On Some Basic Aspects of Ternary Reversible and Quantum Computing

Moraga, Claudio

doi:10.1109/ismvl.2014.39

Cited by 11 publications

(2 citation statements)

References 20 publications

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“…Analogous to the Hadamard in binary, there is a Chrestenson transform that creates a superposition state from the bases states and is written as [96,97]…”

Section: A2 Ternary Quantum Gatesmentioning

confidence: 99%

Ternary Logic Design in Topological Quantum Computing

Ilyas,

Cui,

Perkowski

2022

Preprint

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A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with the environment. It is a real challenge to completely isolate a quantum system to make it free of decoherence. This problem can be circumvented by the use of topological quantum phases of matter. These phases have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When the order of exchange matters, then the anyons are called non-Abelian anyons. Majorana fermions in topological superconductors and quasiparticles in some quantum Hall states are non-Abelian anyons. Such topological phases of matter have a ground state degeneracy. The fusion of two or more non-Abelian anyons can result in a superposition of several anyons. The topological quantum gates are implemented by braiding and fusion of the non-Abelian anyons. The fault-tolerance is achieved through the topological degrees of freedom of anyons. Such degrees of freedom are non-local, hence inaccessible to the local perturbations. In this paper, the Hilbert space for a topological qubit is discussed. The Ising and Fibonacci anyonic models for binary gates are briefly given. Ternary logic gates are more compact than their binary counterparts and naturally arise in a type of anyonic model called the metaplectic anyons. The mathematical model, for the fusion and braiding matrices of metaplectic anyons, is the quantum deformation of the recoupling theory. We proposed that the existing quantum ternary arithmetic gates can be realized by braiding and topological charge measurement of the metaplectic anyons.

show abstract

“…Analogous to the Hadamard in binary, there is a Chrestenson transform that creates a superposition state from the bases states and is written as [96,97]…”

Section: A2 Ternary Quantum Gatesmentioning

confidence: 99%

Ternary Logic Design in Topological Quantum Computing

Ilyas,

Cui,

Perkowski

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Analogous to the Hadamard in binary, there is a Chrestenson transform that creates a superposition state from the bases states and is written as [95,96]…”

Section: A2 Ternary Quantum Gatesmentioning

confidence: 99%

Ternary logic design in topological quantum computing

Ilyas¹,

Cui²,

Perkowski³

2022

J. Phys. A: Math. Theor.

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A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with the environment. It is a real challenge to completely isolate a quantum system to make it free of decoherence. This problem can be circumvented by the use of topological quantum phases of matter. These phases have quasiparticles excitations called anyons. The anyons are charge-flux composites and show exotic fractional statistics. When the order of exchange matters, then the anyons are called non-abelian anyons. Majorana fermions in topological superconductors and quasiparticles in some quantum Hall states are non-abelian anyons. Such topological phases of matter have a ground state degeneracy. The fusion of two or more non-abelian anyons can result in a superposition of several anyons. The topological quantum gates are implemented by braiding and fusion of the non-abelian anyons. The fault-tolerance is achieved through the topological degrees of freedom of anyons. Such degrees of freedom are non-local, hence inaccessible to the local perturbations. In this paper, the Hilbert space for a topological qubit is discussed. The Ising and Fibonacci anyonic models for binary gates are briefly given. Ternary logic gates are more compact than their binary counterparts and naturally arise in a type of anyonic model called the metaplectic anyons. The mathematical model, for the fusion and braiding matrices of metaplectic anyons, is the quantum deformation of the recoupling theory. We proposed that the existing quantum ternary arithmetic gates can be realized by braiding and topological charge measurement of the metaplectic anyons.

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Constructing All Qutrit Controlled Clifford+T gates in Clifford+T

Yeh

Wetering

2022

Lecture Notes in Computer Science

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On Some Basic Aspects of Ternary Reversible and Quantum Computing

Cited by 11 publications

References 20 publications

Ternary Logic Design in Topological Quantum Computing

Ternary Logic Design in Topological Quantum Computing

Ternary logic design in topological quantum computing

Constructing All Qutrit Controlled Clifford+T gates in Clifford+T

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