Abstract

Quantum walks, the quantum analogue to the classical random walk, have been shown to deliver the Dirac equation in the continuum limit. Recent work has shown that ‘lazy’, open quantum walks can be mapped to computational methods for fluid simulation such as lattice Boltzmann method, quantum fluid dynamics, and smoothed-particle hydrodynamics. This work concerns evaluating the ability of near-term hardware to perform small, proof-of-concept quantum walks—but crucially with the inclusion of a rest state to encompass ‘lazy’ quantum walks, providing an integral step towards quantum walks for fluid simulation. We propose the half-adder quantum walk gate circuit as a computationally relevant and transparent algorithmic benchmark that encompasses multiqubit operation fidelity and high qubit connectivity.

Neutral atom hardware is a promising choice of platform for implementing quantum walks due to its ability to implement native multiqubit gates and to dynamically re-arrange qubits. Using detail realistic modelling for near-term multiqubit Rydberg gates via two-photon adiabatic rapid passage, SPAM , and passive error, we present the gate sequences and final state fidelities for quantum walks with and without a rest state on 4 to 16-node rings. This, along with results of an error model with improved two- and three-qubit gate fidelities, leads us to conclude that a native four-qubit gate is highly beneficial for the near-term implementation of interesting quantum walks on neutral atom hardware.