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.
Highlights
Gated quantum dots provide a promising platform for realizing qubits serving as building blocks of a quantum computer [1,2,3,4,5]
We proposed a protocol for producing entanglement between two qubits and studied it analytically and numerically as applied to three geometries of capacitively coupled exchange-only qubits
We have found that the patterns of the entanglement are highly sensitive to the double-qubit geometry and the mechanism of interqubit coupling
Summary
Gated quantum dots provide a promising platform for realizing qubits serving as building blocks of a quantum computer [1,2,3,4,5]. All techniques based on a single quantum dot or double quantum dots require, for performing two-axis rotations of the electron spin (or a pseudospin) on the Bloch sphere, either high-frequency magnetic fields or magnetic-field gradients (from micromagnets or dynamical nuclear polarization), or spin-orbit coupling. Employing triple-dot qubits allows one to perform two-axis rotations by using the Heisenberg exchange only and completely by electrical means, which allows one to achieve fast performance by applying voltages to the gates. Such an approach based on coded qubits with the total electron spin S 1⁄4 1=2 and its projection Sz 1⁄4 1=2 was proposed by DiVincenzo et al [20] and realized experimentally by Laird et al [15]. We apply our protocol to three different schemes of capacitive coupling between two exchangeonly qubits and demonstrate spectacular differences in their dynamics
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