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Scattering with universal quantum computers

Zheyue Hang

Published Dec 9, 2025• 0 citations
Publisher

Abstract

There has been a fast-growing interest in quantum computation in the context of high energy and nuclear physics. One important motivation is calculating real-time evolution in large Hilbert spaces which can be prohibitive with classical computers. It is possible to deal with the rapid oscillations of real-time evolution using quantum computers with a so far limited number of qubits. We have been able to measure phase shifts during the scattering process with real-time evolution for the collision by calculating the time delay between models with and without an external potential. To explore scattering problems with more intricate potentials, we use the phase shift to calculate the transmission probability, to find resonances, and to compare with results obtained by finite volume spectroscopy. Quantum computing shows possible advantages in simulating large quantum systems, which means that we can construct a suitable model in IBM qiskit with quantum gates and circuits to explore more resonances.

DOI
10.25820/etd.008210

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There has been a fast-growing interest in quantum computation in the context of high energy and nuclear physics. One important motivation is calculating real-time evolution in large Hilbert spaces which can be prohibitive with classical computers. It is possible to deal with the rapid oscillations of real-time evolution using quantum computers with a so far limited number of qubits. We have been able to measure phase shifts during the scattering process with real-time evolution for the collision by calculating the time delay between models with and without an external potential. To explore scattering problems with more intricate potentials, we use the phase shift to calculate the transmission probability, to find resonances, and to compare with results obtained by finite volume spectroscopy. Quantum computing shows possible advantages in simulating large quantum systems, which means that we can construct a suitable model in IBM qiskit with quantum gates and circuits to explore more resonances.
Simulations of scattering processes are essential in understanding the physics of our universe. Computing relevant scattering quantities from ab initio methods is extremely difficult on classical devices because of the substantial computational resources needed. This work reports the development of an algorithm that makes it possible to obtain phase shifts for generic nonrelativistic elastic scattering processes on a quantum computer. This algorithm is based on extracting phase shifts from the direct implementation of the real-time evolution. The algorithm is improved by a variational procedure making it more accurate and resistant to the quantum noise. The reliability of the algorithm is first demonstrated by means of classical numerical simulations for different potentials and later tested on existing quantum hardware, specifically on IBM quantum processors.
To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is to simulate Hermitian systems in imaginary time, the other is to simulate non-Hermitian systems in real time. We demonstrate that both approaches lead to the problem of non-unitary quantum evolution which can be solved by combining two quantum algorithms: block encoding and Hadamard test. The combined quantum algorithm does not require mid-circuit measurements or adjustment of the input parameters of the Hamiltonian, and can be easily implemented on quantum computers. Numerical tests on quantum simulators show that both approaches agree with exact solutions for a sufficiently long time before the signal is lost in statistical fluctuations. The results bode well for using non-Hermitian and imaginary-time simulations to circumvent oscillations inherent in real-time simulation of other quantum systems. In particular, the non-Hermitian approach shows a decisive advantage over the imaginary-time one on the number of required ancillary qubits, and hence is more practical to scale up.
We investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in Ref.~\cite{Guo:2023ecc} that relates the integrated correlation functions (ICF) for a trapped system to the infinite volume scattering phase shifts through a weighted integral. The system is first discretized in a finite box with periodic boundary conditions, and the formalism in real time is verified by employing a contact interaction potential with exact solutions. Quantum circuits are then designed and constructed to implement the formalism on current quantum computing architectures. To overcome the fast oscillatory behavior of the integrated correlation functions in real-time simulation, different methods of post-data analysis are proposed and discussed. Test results on IBM hardware show that good agreement can be achieved with two qubits, but complete failure ensues with three qubits due to two-qubit gate operation errors and thermal relaxation errors.
Scattering probes the internal structure of quantum systems. We calculate the two-particle elastic scattering phase shift for a short-ranged interaction on a quantum computer. Short-ranged interactions with a large scattering length or shallow bound state describe a universality class that is of interest in atomic, condensed matter, nuclear, and particle physics. The phase shift is calculated by relating it to the ground-state energy of the interacting particles in a harmonic trap. The relaxation method is used as the variational quantum eigensolver for the ground-state calculation. Schmidt decomposition is used to reduce quantum circuits nominally requiring tens of qubits to two-qubit circuits, thus reducing the noise in quantum measurements. Calculations in multiparticle systems with many-body interactions would benefit from this reduction of qubits in noisy quantum processors.
High-energy nuclear physics aims to explore and understand the physics of matter composed of quarks and gluons. However, it is intrinsically difficult to simulate high-energy nuclear physics from the first principle based quantum chromodynamics by using classical computers. In recent years, quantum computing has received intensive attention because it is expected to provide an ultimate solution for simulating high-energy nuclear physics. In this paper, we firstly review recent advances in quantum simulation of high-energy nuclear physics. Then we introduce some standard quantum algorithms, such as state preparation and measurements of light-cone correlation function. Finally, we demonstrate the advantage of quantum computing for solving the real-time evolution and the sign problems by studying hadronic scattering amplitude and phase structure of finite-temperature and finite-density matter, respectively.
We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient when using noisy quantum computers for which the asymptotic out-state behavior is unreachable. We demonstrate that the challenging Fourier transforms involved in the state preparation and measurements can be implemented in 1+11+11+1 dimensions with current trapped ion devices and IBM quantum computers. We compare quantum computations of the time delays obtained in the one-particle quantum mechanics limit and the scalable quantum field theory formulation with accurate numerical results. We discuss the finite volume effects in the Wigner formula connecting time delays to phase shifts. The results reported involve two- and four-qubit calculations, and we discuss the possibility of larger scale computations in the near future.