Cavity-assisted controlled phase-flip gates

Abstract

Cavity-mediated two-qubit gates, for example between solid-state spins, are attractive for quantum network applications. We propose three schemes to implement a controlled phase-flip gate mediated by a cavity. The main advantage of all these schemes is the possibility to perform them using a cavity with high cooperativity, but not in the strong coupling regime. We calculate the fidelity of each scheme in detail, taking into account the most important realistic imperfections, and compare them to highlight the optimal conditions for each scheme. Using these results, we discuss which quantum system characteristics might favor one scheme over another.

Quantum repeaters based on individual electron spins and nuclear-spin-ensemble memories in quantum dots

“…Note that here emitter pure dephasing is neglected. High cooperativity is achievable in both the bad-cavity regime where κ g γ and the strong-coupling regime where g κ γ [71]. This scheme also requires a single-sided cavity.…”

“…The fidelity definition used here is the square of the definition used in Ref. [71], and as such, we have modified Eqn. 16 to be consistent with the other definitions of fidelity used in our work.…”

“…16 in Ref. [71] assumed that both of the detunings δ 1 and δ 2 were small compared to the optical decay rate γ. Therefore, to get the upper bound on these detunings individually, the next higher order perturbation terms should be considered.…”

“…It is also possible to perform a deterministic gate via the exchange of a virtual cavity photon [71]. In this scheme one transition of the QDs should be in resonance while they are dispersively coupled to a cavity mode.…”

“…Note that in the derivation of the gate fidelity in Ref. [71] it has been assumed that δ eg 2πT −1 o where T o is the optimal gate time and δ eg = |∆E e − ∆E g |. This condition is violated in our system because T o is inversely proportional to the relatively large optical decay rate associated with the QD trion.…”