Multi-Particle Quantum Walks

Swarnadeep Majumder, Austen Couvertier

Konstantinos Poulios, Daniel Fry, Mirko Lobino +12 more

Multi-photon quantum walks on integrated circuits are emonstrated, showing non-classical correlations, in one and two dimensional networks. Time evolution of quantum walks and a scheme for simulating fermionic quantum walks using entanglement are demonstrated.

Luigi Accardi, G. S. Watson

Sachin Kasture, Shaheen Acheche, Loïc Henriet +1 more

Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular we look at how we can compare multi-particle quantum walks and well known classical WL tests and how quantum walks can be used to distinguish hard graphs like CFI graphs which k-WL tests cannot distinguish. We provide theoretical proofs and empirical results to show that a k-QW with input superposition states distinguishes k-CFI graphs. In addition we also prove that a k-1 QW with localized input states distinguishes k-CFI graphs. We also prove some additional results about strongly regular graphs (SRGs).

Takashi Komatsu, Norio Konno, Iwao Sato

Our previous works presented zeta functions by the Konno-Sato theorem or the Fourier analysis for one-particle models including random walks, correlated random walks, quantum walks, and open quantum random walks. This paper introduces a new zeta function for multi-particle models with probabilistic or quantum interactions, called the interacting particle system (IPS). We compute the zeta function for some tensor-type IPSs.

Rong Zhang, Rusheng Qi, Tianhao Chen +1 more