Universal quantum computation with the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>fractional quantum Hall state

Bravyi, Sergey

doi:10.1103/physreva.73.042313

Cited by 251 publications

(366 citation statements)

References 27 publications

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“…͑31͒ and ͑43͔͒. In order to achieve universal quantum computation with such states, quasiparticle braiding 64 must be supplemented by operations that are topologically unprotected 65 or involve changing the topology of the system. 66,67 On the other hand, the non-Abelian statistics of the k = 3 RR state is described by Fibonacci anyons, which are known to have computationally universal braiding.…”

Section: Discussionmentioning

confidence: 99%

Fractional quantum Hall hierarchy and the second Landau level

2008

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We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the =5/ 2 Moore-Read state, we construct explicit trial wave functions to describe the fractional quantum Hall effect in the second Landau level. The resulting hierarchy of states, which reproduces the filling fractions of all observed Hall conductance plateaus in the second Landau level, is characterized by electron pairing in the ground state and an excitation spectrum that includes nonAbelian anyons of the Ising type. We propose this as a unifying picture in which p-wave pairing characterizes the fractional quantum Hall effect in the second Landau level.

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Section: Discussionmentioning

confidence: 99%

Fractional quantum Hall hierarchy and the second Landau level

2008

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“…A comparison to the scheme of Ref. [14] shows the following differences: The present scheme requires only local braiding between the anyons composing a qubit but also additional anyons for an ancilla and an additional parity measurement. The scheme in Ref.…”

Section: Introductionmentioning

confidence: 92%

“…For simplicity, we refer to the composing particles of this kind of qubit as spins-1/2, yet we emphasize that they can have various physical origins. Such encoding schemes result from system-dependent constraints, for instance, seeking a less noisy physical system as in the case of electron spins in double quantum dots [13], or due to topological constraints in the case of ν = 5/2 Ising-type anyons, where two quasiparticles form a two-level system equivalent to a spin-1/2 [14].…”

Section: Introductionmentioning

confidence: 99%

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

2008

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

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“…Quantum information is encoded in the fermionic parity shared between two Majorana zero modes, γ 1 , Γ 1 . In the standard four-Majorana qubit encoding [29], two additional modes, Γ 2 and Γ 3 , serve as a parity reservoir; they do not appear in the mathematical description of our model in any way. The vortices hosting these four Majorana modes are initially located within the same superconducting droplet.…”

Section: Introductionmentioning

confidence: 99%

Quantum information sharing between topologically distinct platforms

2016

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Can topological quantum entanglement between anyons in one topological medium "stray" into a different, topologically distinct medium? In other words, can quantum information encoded non-locally in the combined state of non-Abelian anyons be shared between two distinct topological media? For one-dimensional topological superconductors with Majorana bound states at the end of system, the quantum information store in those Majorana bound states can be transfered by directly coupling nearby Majorana bound states. However, coupling of two one-dimensional Majorana states will produce a gap, indicating that distinct topological regions of one-dimensional wires unite into a single topological region through the information transfer process. In this paper, we consider a setup with two two-dimensional p-wave superconductors of opposite chirality adjacent to each other. Even two co-moving chiral modes at the domain wall between them cannot be gapped through interactions, we demonstrate that information encoded in the fermionic parity of two Majorana zero modes, originally within the same superconducting domain, can be shared between the domains or moved entirely from one domain to another provided that vortices can tunnel between them in a controlled fashion.

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Universal quantum computation with theν=5∕2fractional quantum Hall state

Cited by 251 publications

References 27 publications

Fractional quantum Hall hierarchy and the second Landau level

Fractional quantum Hall hierarchy and the second Landau level

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

Quantum information sharing between topologically distinct platforms

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