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arXiv:2105.08703 · Journal of High Energy Physics

Quantum algorithm for Feynman loop integrals

Selomit Ramírez-Uribe, Andrés E. Rentería-Olivo, Germán Rodrigo A, Germán F. R. Sborlini, Luiz Vale Silva

Published May 16, 2022• 29 citations

Abstract

Abstract We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal singular configurations of multiloop Feynman diagrams. To identify such configurations, we exploit Grover’s algorithm for querying multiple solutions over unstructured datasets, which presents a quadratic speed-up over classical algorithms when the number of solutions is much smaller than the number of possible configurations. A suitable modification is introduced to deal with topologies in which the number of causal states to be identified is nearly half of the total number of states. The output of the quantum algorithm in IBM Quantum and QUTE Testbed simulators is used to bootstrap the causal representation in the loop-tree duality of representative multiloop topologies. The algorithm may also find application and interest in graph theory to solve problems involving directed acyclic graphs.

DOI: 10.1007/jhep05(2022)100

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The first application of a quantum algorithm to Feynman loop integrals is reviewed. The connection between quantum computing and perturbative quantum field theory is feasible due to fact that the two on-shell states of a Feynman propagator are naturally encoded in a qubit. The particular problem to be addressed is the identification of the causal singular configurations of multiloop Feynman diagrams. The identification of such configurations is carried out through the implementation of a modified Grover's quantum algorithm for querying multiple solutions over unstructured datasets.

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. Causality obtained through 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 for querying multiple solutions over the unstructured set of solutions generated after the application of the LTD. The quantum algorithm is successfully implemented on IBM Quantum and QUTE simulators.

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.

The first application of a quantum algorithm to Feynman loop integrals is reviewed. The connection between quantum computing and perturbative quantum field theory is feasible due to fact that the two on-shell states of a Feynman propagator are naturally encoded in a qubit. The particular problem to be addressed is the identification of the causal singular configurations of multiloop Feynman diagrams. The identification of such configurations is carried out through the implementation of a modified Grover's quantum algorithm for querying multiple solutions over unstructured datasets.

Abstract Quantum algorithms provide a promising framework in high-energy physics, in particular, for unraveling the causal configurations of multiloop Feynman diagrams by identifying Feynman propagators with qubits, a challenge analogous to querying directed acyclic graphs in graph theory. In this paper, we present the Minimum Clique-optimised quantum Algorithm (MCA), an automated quantum algorithm designed to efficiently query the causal structures within the Loop-Tree Duality. The MCA quantum algorithm is optimised by exploiting graph theory techniques, specifically, by analogy with the Minimum Clique Partition problem. The evaluation of the MCA quantum algorithm is exhibited by analysing the transpiled quantum circuit depth and quantum circuit area.