Universal Barenco quantum gates via a tunable non-collinear interaction

TL;DR

This paper proposes tunable, non-collinear interaction-based protocols to realize universal Barenco quantum gates, enabling flexible quantum operations with potential implementation in Rydberg atom systems.

Contribution

It introduces two novel protocols for implementing universal Barenco gates using tunable non-collinear interactions, expanding control and flexibility in quantum gate design.

Findings

Protocols enable tuning of all three gate parameters.

First protocol can produce CNOT and Controlled-Y gates.

Implementation feasible with Rydberg atom interactions.

Abstract

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 ($\alpha,\theta$, and $\phi$) though it works in a two-qubit Hilbert space. Here we design $\mathbb{B}$ via a non-collinear interaction $V|r_1r_2\rangle\langle r_1r_3|+$H.c., where $|r_i\rangle$ is a state that can be excited from a qubit state and $V$ is adjustable. We present two protocols of $\mathbb{B}$. The first~(second) protocol consists of two~(six) pulses and one~(two) wait period(s), where the former causes rotations between the qubit states and excited states, and the latter induces gate transformation via the non-collinear interaction. In the first protocol, the variable $\phi$ can be tuned by varying phases of external controls, and the other two variables $\alpha$ and $\theta$, tunable via adjusting the wait duration, have a linear dependence upon each other. Meanwhile, the first protocol can give rise to the CNOT and Controlled-Y gates. In the second protocol, $\alpha,\theta$, and $\phi$ can be varied by changing the interaction amplitudes and wait durations, and the latter two are dependent on $\alpha$ non-linearly. Both protocols can also lead to another universal gate when $\{\alpha,\phi\}=\{1/4,1/2\}\pi$ with appropriate parameters. Implementation of these universal gates is analyzed based on the van der Waals interaction of neutral Rydberg atoms.