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arXiv:2410.03958

Simulating Neutron Scattering on an Analog Quantum Processor

Nora M. Bauer, Victor Ale, Pontus Laurell, Serena Huang, S. Watabe, D. M. Tennant, George Siopsis

Published Oct 4, 2024• 0 citations
arXivHTMLPDF

Abstract

Neutron scattering characterization of materials allows for the study of entanglement and microscopic structure, but is inefficient to simulate classically for comparison to theoretical models and predictions. However, quantum processors, notably analog quantum simulators, have the potential to offer an unprecedented, efficient method of Hamiltonian simulation by evolving a state in real time to compute phase transitions, dynamical properties, and entanglement witnesses. Here, we present a method for simulating neutron scattering on QuEra's Aquila processor by measuring the dynamic structure factor (DSF) for the prototypical example of the critical transverse field Ising chain, and propose a method for error mitigation. We provide numerical simulations and experimental results for the performance of the procedure on the hardware, up to a chain of length $L=25$. Additionally, the DSF result is used to compute the quantum Fisher information (QFI) density, where we confirm bipartite entanglement in the system experimentally.

DOI
10.48550/arxiv.2410.03958

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Neutron scattering characterization of materials allows for the study of entanglement and microscopic structure, but is inefficient to simulate classically for comparison to theoretical models and predictions. However, quantum processors, notably analog quantum simulators, have the potential to offer an unprecedented, efficient method of Hamiltonian simulation by evolving a state in real time to compute phase transitions, dynamical properties, and entanglement witnesses. Here, we present a method for simulating neutron scattering on QuEra's Aquila processor by measuring the dynamic structure factor (DSF) for the prototypical example of the critical transverse field Ising chain, and propose a method for error mitigation. We provide numerical simulations and experimental results for the performance of the procedure on the hardware, up to a chain of length L=25L=25L=25. Additionally, the DSF result is used to compute the quantum Fisher information (QFI) density, where we confirm bipartite entanglement in the system experimentally.
Neutron-scattering characterization of materials allows for the study of entanglement and microscopic structure but is inefficient to simulate classically for comparison to theoretical models and predictions. However, quantum processors, notably analog quantum simulators, have the potential to offer an unprecedented, efficient method of Hamiltonian simulation by evolving a state in real time to compute phase transitions, dynamical properties, and entanglement witnesses. To elucidate the response of materials to neutron scattering, we present a method for simulating the spin dynamics in the transverse field Ising chain on QuEra's Aquila processor by calculating the dynamic structure factor (DSF) and propose a method for error mitigation. We provide numerical simulations and experimental results for the performance of the procedure on the hardware, up to a chain of length L=25L=25L=25. Additionally, the DSF result is used to compute the quantum Fisher information (QFI) density, where we confirm bipartite entanglement in the system experimentally.
Realistic simulation of quantum materials is a central goal of quantum computation. Although quantum processors have advanced rapidly in scale and fidelity, it has remained unclear whether pre-fault-tolerant devices can perform quantitatively reliable material simulations. We demonstrate that a superconducting quantum processor operating on up to 50 qubits can already produce meaningful, quantitative comparisons with inelastic neutron-scattering measurements of KCuF3_33​, a canonical realization of a gapless Luttinger liquid system with a strongly correlated ground state and a spectrum of emergent spinons. The quantum simulation is enabled by a quantum-classical workflow for computing dynamical structure factors (DSFs). The resulting spectra are benchmarked against experimental measurements using multiple metrics, highlighting the impact of circuit depth and circuit fidelity on simulation accuracy. Finally, we extend our simulations to a 1D XXZ Heisenberg model with next-nearest-neighbor (NNN) interactions and a strong anisotropy, producing a gapped excitation spectrum, which could be used to describe the CsCoX3_33​ compounds above the Néel temperature. Our results establish a framework for computing DSFs for quantum materials in classically challenging regimes of strong entanglement and long-range interactions, enabling quantum simulations that are directly testable against laboratory measurements.
The dynamical structure factor is a central observable in condensed-matter physics, providing direct insight into the excitation spectrum and dynamical response of quantum materials. While it is traditionally accessed in real materials through inelastic neutron scattering, recent works have shown that analogous information can be extracted in quantum simulators using suitable dynamical protocols. So far, these approaches have been demonstrated mainly in paradigmatic integrable one-dimensional models. In this work, we use numerical emulations of a neutral-atom quantum processing unit to assess the feasibility of measuring the dynamical structure factor in a broader class of Ising-like spin systems. Beyond the standard one-dimensional transverse-field Ising chain, we benchmark the protocol in chains with dimerized interactions and in the two-dimensional transverse-field Ising model, where spectral properties are difficult to access with classical numerical methods at large scales. We further analyze the robustness of the protocol under realistic experimental conditions, including finite simulation times, pulse modulation, positional disorder, and laser noise. Our results show that neutral-atom quantum simulators can provide a practical route to probing dynamical response functions in regimes where classical simulations become increasingly demanding, paving the way toward experimental implementation.
Multipartite entanglement in the 1-D spin-12\frac{1}{2}21​ Heisenberg Antiferromagnet
Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the Quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as T→0T\rightarrow 0T→0. We argue that this implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale that is determined by universal properties, up to a non-universal amplitude. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. The 1D spin-12\frac{1}{2}21​ antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges non-trivially as ∼log⁡(1/T)3/2\sim \log(1/T)^{3/2}∼log(1/T)3/2. We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in KCuF3_33​, a material well-described by the Heisenberg chain.
Dynamical structure factors (DSF) measured with neutron-scattering experiments provide key insights into the structure of materials. Their computation requires both the preparation of an equilibrium state and the implementation of Hamiltonian dynamics. We demonstrate the feasibility of computing DSF on the Quantinuum Reimei trapped-ion quantum computer, comparing the DSF of 1D Heisenberg model on 202020 sites, and that of the copper sulfate crystal. To that end, we introduce a pumping approach for computing the DSF S(q,ω)S(q,ω)S(q,ω) on quantum computers that enables targeting specific arbitrary values of frequencies ωωω. This method time-evolves the initial state using a time-dependent Hamiltonian perturbed by a source term oscillating at the target frequency ωωω. When targeting only a few frequency values, this approach provides a significant reduction in shot overhead compared to previous methods.
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.