Single-qubit quantum gate at an arbitrary speed

TL;DR

This paper demonstrates the construction of universal single-qubit gates at ultrafast speeds beyond the rotating wave approximation by adjusting driving pulse parameters, revealing a transition in the scaling of the central frequency with gate time.

Contribution

It introduces a method to perform universal single-qubit gates in the strong-coupling, ultrafast regime, surpassing the limitations of the RWA.

Findings

Transition in the scaling behavior of the central frequency from resonant to inverse proportionality with gate time.

Identification of the transition gate time where the scaling exponent changes from 0 to -1.

Universal single-qubit gates are achievable at speeds comparable to or shorter than the qubit period.

Abstract

Quantum information processing comprises physical processes, which obey the quantum speed limit (QSL): high speed requires strong driving. Single-qubit gates using Rabi oscillation, which is based on the rotating wave approximation (RWA), satisfy this bound in the form that the gate time $T$ is inversely proportional to the Rabi frequency $\Omega$, characterizing the driving strength. However, if the gate time is comparable or shorter than the qubit period $T_{0} \equiv 2\pi / \omega_{0}$, the RWA actually breaks down since the Rabi frequency has to be large compared to the qubit frequency $\omega_{0}$ due to the QSL, which is given as $T \gtrsim \pi/\Omega$. We show that it is possible to construct a universal set of single-qubit gates at this strong-coupling and ultrafast regime, by adjusting the central frequency $\omega$ and the Rabi frequency $\Omega$ of the driving pulse. We observe a transition in the scaling behavior of the central frequency from the long-gate time regime ($T \gg T_{0}$) to the short-gate time ($T \ll T_{0}$) regime. In the former, the central frequency is nearly resonant to the qubit, i.e., $\omega \simeq \omega_{0}$, whereas in the latter, the central frequency is inversely proportional to the gate time, i.e., $\omega \sim \pi/T$. We identify the transition gate time at which the scaling exponent $n$ of the optimal central frequency $\omega \sim T^{n}$ changes from $n=0$ to $n=-1$.