Quantum Walks: First Hitting Times with Weak Measurements

TL;DR

This paper investigates the first hitting times in continuous-time quantum walks using weak measurements, providing a minimally invasive monitoring method validated through simulations and IBM quantum experiments.

Contribution

It introduces a novel weak measurement protocol for quantum walks, extending the theoretical framework and enabling first recurrence time analysis within the system's Hilbert space.

Findings

First hitting time scales inversely with coupling strength.

Weak measurements allow minimally invasive monitoring.

Experimental validation on IBM quantum computer.

Abstract

We study the first detected recurrence time problem of continuous-time quantum walks on graphs. While previous works have employed projective measurements to determine the first return time, we implement a protocol based on weak measurements on a dilated system, enabling minimally invasive monitoring throughout the evolution. To achieve this, we extend the theoretical framework and complement it with both numerical simulations and experimental investigations on an IBM quantum computer. Despite the implementation of a generalized measurement, our modified formalism of weak recurrence provides a description purely within the Hilbert space of the quantum system. Our results reveal that the first hitting time scales inversely with the coupling parameter between the ancilla and the quantum system.