Universal Barenco quantum gates via a tunable noncollinear interaction
Xiaofeng Shi · Physical Review A · 2018
The Barenco gate ($\mathbb{B}$) is a type of two-qubit quantum gate based on which alone universal quantum computation can be achieved. Each $\mathbb{B}$ is characterized by three angles ($\ensuremath{\alpha}$, $\ensuremath{\theta}$, and $\ensuremath{\phi}$), though it works in a two-qubit Hilbert space. Here we design $\mathbb{B}$ via a noncollinear interaction $V|{r}_{1}{r}_{2}\ensuremath{\rangle}\ensuremath{\langle}{r}_{1}{r}_{3}|+\mathrm{H}.\mathrm{c}.$, where $|{r}_{i}\ensuremath{\rangle}$ is a state that can be excited from a qubit state and $V$ is adjustable. We present two protocols for $\mathbb{B}$. The first (second) protocol consists of two (six) pulses and one (two) wait period(s), where the former causes rotations between qubit states and excited states, and the latter induces gate transformation via the noncollinear interaction. In the first protocol, the variable $\ensuremath{\phi}$ can be tuned by varying the phases of external controls, and the other two variables $\ensuremath{\alpha}$ and $\ensuremath{\theta}$, tunable via adjustment of the wait duration, have a linear dependence on each other. Meanwhile, the first protocol can give rise to cnot and controlled-y gates. In the second protocol, $\ensuremath{\alpha},\ensuremath{\theta}$, and $\ensuremath{\phi}$ can be varied by changing the interaction amplitudes and wait durations, and the latter two are dependent on $\ensuremath{\alpha}$ nonlinearly. Both protocols can also lead to another universal gate when ${\ensuremath{\alpha},\ensuremath{\phi}}={1/4,1/2}\ensuremath{\pi}$ with appropriate parameters. Implementation of these universal gates is analyzed based on the van der Waals interaction of neutral Rydberg atoms.