Systematically generated two-qubit anyon braids

Carnahan, Caitlin; Zeuch, Daniel; Bonesteel, N. E.

doi:10.1103/physreva.93.052328

Cited by 11 publications

(25 citation statements)

References 28 publications

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“…Alternatives and variants to this method are presented in (Carnahan et al, 2016;Hormozi et al, 2009Hormozi et al, , 2007Xu and Wan, 2008), but the principle of divide and conquer and dimension reduction to produce two qubit operations remains.…”

Section: Compiling Two Qubit Braidsmentioning

confidence: 99%

Introduction to topological quantum computation with non-Abelian anyons

Field

Simula

2018

Quantum Sci. Technol.

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Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows for universal quantum computation by particle exchange or braiding alone is the Fibonacci anyon model. One classically hard problem that can be solved efficiently using quantum computation is finding the value of the Jones polynomial of knots at roots of unity. We aim to provide a pedagogical, self-contained, review of topological quantum computation with Fibonacci anyons, from the braiding statistics and matrices to the layout of such a computer and the compiling of braids to perform specific operations. Then we use a simulation of a topological quantum computer to explicitly demonstrate a quantum computation using Fibonacci anyons, evaluating the Jones polynomial of a selection of simple knots. In addition to simulating a modular circuit-style quantum algorithm, we also show how the magnitude of the Jones polynomial at specific points could be obtained exactly using Fibonacci or Ising anyons. Such an exact algorithm seems ideally suited for a proof of concept demonstration of a topological quantum computer.

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Section: Compiling Two Qubit Braidsmentioning

confidence: 99%

Introduction to topological quantum computation with non-Abelian anyons

Field

Simula

2018

Quantum Sci. Technol.

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“…The convergence is double exponentially fast and the space complexity is O(log(1/ǫ)) to reach the limit within precision ǫ > 0. The above technique is also heavily utilized to design composite pulse sequence for quantum error correction [9] and to generate leakage-free entangling 2-qubit gates in the Fibonacci model [2,3].…”

Section: Introductionmentioning

confidence: 99%

“…[3]) and hence Equation 1 can be used in this model. The theory SU (2) p is also defined for any p ≥ 1, and for odd p, braiding of anyons gives the diagonal gate D( π p+2 ). This can be obtained from the R-symbols of the theory (Ref.…”

Section: Introductionmentioning

confidence: 99%

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Constructing Approximately Diagonal Unitary Gates

Colton¹,

Cui²

2021

Preprint

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We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are conjectured to converge to diagonal gates doubly exponentially fast and are verified for small integers. We systemically study this conjecture and prove several important partial results. Some techniques are developed to pave the way for a final resolution of the conjecture. The sequences provided here have applications in quantum search algorithms, quantum circuit compilation, generation of leakage-free entangled gates in topological quantum computing, etc.

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“…Carnahan, Zeuch and Bonesteel [2] construct a braid that approximates an entangling gate and has arbitrarily small leakage. However, there is no known braid that performs an entangling gate with zero leakage.…”

Section: Introductionmentioning

confidence: 99%

An Exact Entangling Gate Using Fibonacci anyons

Bigelow

Levaillant²

2018

Bull. Aust. Math. Soc.

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Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there is no known "leakage-free" entangling gate made by braiding. In this paper, we provide a remedy to this problem by supplementing braiding with measurement operations in order to produce an exact controlled rotation gate on two qubits.

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Systematically generated two-qubit anyon braids

Cited by 11 publications

References 28 publications

Introduction to topological quantum computation with non-Abelian anyons

Introduction to topological quantum computation with non-Abelian anyons

Constructing Approximately Diagonal Unitary Gates

An Exact Entangling Gate Using Fibonacci anyons

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