相关论文: Estimating Jones polynomials is a complete problem…

The Jones and HOMFLY polynomials are link invariants with close connections to quantum computing. It was recently shown that finding a certain approximation to the Jones polynomial of the trace closure of a braid at the fifth root of unity…

We analyze relationships between quantum computation and a family of generalizations of the Jones polynomial. Extending recent work by Aharonov et al., we give efficient quantum circuits for implementing the unitary Jones-Wenzl…

Motivated by the result that an `approximate' evaluation of the Jones polynomial of a braid at a $5^{th}$ root of unity can be used to simulate the quantum part of any algorithm in the quantum complexity class BQP, and results relating BQP…

We present an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer, namely computing the value of the Jones polynomial at the fifth root of unity within additive…

This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an example of a…

We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the…

This paper investigates the power of polynomial-time quantum computation in which only a very limited number of qubits are initially clean in the |0> state, and all the remaining qubits are initially in the totally mixed state. No…

The one clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single input qubit is pure and all other input qubits are maximally mixed. In spite of the severe restriction, the model can solve several…

We analyze the connections between the mathematical theory of knots and quantum physics by addressing a number of algorithmic questions related to both knots and braid groups. Knots can be distinguished by means of `knot invariants', among…

The one-clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single qubit of the initial state is pure and others are maximally mixed. Although the model is not universal, it can efficiently solve…

The Jones polynomial, discovered in 1984, is an important knot invariant in topology. Among its many connections to various mathematical and physical areas, it is known (due to Witten) to be intimately connected to Topological Quantum Field…

A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…

The evaluation of the Jones polynomial at roots of unity is a paradigmatic problem for quantum computers. In this work we present experimental results obtained from existing noisy quantum computers for special cases of this problem, where…

It is a challenging problem to construct an efficient quantum algorithm which can compute the Jones' polynomial for any knot or link obtained from platting or capping of a $2n$-strand braid. We recapitulate the construction of braid-group…

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…

Deterministic quantum computation with one quantum bit (DQC1), or the one clean qubit model, [E. Knill and R. Laflamme, Phys. Rev. Lett. {\bf81}, 5672 (1998)] is a model of quantum computing where the input is the tensor product of a single…

We construct a quantum algorithm to approximate efficiently the colored Jones polynomial of the plat presentation of any oriented link L at a fixed root of unity q. Our construction is based on SU(2) Chern-Simons topological quantum field…

Consider the model of computation where we start with two halves of a $2n$-qubit maximally entangled state. We get to apply a universal quantum computation on one half, measure both halves at the end, and perform classical postprocessing.…

A celebrated important result due to Freedman, Larsen and Wang states that providing additive approximations of the Jones polynomial at the k'th root of unity, for constant k=5 and k>6, is BQP-hard. Together with the algorithmic results of…

There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical…