Quantum Magic in Discrete-Time Quantum Walk

TL;DR

This paper explores how discrete-time quantum walks can generate and evolve quantum magic, a resource for universal quantum computation, highlighting their potential as controllable platforms for quantum information processing.

Contribution

It demonstrates that DTQWs can dynamically produce significant quantum magic, with the amount depending on initial states, and explores the complex relationship between magic and entanglement.

Findings

DTQWs can generate significant quantum magic.

Magic depends strongly on initial coin states.

Magic and entanglement exhibit a nontrivial relationship.

Abstract

Quantum magic, which accounts for the non-stabilizer content of a state, is essential for universal quantum computation beyond classically simulable resources. We investigate the generation and evolution of quantum magic in discrete-time quantum walks (DTQWs) using the Stabilizer Renyi Entropy as a measure of quantum magic. We investigate single- and two-walker quantum walks on a one-dimensional lattice, considering a wide range of initial coin states. Our results reveal that DTQWs can dynamically generate significant magic, with the amount and structure strongly dependent on the initial state of the coin. In the case of a single walker, the relationship between magic and entanglement is found to be nontrivial and complementary at long times. These findings position DTQWs as accessible and controllable platforms for producing quantum magic, offering a new perspective on their role in quantum information processing and reliable quantum computation.