String order parameters for 1d Floquet Symmetry Protected Topological Phases

TL;DR

This paper introduces non-local string order parameters to detect 1d Floquet SPT phases, proposes a superconducting-qubit implementation, and an interferometric measurement scheme for these topological phases.

Contribution

It constructs non-local string order parameters for 1d Floquet SPT phases and proposes a feasible quantum computing implementation and measurement method.

Findings

Non-local string order parameters can detect 1d FSPT order.

A superconducting-qubit array realization of Ising-FSPT is feasible.

An interferometric scheme enables direct measurement of string order.

Abstract

Floquet symmetry protected topological (FSPT) phases are non-equilibrium topological phases enabled by time-periodic driving. FSPT phases of 1d chains of bosons, spins, or qubits host dynamically protected edge states that can store quantum information without decoherence, making them promising for use as quantum memories. While FSPT order cannot be detected by any local measurement, here we construct non-local string order parameters that directly measure general 1d FSPT order. We propose a superconducting-qubit array based realization of the simplest Ising-FSPT, which can be implemented with existing quantum computing hardware. We devise an interferometric scheme to directly measure the non-local string order using only simple one- and two- qubit operations and single-qubit measurements.