Exact CNOT Gates with a Single Nonlocal Rotation for Quantum-Dot Qubits

TL;DR

This paper demonstrates that by exploiting spin conservation in capacitively coupled quantum dot qubits, one can realize exact CNOT gates with a single nonlocal rotation, significantly reducing the complexity of quantum circuits.

Contribution

It proves analytically and numerically that conservation of individual qubit spins enables exact CNOT gates with a single nonlocal operation in quantum-dot qubits.

Findings

Infinite solutions for qubit parameters yield exact CNOT gates.

Conservation of spin quantum numbers enhances two-qubit gate performance.

Capacitive coupling allows for simplified, exact entangling gates.

Abstract

We investigate capacitively coupled two-qubit quantum gates based on quantum dots. For exchange-only coded qubits electron spin $S$ and its projection $S_z$ are exact quantum numbers. Capacitive coupling between qubits, as distinct from interqubit exchange, preserves these quantum numbers. We prove, both analytically and numerically, that conservation of the spins of individual qubits has dramatic effect on performance of two-qubit gates. By varying the level splittings of individual qubits, $J_a$ and $J_b$, and the interqubit coupling time $t$, we can find an infinite number of triples $(J_a, J_b, t)$ for which the two-qubit entanglement, in combination with appropriate single-qubit rotations, can produce an exact CNOT gate. This statement is true for practically arbitrary magnitude and form of capacitive interqubit coupling. Our findings promise a large decrease in the number of nonlocal (two-qubit) operations in quantum circuits.