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From vacuum amplitudes to qubits

Germán Rodrigo

Abstract

High-energy colliders, exemplified by the CERN's Large Hadron Collider (LHC), constitute genuine quantum machines. In alignment with Richard Feynman's foundational vision for quantum computing, collider physics emerge therefore as a prime candidate for quantum simulations. Prospective applications include Quantum Machine Learning for collider data analysis, accelerated evaluation of complex multiloop Feynman diagrams, efficient jet clustering, enhanced parton shower simulations, and related computational challenges. We discuss two specific applications: the identification of causal structures in multiloop vacuum amplitudes, a fundamental component of the Loop-Tree Duality exhibiting deep connections to graph theory; and high-dimensional function integration and sampling. The latter constitutes an initial step toward realizing a fully fleged quantum event generator capable of operating at high perturbative orders.

From vacuum amplitudes to qubits

Abstract

High-energy colliders, exemplified by the CERN's Large Hadron Collider (LHC), constitute genuine quantum machines. In alignment with Richard Feynman's foundational vision for quantum computing, collider physics emerge therefore as a prime candidate for quantum simulations. Prospective applications include Quantum Machine Learning for collider data analysis, accelerated evaluation of complex multiloop Feynman diagrams, efficient jet clustering, enhanced parton shower simulations, and related computational challenges. We discuss two specific applications: the identification of causal structures in multiloop vacuum amplitudes, a fundamental component of the Loop-Tree Duality exhibiting deep connections to graph theory; and high-dimensional function integration and sampling. The latter constitutes an initial step toward realizing a fully fleged quantum event generator capable of operating at high perturbative orders.
Paper Structure (8 sections, 4 equations, 4 figures)

This paper contains 8 sections, 4 equations, 4 figures.

Table of Contents

  1. Introduction
  2. A new sort of Qubits motivated by Causality
  3. Mapping Cycles to Multicontrolled Toffoli Quantum Gates
  4. Graph-Theory Principles to Optimize the Quantum Oracle
  5. Quantum Integration of Multidimensional Functions
  6. Quantum Fourier Iterative Amplitude Estimation (QFIAE)
  7. Quantum Adaptive Importance Sampling (QAIS)
  8. Conclusions

Figures (4)

  • Figure 1: Three-loop vacuum amplitude (left). Phase-space residue with three external particles representing the interference of a one-loop amplitude with a tree-level amplitude (centre). Phase-space residue with four external particles representing the interference of two tree-level amplitudes (right).
  • Figure 2: Graph representing the adjacency matrix of mutually exclusive clauses of a three-eloop topology with twelve edges, generated with the MutualAuxMatrix algorithm (left), and corresponding MAUXc$^{(3,12)}$ obtained with the GraphConditionCombination algorithm (right) Ochoa-Oregon:2025opz. Colours indicate the different cliques.
  • Figure 3: 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 4: Average uncertainty for 100 independent integration runs using the same proposal PDF for the benchmark integral in Eq. (\ref{['eq:benchmark_int']}), across the full standard MC sampling range. The shaded areas, correspond to the $\pm 1 \sigma$ dispersion of these 100 runs. The VEGAS result presented corresponds to its best iteration.