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arXiv:2609.31889

Scattering amplitudes from quantum hardware a la RESOs

Raul A Briceno, Ivan M Burbano, Anthony N Ciavarella, Ermal Rrapaj, Thomas R Richardson, Andre Walker-Loud

quant-phhep-latnucl-thSubmitted Sep 25, 2026• Announced Sep 29, 2026• 0 citations
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Abstract

We report the first quantum-hardware implementation of Real-time Estimators for Scattering Observables (RESOs). The physical model is a one-dimensional lattice theory of non-relativistic spin-1/2 fermions with a single contact interaction. The lattice sizes studied are up to $N_x=54$ lattice sites and up to $20$ time steps. Spacetime correlation functions were computed on IBM's quantum computers, using $109$ qubits with $10,806$ CZ gates applied, reaching a two-qubit gate depth of $246$. We demonstrate how to study bound states and extract scattering amplitudes from these correlation functions.

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11 pages, 3 figures

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We report the first quantum-hardware implementation of Real-time Estimators for Scattering Observables (RESOs). The physical model is a one-dimensional lattice theory of non-relativistic spin-1/2 fermions with a single contact interaction. The lattice sizes studied are up to Nx=54N_x=54Nx​=54 lattice sites and up to 202020 time steps. Spacetime correlation functions were computed on IBM's quantum computers, using 109109109 qubits with 10,80610,80610,806 CZ gates applied, reaching a two-qubit gate depth of 246246246. We demonstrate how to study bound states and extract scattering amplitudes from these correlation functions.
The calculation of dynamic response functions is expected to be an early application benefiting from rapidly developing quantum hardware resources. The ability to calculate real-time quantities of strongly correlated quantum systems is one of the most exciting applications that can easily reach beyond the capabilities of traditional classical hardware. Response functions of fermionic systems at moderate momenta and energies corresponding roughly to the Fermi energy of the system are a potential early application because the relevant operators are nearly local, and the energies can be resolved in moderately short real time, reducing the spatial resolution and gate depth required. This is particularly the case in quasielastic electron and neutrino scattering from nuclei, a topic of great interest in the nuclear and particle physics communities and directly related to experiments designed to probe neutrino properties. In this work we use current quantum hardware and error mitigation protocols to calculate response functions for a highly simplified nuclear model through calculations of a 2-point real time correlation function for a modified Fermi-Hubbard model in two dimensions with three distinguishable nucleons on four lattice sites.
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Utilizing the Lehmann-Symanzik-Zimmermann reduction formula, we present a new general framework for computing scattering amplitudes in quantum field theory with quantum computers in a fully nonperturbative way. In this framework, one only has to construct one-particle states of zero momentum, and no wave packets of incoming particles are needed. The framework is able to incorporate scatterings of bound states, and is ideal for scatterings involving a small number of particles. We expect this framework to have particular advantages when applied to exclusive hadron scatterings. As a proof of concept, by simulations on classical hardware, we demonstrate that in the one-flavor Gross-Neveu model, the fermion propagator, the connected fermion four-point function, and the propagator of a fermion-antifermion bound state obtained from our proposed quantum algorithm have the desired pole structure crucial to the implementation of the Lehmann-Symanzik-Zimmermann reduction formula.
The last few years have seen rapid development of applications of quantum computation to quantum field theory. The first algorithms for quantum simulation of scattering have been proposed in the context of scalar and fermionic theories, requiring thousands of logical qubits. These algorithms are not suitable to simulate scattering of incoming bound states, as the initial-state preparation relies typically on adiabatically transforming wavepackets of the free theory into wavepackets of the interacting theory. In this paper we present a strategy to excite wavepackets of the interacting theory directly from the vacuum of the interacting theory, allowing the preparation of states of composite particles. This is the first step towards digital quantum simulation of scattering of bound states. The approach is based on the Haag-Ruelle scattering theory, which provides a way to construct creation and annihilation operators of a theory in a full, nonperturbative framework. We provide a quantum algorithm requiring a number of ancillary qubits that is logarithmic in the size of the wavepackets, and with a success probability vanishing at most like a polynomial in the lattice parameters and the energy of the wavepacket. The gate complexity for a single iteration of the circuit is equivalent to that of a time evolution for a fixed time. Furthermore, we propose a complete protocol for scattering simulation using this algorithm. We study its efficiency and find improvements with respect to previous algorithms in the literature. Published by the American Physical Society 2024
Abstract Time evolution and scattering simulation in phenomenological models are of great interest for testing and validating the potential for near-term quantum computers to simulate quantum field theories. Here, we simulate one-particle propagation and two-particle scattering in the one-dimensional transverse Ising model for 3 and 4 spatial sites with periodic boundary conditions on a quantum computer. We use the quantum Lanczos algorithm to obtain all energy levels and corresponding eigenstates of the system. We simplify the quantum computation by taking advantage of the symmetries of the system. These results enable us to compute one- and two-particle transition amplitudes, particle numbers for spatial sites, and the transverse magnetization as functions of time. The quantum circuits were executed on various IBM Q superconducting hardware. The experimental results are in very good agreement with the values obtained using exact diagonalization.