Optimized quantum algorithms for simulating the Schwinger effect

In this work, we estimate the logical resource requirements for a fault-tolerant quantum computer to simulate physically relevant processes in Schwinger model, a quantum electrodynamics model in (1+1) space-time dimensions [1]. The aim of such an end-to-end simulation would be to study a phenomenon known as the Schwinger effect: the production of particle-antiparticle pairs by electric fields. Our analysis considers different problem parameter regimes, in which we expect to observe the Schwinger effect, and where the simulation reliably represents the physical scenario. Besides the resource estimates, we provide optimized circuit implementations for time-evolution algorithms based on product-formula [2] and interaction-picture [3] approaches. A comparison confirms that the interaction-picture approach outperforms the product-formula approach, especially when rigorous bounds are applied to the electric-field cutoff, i.e. when we are in a regime where the Schwinger effect is proven to be reliably simulable [4]. Our quantum simulation methods and end-to-end analysis can be generalized to more realistic models, e.g. theories in higher dimensions and of other gauge groups, in or beyond high-energy physics.

[1] J. Schwinger, Phys. Rev. 128, 2425 (1962)

[2] A. M. Childs et al., Phys. Rev. X 11, 011020 (2021)

[3] G. H. Low and N. Wiebe, arXiv:1805.00675 (2018)

[4] Y. Tong et al., Quantum 6, 816 (2022)