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

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Zilberberg, Oded
Braunecker, Bernd
Loss, Daniel
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Abstract
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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.
Comment: 8 pages, 6 figures, updated references
Keywords
Condensed Matter - Mesoscale and Nanoscale Physics, Quantum Physics
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