Grover's Quantum Search Algorithm of Causal Multiloop Feynman Integrals

TL;DR

This paper demonstrates a modified Grover's quantum search algorithm applied to multiloop Feynman integrals within the Loop-Tree Duality framework, showcasing successful implementation on quantum simulators.

Contribution

It introduces a novel modification of Grover's algorithm tailored for Feynman integrals and demonstrates its feasibility on current quantum hardware.

Findings

Successful implementation on IBM Quantum and QUTE simulators

Effective encoding of propagator states on qubits

Potential for quantum advantage in complex Feynman integral calculations

Abstract

A proof-of-concept application of a quantum algorithm to multiloop Feynman integrals in the Loop-Tree Duality (LTD) framework is applied to a representative four-loop topology. Bootstrapping causality in the LTD formalism, is a suitable problem to address with quantum computers given the straightforward possibility to encode the two on-shell states of a propagator on the two states of a qubit. A modification of Grover's quantum search algorithm is developed and the quantum algorithm is successfully implemented on IBM Quantum and QUTE simulators.