Quantum Simulations of Hadron Dynamics in the Schwinger Model using 112 Qubits

TL;DR

This paper demonstrates the simulation of hadron dynamics in the Schwinger model on a 112-qubit quantum computer, showcasing advanced state preparation, time evolution, and error mitigation techniques, with results aligning with classical simulations.

Contribution

It introduces a scalable method for preparing hadron wavepackets and simulating their dynamics on large quantum computers, utilizing adaptive algorithms and approximate interactions.

Findings

Successful preparation of hadron wavepackets on 112 qubits

Implementation of time evolution with up to 14 Trotter steps

Results agree with classical Matrix Product State simulations

Abstract

Hadron wavepackets are prepared and time evolved in the Schwinger model using 112 qubits of IBM's 133-qubit Heron quantum computer ibm_torino. The initialization of the hadron wavepacket is performed in two steps. First, the vacuum is prepared across the whole lattice using the recently developed SC-ADAPT-VQE algorithm and workflow. SC-ADAPT-VQE is then extended to the preparation of localized states, and used to establish a hadron wavepacket on top of the vacuum. This is done by adaptively constructing low-depth circuits that maximize the overlap with an adiabatically prepared hadron wavepacket. Due to the localized nature of the wavepacket, these circuits can be determined on a sequence of small lattices using classical computers, and then robustly scaled to prepare wavepackets on large lattices for simulations using quantum computers. Time evolution is implemented with a second-order Trotterization. To reduce both the required qubit connectivity and circuit depth, an approximate quasi-local interaction is introduced. This approximation is made possible by the emergence of confinement at long distances, and converges exponentially with increasing distance of the interactions. Using multiple error-mitigation strategies, up to 14 Trotter steps of time evolution are performed, employing 13,858 two-qubit gates (with a CNOT depth of 370). The propagation of hadrons is clearly identified, with results that compare favorably with Matrix Product State simulations. Prospects for a near-term quantum advantage in simulations of hadron scattering are discussed.