Hamiltonian truncation and quantum simulation of strong-field QED beyond tree level

TL;DR

The work develops a real-time, Hamiltonian-based framework for simulating one-loop SFQED polarization flip in a plane-wave background using light-front momentum-space truncation. It derives the one-loop Hamiltonian, identifies and renormalizes unphysical cutoff artifacts with counterterms, and analyzes both delta-pulse and general-plane-wave backgrounds via EFT. The authors implement classical Hamiltonian truncation simulations and propose quantum simulations with an $n$-choose-$k$ encoding, detailing circuit decompositions via multi-controlled rotations and Givens rotations, as well as resource estimates and the impact of Trotterization. The study demonstrates that counterterms are essential to remove spurious effects, provides a practical truncation and encoding strategy, and outlines the path toward near-term quantum simulations of SFQED processes, while acknowledging current hardware limitations.

Abstract

Quantum electrodynamics in strong background fields provides an interesting class of problems for classical and quantum simulation. In this paper we formulate simulations of polarization (helicity) flip for a photon colliding with a high-intensity plane wave. Polarization flip is a one loop effect, which requires addressing new issues that do not arise in simulations of tree-level processes. Working in the momentum-space Fock basis, while convenient for the extraction of scattering amplitudes, requires tuning counterterms to cancel large cutoff effects. We compute analytic formulas for the counterterms at one loop. We then construct circuits for quantum simulations of the process, perform noiseless simulations on classical computers to assess discretization errors, and discuss resource estimates for future simulations on quantum hardware.

Figures (10)

• Figure 1: One-loop Feynman diagram for polarization flip. A photon with given polarization encounters a background field; unlike in vacuum, the photon can flip to an orthogonal polarization state through the one-loop interaction shown. Fermions interact directly with the background, and the double-line indicates that this interaction is accounted for non-perturbatively.
• Figure 2: Quantifying cutoff and discretization effects. We compare the accuracy of the cut-off polarization flip probability, calculated with \ref{['cut_off_amp']} and $\Lambda=5m$, with the exact probability from \ref{['pi_ineqj_delta']}. We also compare the cut-off and discretized probability, found with \ref{['cut_off_disc_amp']} and $(K,N)=(12,13)$, with the cut-off probability. Here, $(k^+,\xi)=(m,1)$ and the delta-pulse spacing $T$ is varied. The band marked "$\pm 10\%$ Exact" shows the window in which the exact probability varies by 10%. The band marked "$\pm 10\%$ Cut-off" shows the same around the probability computed with the cut-off amplitude.
• Figure 3: Convergence of Trotter simulation and perturbation theory. The figure above compares polarization flip probabilities obtained from Trotterization versus cut-off and discretized perturbation theory for several values of $T$. Probabilities are obtained from the late-time state after a period of adiabatic turn-off of the coupling. See figure \ref{['classical_sim']} for a sample simulation that produced the Trotterization data point at $T=5$.
• Figure 4: Time-dependent polarization flip probabilities obtained from Trotterization. Here, $\Delta x^+ = 0.1$ and $T=5$. Adiabatic turn-on starts at $x^+=-10$ and ends at $x^+=0$. From $x^+=0$ to $x^+=10$, the coupling is held at $e=0.303$. The black dashed lines show where an initial delta pulse appears at $x^+=0$ and is later canceled by an opposite-sign pulse at $x^+=5$. The gray dashed line shows when adiabatic turn-off begins, lasting until $x^+=20$ where $e=0$.
• Figure 5: Robustness of the discretization procedure to changes in background field strength. This figure shows the percent difference of cut-off and discretized probabilities, averaged over a large-$T$ interval, with the expected probabilities calculated with \ref{['large_T']} for various values of $\xi$. $(K,N)=(12,13)$ was kept fixed, but $\Lambda$ was adjusted for each $\xi$.