Controlled-NOT for multiparticle qubits and topological quantum computation based on parity measurements

TL;DR

This paper proposes a measurement-based scheme for implementing a controlled-NOT (CNOT) gate for multiparticle qubits, extending previous methods to systems like spin-1/2 particles and topological anyons, with practical realizations discussed.

Contribution

It introduces a general approach to realize a CNOT gate via local parity measurements for complex qubit systems, including topological quantum computation.

Findings

Feasible qubit-parity measurement scheme for multiparticle qubits

Implementation proposals using electron spins in quantum dots

Topological quantum computation with non-Abelian anyons

Abstract

We discuss a measurement-based implementation of a controlled-NOT (CNOT) quantum gate. Such a gate has recently been discussed for free electron qubits. Here we extend this scheme for qubits encoded in product states of two (or more) spins-1/2 or in equivalent systems. The key to such an extension is to find a feasible qubit-parity meter. We present a general scheme for reducing this qubit-parity meter to a local spin-parity measurement performed on two spins, one from each qubit. Two possible realizations of a multiparticle CNOT gate are further discussed: electron spins in double quantum dots in the singlet-triplet encoding, and nu=5/2 Ising non-Abelian anyons using topological quantum computation braiding operations and nontopological charge measurements.