Quantum Experiments and Graphs II: Quantum Interference, Computation and State Generation

TL;DR

This paper introduces a graph-theoretic framework for describing photonic quantum experiments, revealing new interference phenomena, computational complexity results, and insights into quantum state generation and protocols.

Contribution

It presents a novel graph-based approach to model quantum experiments, uncovering new interference effects and complexity results, and providing a new perspective on quantum photonic technologies.

Findings

Identification of a new multiphoton interference phenomenon

Computational intractability of simulating experiments (#P-hard)

Application of graph theory to quantum protocols like entanglement swapping

Abstract

We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that introducing complex weights in graphs naturally leads to quantum interference. The new viewpoint immediately leads to many interesting results, some of which we present here. Firstly, we identify a new and experimentally completely unexplored multiphoton interference phenomenon. Secondly, we find that computing the results of such experiments is #P-hard, which means it is a classically intractable problem dealing with the computation of a matrix function Permanent and its generalization Hafnian. Thirdly, we explain how a recent no-go result applies generally to linear optical quantum experiments, thus revealing important insights to quantum state generation with current photonic technology. Fourthly, we show how to describe quantum protocols such as entanglement swapping in a graphical way. The uncovered bridge between quantum experiments and Graph Theory offers a novel perspective on a widely used technology, and immediately raises many follow-up questions.