Controlled-{\small{NOT}} gate for multiparticle qubits and topological quantum computation based on parity measurements
Oded Zilberberg, Bernd Braunecker, and Daniel Loss

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 multi-particle CNOT 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.

© 2008 The American Physical Society.