What question did this study set out to answer?

To construct families of graphs from linear groups that allow for perfect state transfer via quantum walks.

March 5, 2026Open Access

Perfect state transfer in graphs related to linear groups in two dimensions

Key Points

To construct families of graphs from linear groups that allow for perfect state transfer via quantum walks.
Constructed graphs from the linear groups SL(2,q), GL(2,q), and GU(2,q).
Analyzed the continuous-time quantum walks on the formed networks.
Investigated the property of perfect state transfer in the associated qubit networks.
Identified specific graph structures that support perfect state transfer.
Established the relationship between linear groups and the properties of graph networks for quantum applications.

Abstract

We construct families of graphs from linear groups SL ( 2 , q ) , GL ( 2 , q ) and GU ( 2 , q ) , where q is an odd prime power, with the property that the continuous-time quantum walks on the associated networks of qubits admit perfect state transfer.

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