Quantum computation via Floquet topological edge modes

TL;DR

This paper proposes a new approach to quantum computation using Floquet topological edge modes, demonstrating how multiple Majorana modes in driven systems can encode qubits and perform quantum algorithms efficiently.

Contribution

It introduces a novel method leveraging Floquet SPT phases with multiple edge modes for holonomic quantum computation, showing resource savings over traditional Majorana-based systems.

Findings

Three pairs of Majorana edge modes encode two logical qubits.

Quantum gates and algorithms are implemented via adiabatic lattice deformation.

Floquet SPT phases enable resource-efficient quantum computation.

Abstract

Floquet topological matter has emerged as one exciting platform to explore rich physics and game-changing applications of topological phases. As one remarkable and recently discovered feature of Floquet symmetry protected topological (SPT) phases, in principle a simple periodically driven system can host an arbitrary number of topological protected zero edge modes and pi edge modes, with Majorana zero modes and Majorana pi modes as examples protected by the particle-hole symmetry. This work advocates a new route to holonomic quantum computation by exploiting the co-existence of many Floquet SPT edge modes, all of which have trivial dynamical phases during a computation protocol. As compelling evidence supporting this ambitious goal, three pairs of Majorana edge modes, hosted by a periodically driven one-dimensional (1D) superconducting superlattice, are shown to suffice to encode two logical qubits, realize quantum gate operations, and execute two simple quantum algorithms through adiabatic lattice deformation. When compared with early studies on quantum computation based on Majorana zero modes of topological quantum wires, significant resource saving is now made possible by use of Floquet SPT phases. This paper is thus hoped to motivate a series of future studies on the potential of Floquet topological matter in quantum computation.