Observation of hadron scattering in a lattice gauge theory on a quantum computer (2505.20387v1)

Abstract: Scattering experiments are at the heart of high-energy physics (HEP), breaking matter down to its fundamental constituents, probing its formation, and providing deep insight into the inner workings of nature. In the current huge drive to forge quantum computers into complementary venues that are ideally suited to capture snapshots of far-from-equilibrium HEP dynamics, a major goal is to utilize these devices for scattering experiments. A major obstacle in this endeavor has been the hardware overhead required to access the late-time post-collision dynamics while implementing the underlying gauge symmetry. Here, we report on the first quantum simulation of scattering in a lattice gauge theory (LGT), performed on \texttt{IBM}'s \texttt{ibm_marrakesh} quantum computer. Specifically, we quantum-simulate the collision dynamics of electrons and positrons as well as mesons in a $\mathrm{U}(1)$ LGT representing $1+1$D quantum electrodynamics (QED), uncovering rich post-collision dynamics that we can precisely tune with a topological $\Theta$-term and the fermionic mass. By monitoring the time evolution of the scattering processes, we are able to distinguish between two main regimes in the wake of the collision. The first is characterized by the delocalization of particles when the topological $\Theta$-term is weak, while the second regime shows localized particles with a clear signature when the $\Theta$-term is nontrivial. Furthermore, we show that by quenching to a small mass at the collision point, inelastic scattering occurs with a large production of matter reminiscent of quantum many-body scarring. Our work provides a major step forward in the utility of quantum computers for investigating the real-time quantum dynamics of HEP collisions.

• The paper describes a pioneering quantum simulation of hadron scattering within lattice gauge theory on an IBM quantum computer.
• The study employed Trotterization and error mitigation on systems up to 45 qubits, observing distinct post-collision dynamics based on system parameters.
• Results were validated against classical simulations, demonstrating the potential of quantum computers to effectively emulate complex high-energy physics dynamics.

Observation of Hadron Scattering in a Lattice Gauge Theory on a Quantum Computer

The paper "Observation of Hadron Scattering in a Lattice Gauge Theory on a Quantum Computer" details a pioneering quantum simulation of scattering processes in lattice gauge theory (LGT) achieved using IBM's quantum computing platform, specifically the ibm_marrakesh quantum computer. This research attempts to harness lattice gauge theories to simulate quantum electrodynamics (QED) dynamics, providing an innovative approach to the paper of high-energy physics (HEP) using digital quantum simulators.

The paper focuses on simulating electron-positron and meson collisions within a $\mathrm{U}(1)$ LGT framework, specifically targeting $1+1$ dimensional QED. Quantum simulation is performed by discretizing the gauge fields, transitioning the theoretical formulations to a computationally feasible format. Utilizing first-order Trotterization of the LGT Hamiltonian's time-evolution operator, the paper constructs quantum circuits that implement gauge-invariant dynamics necessary for exploring particle collisions on quantum devices.

Quantum Simulation Implementation

Initial states encoding particle configurations are directly prepared using single-qubit rotations, effectively creating formats that are suitable for the initialization of quantum simulations. The research explores post-collision dynamics by specifically tuning parameters such as the topological $\Theta$-term and fermionic mass. The tuning of these parameters allows for controlling regimes characterized by particle delocalization when the $\Theta$-term is weak, or localized particle dynamics when the term is nontrivial. By adjusting the mass at the collision point (quenched dynamics), inelastic scattering can be induced, highlighting processes that resemble quantum many-body scarring.

Numerical and Experimental Results

Quantum simulations on systems scaling up to 45 qubits were conducted, reaching gate depths of up to 280 two-qubit gate layers for 35 Trotter steps. Such expansive simulations require robust error mitigation techniques to achieve reliable results, leading to the application of a marginal Distribution Error Mitigation (mDEM), enhancing the fidelity of local expectation values despite quantum hardware constraints.

The experimental results indicate two distinct regimes arising from the post-collision dynamics. Without confinement (i.e., when the confining potential $\chi=0$), the electron-positron pair demonstrate elastic collisions with delocalized propagation. Contrastingly, a confining potential prevents their ballistic departure, resulting in oscillatory mesonic states indicated by stable central electric flux measurements.

Furthermore, experiments exploring mass quenches reveal different dynamics; low-mass post-collision states led to persistent meson production indicative of inelastic scattering, while others approach near-complete matter annihilation at critical mass settings ($m_c$) — an effective probe of quantum many-body scarring.

Implications and Future Directions

The research illustrates that quantum simulators can effectively emulate HEP dynamics, opening avenues for exploring real-time dynamics in complex gauge theories and higher dimensional settings. Coupled with validating results against classical matrix product state (MPS) simulations, which show strong congruence, these methodologies highlight the credibility and potential of quantum simulations in advancing our understanding of HEP processes with quantum advantage.

The research discusses possible future explorations involving different gauge groups and more complex spatial dimensions, reinforcing the utility of quantum computing as a complementary tool to traditional particle colliders. As quantum hardware continues evolving, allowing longer simulation times and larger systems, the potential for achieving quantum advantage in these domains becomes increasingly tangible.

In conclusion, the paper proposes a robust schema demonstrating how quantum computers can simulate scattering processes, adding significant depth to theoretical frameworks, and paving the path for future empirical breakthroughs in HEP through quantum computation.