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Qubits and Vacuum Amplitudes

Germán Rodrigo

TL;DR

High-energy collider predictions involve computing highly dimensional multiloop scattering amplitudes in quantum field theory, which strains classical methods. The authors propose encoding Feynman propagators as qubits and enforcing causality via Loop-Tree Duality, then tackle the remaining multidimensional integrals with two quantum integration strategies, QFIAE and QAIS. They also introduce graph-theory‑driven optimizations to reduce quantum resources, notably using MEC and MCP to dramatically lower ancilla counts. Overall, the work demonstrates viable quantum approaches to both identifying causal configurations and performing high‑dimensional integration, with QAIS showing especially strong scaling that could enable quantum event generators at higher perturbative orders on future hardware.

Abstract

High-energy colliders, such as the Large Hadron Collider (LHC) at CERN, are genuine quantum machines, so, in line with Richard Feynman's original motivation for Quantum Computing, the scattering processes that take place there are natural candidates to be simulated on a quantum system. Potential applications range from quantum machine learning methods for collider data analysis, to faster and more precise evaluations of intricate multiloop Feynman diagrams, more efficient jet clustering, improved simulations of parton showers, and many other tasks. In this work, the focus will be on two specific applications: first, the identification of the causal structure of multiloop vacuum amplitudes, a key ingredient of the Loop-Tree Duality and an area with deep connections to graph theory; and second, the integration and sampling of high-dimensional functions. The latter constitutes a first step toward the realization of a fully fledged quantum event generator operating at high perturbative orders.

Qubits and Vacuum Amplitudes

TL;DR

High-energy collider predictions involve computing highly dimensional multiloop scattering amplitudes in quantum field theory, which strains classical methods. The authors propose encoding Feynman propagators as qubits and enforcing causality via Loop-Tree Duality, then tackle the remaining multidimensional integrals with two quantum integration strategies, QFIAE and QAIS. They also introduce graph-theory‑driven optimizations to reduce quantum resources, notably using MEC and MCP to dramatically lower ancilla counts. Overall, the work demonstrates viable quantum approaches to both identifying causal configurations and performing high‑dimensional integration, with QAIS showing especially strong scaling that could enable quantum event generators at higher perturbative orders on future hardware.

Abstract

High-energy colliders, such as the Large Hadron Collider (LHC) at CERN, are genuine quantum machines, so, in line with Richard Feynman's original motivation for Quantum Computing, the scattering processes that take place there are natural candidates to be simulated on a quantum system. Potential applications range from quantum machine learning methods for collider data analysis, to faster and more precise evaluations of intricate multiloop Feynman diagrams, more efficient jet clustering, improved simulations of parton showers, and many other tasks. In this work, the focus will be on two specific applications: first, the identification of the causal structure of multiloop vacuum amplitudes, a key ingredient of the Loop-Tree Duality and an area with deep connections to graph theory; and second, the integration and sampling of high-dimensional functions. The latter constitutes a first step toward the realization of a fully fledged quantum event generator operating at high perturbative orders.
Paper Structure (8 sections, 1 equation, 3 figures)

This paper contains 8 sections, 1 equation, 3 figures.

Table of Contents

  1. Introduction
  2. Qubits and Causality in Particle Physics
  3. Mapping Feynman Diagrams to Quantum Circuits
  4. Optimizing the Oracle with Graph-Theory Principles
  5. Quantum Integration of Scattering Amplitudes
  6. Quantum Fourier Iterative Amplitude Estimation (QFIAE)
  7. Quantum Adaptive Importance Sampling (QAIS)
  8. Conclusions

Figures (3)

  • Figure 1: Optimal oracle of a three-loop topology with $12$ propagators, represented by qubits $e_0$ to $e_{11}$. Only $3$ ancillary qubits ($a_0$ to $a_2$) are required.
  • Figure 2: Vacuum diagrams contributing to the decay rate $\gamma^*\to q\bar{q} (g)$ at NLO (left), and integrated results as a function of the quark mass using QFIAE partially in quantum hardware (right).
  • Figure 3: Ring-shaped two-dimensional integrand and the corresponding PDFs in QAIS and VEGAS.