Abstract We develop and demonstrate methods for simulating the scattering of particle wave packets in the interacting Thirring model on digital quantum computers, with hardware implementations on up to 80 qubits. We identify low-entanglement time slices of the scattering dynamics and exploit their efficient representation by tensor networks. Circuit compression based on matrix product state techniques yields on average a reduction by a factor of 3.2 in circuit depth compared to conventional approaches, allowing longer evolution times to be evaluated with higher fidelity on contemporary quantum processors. Utilizing zero-noise extrapolation in combination with Pauli twirling, on quantum hardware we accurately simulate the full scattering dynamics on 40 qubits, and further demonstrate the tensor networks compressed state preparation on 80 qubits.
Abstract We develop and demonstrate methods for simulating the scattering of particle wave packets in the interacting Thirring model on digital quantum computers, with hardware implementations on up to 80 qubits. We identify low-entanglement time slices of the scattering dynamics and exploit their efficient representation by tensor networks. Circuit compression based on matrix product state techniques yields on average a reduction by a factor of 3.2 in circuit depth compared to conventional approaches, allowing longer evolution times to be evaluated with higher fidelity on contemporary quantum processors. Utilizing zero-noise extrapolation in combination with Pauli twirling, on quantum hardware we accurately simulate the full scattering dynamics on 40 qubits, and further demonstrate the tensor networks compressed state preparation on 80 qubits.
Collider experiments play a central role in understanding the subatomic structure of matter, as well as developing and verifying the fundamental theory of elementary particle interactions. However, comprehending scattering processes at a fundamental level in theory remains a significant challenge. The necessary involved time evolution and the with time rapidly increasing bond dimension in Tensor Networks make simulating the scattering process with this classical method challenging. On the other hand, quantum computers hold great promise to efficiently simulate real-time dynamics of lattice field theories. In this work, we take the first step in this direction toward simulating fermionic scattering using a digital-quantum computing approach. Specifically, we propose a method based on Givens rotation to prepare the initial state of the fermionic scattering process, which consists of two fermionic wave packets with opposite momenta. With a time evolution operator based on the underlying Hamiltonian acting on the initial state, the two fermionic wave packets propagate and interact with each other. Using the lattice Thirring model as the test bed and the Qiskit Statevector simulator, we observe an elastic scattering between fermions and antifermions in the strong interaction region. In addition, we clearly observe an entanglement production in the scattering process. We consider our work also as an indispensable step towards a quantum simulation of a scattering process on a real quantum device.
Quantum computing provides a novel avenue towards simulating dynamical phenomena, and, in particular, scattering processes relevant for exploring the structure of matter. However, preparing and evolving particle wave packets on a quantum device is a nontrivial task. In this work, we propose a method to prepare Gaussian wave packets with momentum on top of the interacting ground state of a fermionic Hamiltonian. Using Givens rotation, we show how to efficiently obtain expectation values of observables throughout the evolution of the wave packets on digital quantum computers. We demonstrate our technique by applying it to the staggered lattice formulation of the Thirring model and studying the scattering of two wave packets. Monitoring the particle density and the entropy produced during the scattering process, we characterize the phenomenon and provide a first step towards studying more complicated collision processes on digital quantum computers. In addition, we perform a small-scale demonstration on IBM's quantum hardware, showing that our method is suitable for current and near-term quantum devices.
Scattering processes are essential for understanding the structure of matter, yet their real-time dynamics remain challenging to simulate classically. Quantum computers offer a promising path toward efficient simulation of such physical systems. Here, we present a general and scalable framework for simulating meson scattering in lattice gauge theories on digital quantum hardware. Our approach addresses two key challenges: First, we introduce a symmetry-preserving quantum subspace expansion method for constructing high-fidelity meson creation operators across a wide range of coupling and momenta. Second, we design a quantum circuit for meson wave packet preparation using Givens rotations, improving accuracy while reducing circuit depth compared to existing approaches. We demonstrate the method in a ( 1 + 1 )-dimensional Z 2 gauge theory and explore meson scattering dynamics with tensor network simulations. We study both elastic and inelastic scattering and provide a comprehensive characterization of the scattering process in terms of energy transfer, entanglement entropy, and heavier particle production during the dynamics. Our work provides a scalable, nonvariational approach for simulating meson scattering on near-term quantum devices and offers a concrete strategy for probing nonperturbative dynamics in confining gauge theories.
Scattering processes are a crucial ingredient for the investigation of fundamental interactions. The ever-increasing amount of data produced at particle colliders has fuelled recent progresses in the field of scattering amplitudes computation. To date, on the numerical side, the results achieved are mainly based on Monte-Carlo simulations. In this Thesis the problem is attacked with a different approach: a real-time simulation of the dynamics of a 1+1 dimensional quantum field theory is performed, exploiting the powerful tensor network methods from many-body theory. A matrix product state representation of the asymptotic input states is identified, allowing for the preparation of the initial momentum wave packets. This initial state is then evolved and we aim to compute the S-matrix elements from the knowledge of the final state. We focus on a specific fermionic U(1)-gauge model, developing a set of tools which are relevant for a broader class of 1+1 dimensional quantum field theories with global or local symmetries.
Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the Z 2 and U ( 1 ) lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the Z 2 lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.
Simulating the real-time dynamics of particle collisions is a promising application of quantum simulators, because classical methods such as tensor networks struggle to capture the highly entangled states generated in high-energy scattering. Realizing such simulations requires both the preparation of incoming wave packets and the detection of the outgoing scattering products. In this work, we propose protocols that address both challenges on programmable analog and digital quantum simulation platforms. Our state-preparation scheme uses a weakly coupled auxiliary qubit - or, more generally, a customized local quench - to inject a single quasiparticle with well-defined momentum. Because it relies only on conservation of energy, this scheme requires no fine-tuning or prior knowledge about particle eigenstates, making it robust against errors in calibration and implementation. The momenta of scattering products are then extracted, using only local measurements, from the interference pattern that arises when particles are reflected at the system's boundary. We validate our protocols through numerical simulations, first in a simple single-particle model and subsequently in two interacting many-body systems: a Rydberg atom chain and an Ising chain in a mixed field. We demonstrate how high-energy regimes, necessary to access inelastic scattering processes, can be reached through an adiabatic ramp, and how the wave packet shape can be optimized by spatially modulating the Hamiltonian. Finally, we show how the protocol can be generalized to systems with more than one spatial dimension. Our proposal provides a versatile approach to the quantum simulation of scattering phenomena, and is compatible with several quantum simulation platforms that are already experimentally available.