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Real-Time Digital Quantum Simulation of the Schwinger Model under High-Field Laser Quenches for ELI-NP Physics Regimes

Alexandru-Florin Boboc

Published Oct 31, 2026• 0 citations
Publisher

Abstract

Overview This repository contains the computational code, simulation scripts, and diagnostic notebooks for simulating the 1+1-dimensional Schwinger model (Quantum Electrodynamics) on a quantum processor emulator. The project investigates real-time vacuum decay and electron-positron pair production under extreme laser electric field quenches, utilizing parameters chosen to align with high-field physics regimes studied at facilities like the Extreme Light Infrastructure - Nuclear Physics (ELI-NP) project. Repository Contents The core material is contained within a self-contained Jupyter Notebook designed as a computational essay that links theoretical derivations directly to code execution. The pipeline covers: Lattice Hamiltonian Construction: Setting up the $N=6$ site Kogut-Susskind staggered fermion model via Jordan-Wigner transformation and native SparsePauliOp arithmetic. Laser Quench Evolution: Implementing a time-dependent Gaussian-envelope oscillating electric field coupled via site-dependent driving operators, evolved using first-order Suzuki-Trotter decomposition (PauliEvolutionGate). NISQ Noise Modeling & ZNE Mitigation: Executing noisy density matrix simulations via Qiskit Aer (AerSimulator) under a standard depolarizing noise model ($\epsilon_{1\text{q}} = 0.002$, $\epsilon_{2\text{q}} = 0.015$), followed by Zero-Noise Extrapolation using scale-factor circuit folding ($sf \in \{1, 3\}$) and linear fitting. Advanced Quantum Diagnostics: Tracking the growth of Von Neumann entanglement entropy across a spatial bipartition as a proxy for string breaking, alongside spatiotemporal heatmaps mapping site-resolved chiral condensate melting ($\langle \bar{\psi}\psi \rangle_i$). Software Requirements & Dependencies To run the simulation and generate the diagnostic figures, the code requires Python along with the following libraries: qiskit qiskit-aer numpy matplotlib

DOI
10.5281/zenodo.23835273

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Shortcuts to adiabaticity with a quantum control field — Code & data========================================================== This repository contains a Jupyter notebook and supporting data files (csv) to reproduce the numerical results and figures in our manuscript (arXiv 2508.06304), which investigates adiabatic shortcuts mediated by a quantum control field.The code implements a Landau–Zener two-level system coupled to a spectator qubit, time evolution of the full system (LZ qubit + spectator) via QuTiP, parameter sweeps (parallelized with joblib), and plotting utilities for the manuscript figures. Related publication----------------------------This code is complementary to the preprint: https://arxiv.org/abs/2508.06304. Requirements---------------------The simulations were developed for and tested on Python 3.9+. Recommended packages and minimum versions: - Python >= 3.9- numpy >= 1.22- scipy >= 1.8- matplotlib >= 3.5- qutip >= 4.6 (install a recent stable qutip; some installations require `pip install qutip` or `conda` channels)- joblib >= 1.2- tqdm >= 4.60- pandas (optional, for CSV handling)- jupyterlab / notebook (for interactive use) Running the notebook (interactive) Open the notebook with JupyterLab or Jupyter Notebook. Execute cells sequentially in the order indicated by the notebook outline.The sections “Definitions” and “Figure imports and setup” must be executed before generating any data or figures, as they define all operators, and helper functions. The notebook is organized into separate sections for each figure of the manuscript, allowing you to re-run only the figure(s) of interest. Note: Figure 4 (Density plot) is configured to load precomputed data files to reduce computational cost. To reproduce Figure 4 without recomputing the full dataset, ensure the required .csv files are downloaded and located in the same directory as the notebook. To explore different parameter regimes: Modify the relevant parameter definitions (e.g., anneal_window, g, epsilon, omega_c, x0, x0_vals, q_vals). To include dissipation of the spectator (ancilla) qubit, set the parameter kappa> 0. For questions about reproducing the figures or about parameter choices used in the paper, contact the corresponding authors listed in the preprint. If you reuse this data/code, please cite the associated preprint and this code archive.
This note discusses a method for computing the energy spectra of quantum field theory utilizing digital quantum simulation. A quantum algorithm, called coherent imaging spectroscopy, quenches the vacuum with a time-oscillating perturbation and then reads off the excited energy levels from the loss in the vacuum-to-vacuum probability following the quench. As a practical demonstration, we apply this algorithm to the (1+1)-dimensional quantum electrodynamics with a topological term known as the Schwinger model, where the conventional Monte Carlo approach is practically inaccessible. In particular, on a classical simulator, we prepare the vacuum of the Schwinger model on a lattice by adiabatic state preparation and then apply various types of quenches to the approximate vacuum through Suzuki-Trotter time evolution. We discuss the dependence of the simulation results on the specific types of quenches and introduce various consistency checks, including the exact diagonalization and the continuum limit extrapolation. The estimation of the computational complexity required to obtain physically reasonable results implies that the method is likely efficient in the coming era of early fault-tolerant quantum computers.
We discuss a method to efficiently compute energy spectra in quantum field theories by digital quantum simulation. We utilize a quantum algorithm called coherent imaging spectroscopy which quenches the ground state with a perturbation oscillating periodically in time for various frequencies and then reads off excited energy levels from values of frequencies having loss of the vacuum-to-vacuum probability by the quench. We demonstrate this method in the Schwinger model which is the (1+1)-dimensional quantum electrodynamics with a topological term. In particular, the ground state of the Schwinger model on lattice is prepared by adiabatic state preparation and then we apply various types of quenches to the approximate ground state via Suzuki-Trotter time evolution. We benchmark the types of quenches and argue their (dis)advantages especially in the context of studying quantum field theories. We also estimate the computational complexity to obtain physically reasonable results which likely implies efficiency of the method in the early fault-tolerant quantum computer era
The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on N / 2 physical sites with coupling constant x − 1 / 2 and electric field cutoff x − 1 / 2 Λ can be simulated on a quantum computer for time 2 x T using a number of T -gates or CNOTs in O ~ ( N 3 / 2 T 3 / 2 x Λ ) for fixed operator error. This scaling with the truncation Λ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable–the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.
We use the (1+1)-dimensional Schwinger model to investigate the nonequilibrium dynamics of a finite lattice system under a constant external electric field. The lattice Hamiltonian is constructed under open boundary conditions. The vacuum state is prepared using the variational quantum eigensolver (VQE). Scans over the external field strength show the flip of the vacuum state at several field strengths. The critical field strengths agree with theoretical predictions. We further investigate the real-time evolution of the zero-field vacuum under an external electric field using a second-order Trotter-Suzuki decomposition. By comparison with exact diagonalization (ED), we verify that the quantum-simulation protocol reproduces the main features of field-induced boundary charge separation, decay of the vacuum-state fidelity, and quasiperiodic energy redistribution between the electric-field energy term and the fermionic sector. Our results indicate that combining VQE-based state preparation with digital real-time evolution provides a useful approach for studying nonequilibrium dynamics in strong-field lattice gauge theories.