Nonunitary quantum circuit

TL;DR

This paper introduces a nonunitary quantum circuit model utilizing measurement-based gates, demonstrating universality without ancillas and potential advantages for fault-tolerant quantum computing.

Contribution

It establishes the universality of a nonunitary gate set including controlled-NOT and all one-qubit unitary gates without ancillas, and explores measurement schemes to enhance success probability.

Findings

Controlled-NOT and all one-qubit unitary gates form a universal set for nonunitary circuits.

Reversing measurement schemes improve the success probability of nonunitary gates.

Nonunitary circuits can reduce qubit overhead in fault-tolerant quantum computation.

Abstract

A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all one-qubit unitary gates constitute a universal set of gates for the nonunitary quantum circuit, without the necessity of introducing ancilla qubits. A reversing measurement scheme is used to improve the probability of successful nonunitary gate operation. A quantum NAND gate and Abrams-Lloyd's nonlinear gate are analyzed as examples. Our nonunitary circuit can be used to reduce the qubit overhead needed to ensure fault-tolerant quantum computation.