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

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 ν = 5/2 Ising non-Abelian anyons using topological quantum computation braiding operations and nontopological charge measurements.

Quantum memories at finite temperature

“…Faulttolerant computational operations are also realized by the manipulation of holes (Raussendorf, Harrington, and Goyal, 2006;Bombin and Martin-Delgado, 2009;, twist defects (Bombin, 2010a;Barkeshli, Jian, and Qi, 2013;Barkeshli et al, 2014), or by other means (Wootton and Pachos, 2011b). It is also noteworthy that research in the direction of computation using experimentally amenable anyon models (Bravyi, 2006;Zilberberg, Braunecker, and Loss, 2008) that do not support a universal set of topological computational operations has led to schemes to supplement such systems with nontopological operations to complete their computational gate set (Bravyi and Kitaev, 2005;Wootton, Lahtinen, and Pachos, 2009). Consideration of topologically ordered systems as a basis for quantum memories therefore allows us to draw from this wealth of established knowledge to realize a fault-tolerant computational model.…”

Majorana fermions in semiconductor nanowires

“…The non-locality of these modes provides the ability to exchange and manipulate fractionalized quasiparticles and leads to non-Abelian braiding statistics [8][9][10][11][12][13][14]. Hence, in addition to being of paramount importance for fundamental physics, this property of the Majoranas places them at the heart of topological quantum computing schemes [13,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. We mention that solid-state systems, where the Majorana mode emerges as a zero energy state of an effective (but realistic) low-energy Hamiltonian, enable the realization of the Majorana operator itself, not just of the Majorana particle.…”

On-demand maximally entangled states with a parity meter and continuous feedback

“…While the readout of individual qubits is typically associated with the irreversible destruction of the given coherent state, it has been shown that a joint measurement of two qubits can serve as an effective mechanism to generate entanglement between two measured qubits initially in a product state, [1][2][3][4][5][6][7][8][9][10][11][12] and may be used for error correction schemes. 13,14 This measurement-based creation of entanglement is achieved by operating the detector as a parity meter.…”