Driven nonlinear dynamics of two coupled exchange-only qubits

TL;DR

This paper develops a nonlinear dynamic theory for two capacitively coupled exchange-only qubits under strong resonant driving, revealing how weak coupling can be detected via response and how entanglement and irregular dynamics depend on system geometry and coupling mechanisms.

Contribution

It introduces a comprehensive model for driven coupled exchange-only qubits, analyzing nonlinear dynamics, entanglement, and stability, with insights into controlling irregular behavior.

Findings

Coupling as low as 1% of level splittings can be detected through qubit response.

Irregular dynamics can develop but can be mitigated with optimal coupling strength.

System geometry and coupling mechanisms significantly influence qubit dynamics and entanglement.

Abstract

Inspired by creation of a fast exchange-only qubit (Medford et al., Phys. Rev. Lett., 111, 050501 (2013)), we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven resonantly at a frequency equal to its level splitting. We include conditions of strong driving, where the Rabi frequency is a significant fraction of the level splitting, and we consider situations where the splitting for the second qubit may be the same or different than the first. We demonstrate that coupling between qubits can be detected by reading the response of the second qubit, even when the coupling between them is only of about $1\%$ of their level splittings, and calculate entanglement between qubits. Patterns of nonlinear dynamics of coupled qubits and their entanglement are strongly dependent on the geometry of the system, and the specific mechanism of inter-qubit coupling deeply influences dynamics of both qubits. In particular, we describe the development of irregular dynamics in a two-qubit system, explore approaches for inhibiting it, and demonstrate existence of an optimal range of coupling strength maintaining stability during the operational time.