition and a block-encoding circuit suitable for qubitization.<n>Asymptotically, the Toffoli cost scales as $mathcalO(N_k3)$ when refining the $k$-mesh and as $mathcalO(N_a3.5)$ when enlarging the supercell.
  arXiv  Detail & Related papers  (2026-04-13T23:46:58Z)
• Analysis of Hessian Scaling for Local and Global Costs in Variational Quantum Algorithm [0.42970700836450487]
  We quantify the entrywise resolvability of the Hessian for Variational Quantum Algorithms.<n>We show two distinct scaling regimes that govern the sample complexity required to resolve Hessian entries against shot noise.
  arXiv  Detail & Related papers  (2026-01-31T15:49:23Z)
• When Less is More: Approximating the Quantum Geometric Tensor with Block Structures [43.39839287869652]
  We introduce a block-diagonal quantum geometric tensor that partitions the metric by network layers, analogous to block-structured Fisher methods such as K-FAC.<n> Experiments on Heisenberg and frustrated $J_1$-$J$ models show faster convergence, lower energy, and improved stability.
  arXiv  Detail & Related papers  (2025-10-09T16:44:30Z)
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories [40.772310187078475]
  We propose a novel variational ansatz for the ground-state preparation of the $mathbbZ$ lattice gauge theory (LGT) in quantum simulators. It combines dissipative and unitary operations in a completely deterministic scheme with a circuit depth that does not scale with the size of the considered lattice. We find that, with very few variational parameters, the ansatz can achieve $>!99%$ precision in energy in both the confined and deconfined phase of the $mathbbZ$ LGT.
  arXiv  Detail & Related papers  (2023-08-07T14:23:00Z)
• Quantum simulation of dissipation for Maxwell equations in dispersive media [0.0]
  dissipation appears in the Schr"odinger representation of classical Maxwell equations as a sparse diagonal operator occupying an $r$-dimensional subspace. The unitary operators can be implemented through qubit lattice algorithm (QLA) on $n$ qubits. The non-unitary-dissipative part poses a challenge on how it should be implemented on a quantum computer.
  arXiv  Detail & Related papers  (2023-07-31T18:22:40Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• Targeted free energy estimation via learned mappings [66.20146549150475]
  Free energy perturbation (FEP) was proposed by Zwanzig more than six decades ago as a method to estimate free energy differences. FEP suffers from a severe limitation: the requirement of sufficient overlap between distributions. One strategy to mitigate this problem, called Targeted Free Energy Perturbation, uses a high-dimensional mapping in configuration space to increase overlap.
  arXiv  Detail & Related papers  (2020-02-12T11:10:00Z)

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.