Quantum Monte Carlo Simulations for predicting electron-positron pair production via the linear Breit-Wheeler process

TL;DR

The study tackles predicting electron-positron pair production in the linear Breit-Wheeler process within strong-field QED using quantum Monte Carlo integration. It develops a NISQ-friendly workflow based on Iterative Quantum Amplitude Estimation (IQAE) that loads an energy distribution, embeds a polynomial approximation of the cross-section $ ilde{p}(x)=a_0+a_1x+a_2x^2$, and extracts the expected number of pairs, enabling a potential quadratic speedup over classical Monte Carlo under ideal conditions. The authors demonstrate near-analytic accuracy in ideal simulations (≈99.8%) and solid hardware performance on IonQ Forte (≈87–90%), with mean errors below 0.2% for multiple state-preparation schemes, and show QMCI outperforms classical MC with the same query budget. They discuss pathways to integrate QMC with classical high-performance codes and outline extensions to multivariable SFQED problems, highlighting the practical impact of quantum speedups for stochastic sampling in high-energy physics and HPC workflows.

Abstract

Quantum computing (QC) has the potential to revolutionise the future of scientific simulations. To harness the capabilities that QC offers, we can integrate it into hybrid quantum-classical simulations, which can boost the capabilities of supercomputing by leveraging quantum modules that offer speedups over classical counterparts. One example is quantum Monte Carlo integration, which is theorised to achieve a quadratic speedup over classical Monte Carlo, making it suitable for high-energy physics, strong-field QED, and multiple scientific and industrial applications. In this paper, we demonstrate that quantum Monte Carlo can be used to predict the number of pairs created when two photon beams collide head-on, a problem relevant to high-energy physics and intense laser-matter interactions. The results from the quantum simulations demonstrate high accuracy relative to theoretical predictions. The accuracy of the simulations is only constrained by the approximations required to embed polynomials and to initialise the quantum state. We also demonstrate that our algorithm can be used in current quantum hardware, providing up to 90 % accuracy relative to theoretical predictions. Furthermore, we propose pathways towards integrations with classical simulation codes.

Figures (10)

• Figure 1: Cartoon showing the algorithm composed of its quantum and classical part. Within the quantum part, we have the initialisation of the probability distribution of the beam with a Gaussian energy distribution, the embedding of the probabilities to an ancillary function via controlled rotations; the amplitude amplificaction, of the "good" state in the ancillary qubit. In the classical part, we have the post-processing part, where we the amplitudes of the probability in the "good" state are read and interpreted to number of pairs produced via linear Breit-Wheeler.
• Figure 2: Cartoon showing an experimental setup of two beams colliding and creating electron-positron pairs via the linear Breit-Wheeler process.
• Figure 3: Panel a): Comparison between the theoretically predicted number of pairs (solid blue) and different state initialisation methods using a variational approach (spaced-dashed orange), Fourier Series Loader (FSL, dot-dashed green), and the initialisation method from Qiskit (dotted red). Panel b) comparison of the relative error with the different initialisation methods. The energy of the mono-energetic beam is from $2$ to $10~\textrm{MeV}$.
• Figure 4: Panel a): Comparison between the theoretically predicted number of pairs (solid blue) and different state initialisation methods using a variational approach (spaced-dashed orange), Fourier Series Loader (FSL, dot-dashed green), and the initialise method from Qiskit (dotted red). Panel b) comparison of the relative error with the different initialisation methods. The number of qubits is varied.
• Figure 5: Panel a): Comparison between the theoretically predicted number of pairs (solid blue) and different state initialisation methods using a variational approach (spaced-dashed orange), Fourier Series Loader (FSL, dot-dashed green), and the initialise method from Qiskit (dotted red). Panel b) comparison of the relative error with the different initialisation methods. The spread of the distribution is varied.