Reducing the number of ancilla qubits and the gate count required for creating large controlled operations

TL;DR

This paper presents a method to create large controlled unitaries with fewer gates and the same number of ancilla qubits, optimizing quantum circuit efficiency especially in architectures where qubit initialization is costly.

Contribution

It adapts a qudit-based controlled-Toffoli scheme for qubits, achieving gate efficiency comparable to the best known methods while maintaining minimal ancilla qubits.

Findings

Most gate-efficient large controlled unitaries known

Uses fewer gates with same ancilla qubits as recent optimized methods

Applicable in architectures with cheap gates but expensive qubit initialization

Abstract

In this paper we show that it is possible to adapt a qudit scheme for creating a controlled-Toffoli created by Ralph et al. [Phys. Rev. A 75 011213] to be applicable to qubits. While this scheme requires more gates than standard schemes for creating large controlled gates, we show that with simple adaptations it is directly equivalent to the standard scheme in the literature. This scheme is the most gate-efficient way of creating large controlled unitaries currently known, however it is expensive in terms of the number of ancilla qubits used. We go on to show that using a combination of these standard techniques presented by Barenco et al. [Phys. Rev. A 52 3457 (1995)] we can create an n-qubit version of the Toffoli using less gates and the same number of ancilla qubits as recent work using computer optimization. This would be useful in any architecture of quantum computing where gates are cheap but qubit initialization is expensive.