A Josephson ternary memory circuit

Morisue, M.; Morooka, T.; Shimizu, Nobuhiro; Sakamoto, Masahiro

doi:10.1109/ismvl.1998.679270

Cited by 6 publications

(6 citation statements)

References 5 publications

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“…[98] for an ion-trap quantum computer, by Ref. [99,100] for a Josephson junction, by Ref. [101] for cold atoms, and by Ref.…”

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.

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“…[98] for an ion-trap quantum computer, by Ref. [99,100] for a Josephson junction, by Ref. [101] for cold atoms, and by Ref.…”

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

“…The physical realization of ternary logic was suggested by reference [97] for an ion-trap quantum computer, by references [98,99] for a Josephson junction, by reference [100] for cold atoms, and by reference [101] for entangled photons. Some circuit architectures are better described by the multi-valued logic.…”

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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“…(A brief history note on this line of thought can be found in section 4.1 of [28].) Experimental implementation of computation with ternary logic, for example with Josephson junctions, dates back to 1989 [34,35]. More recently, multi-valued logic has been proposed for linear ion traps [36], cold atoms [43], and entangled photons [30].…”

Section: Introductionmentioning

confidence: 99%

Factoring with qutrits: Shor's algorithm on ternary and metaplectic quantum architectures

2017

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We determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the availability of the ternary Clifford gates, projective measurements, classical control as its natural instrumentation set; (ii) a model based on a metaplectic topological quantum computer (MTQC). A natural choice to implement Shor's algorithm on a ternary quantum computer is to translate the entire arithmetic into a ternary form. However, it is also possible to emulate the standard binary version of the algorithm by encoding each qubit in a three-level system. We compare the two approaches and analyze the complexity of implementing Shor's period finding function in the two models. We also highlight the fact that the cost of achieving universality through magic states in MTQC architecture is asymptotically lower than in generic ternary case.

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A Josephson ternary memory circuit

Cited by 6 publications

References 5 publications

Ternary Logic Design in Topological Quantum Computing

Ternary Logic Design in Topological Quantum Computing

Ternary logic design in topological quantum computing

Factoring with qutrits: Shor's algorithm on ternary and metaplectic quantum architectures

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