Quantum algorithm for Feynman loop integrals

Abstract

We present the first flagship application of a quantum algorithm to Feynman loop integrals. The two onshell 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. Since the number of causal states to be identified is nearly half of the total number of states in most cases, an efficient modification of Grover's algorithm is introduced, requiring only O(1) iterations. The output of the quantum algorithm in the IBM quantum simulator 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.

Geometry and causality for efficient multiloop representations

“…Since the computational complexity scales exponentially with the number of multi-edges, this could be a potential bottleneck for multileg multi-loop amplitudes. For this reason, novel strategies based on quantum algorithms are starting to be explored [37,41].…”

“…Using a geometrical construction inspired by graph theory, we establish a set of rules that allows to compute all the possible entangled thresholds contributing to the causal representation [36]. We rely on the identification of binary connected partitions of diagrams (which strictly corresponds to the socalled causal propagators) and compatible momenta orientations (usually called causal fluxes) [37]. This geometrical approach is closely related to the all-order representations presented in Refs.…”

Quantum integration of elementary particle processes

“…Applications to parton-distribution functions (PDF) have also been carried out by several groups [26,27] in a quantum context. In addition, several investigations of quantum parton shower as well as matrix elements evaluation [28,29] have been carried out [30,28,31]. Finally, in Ref.…”