The complexity of Boolean functions
The complexity of Boolean functions
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
The computational complexity of knot and link problems
Journal of the ACM (JACM)
Quantum computing and quadratically signed weight enumerators
Information Processing Letters
Quantum computation and quantum information
Quantum computation and quantum information
A polynomial quantum algorithm for approximating the Jones polynomial
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Computing with highly mixed states
Journal of the ACM (JACM)
A quantum circuit for shor's factoring algorithm using 2n + 2 qubits
Quantum Information & Computation
Quantum Information Processing
A new connection between quantum circuits, graphs and the Ising partition function
Quantum Information Processing
Quantum Computation and the Evaluation of Tensor Networks
SIAM Journal on Computing
Permutational quantum computing
Quantum Information & Computation
Estimating Jones and Homfly polynomials with one clean qubit
Quantum Information & Computation
Quantum algorithms for invariants of triangulated manifolds
Quantum Information & Computation
On upper bounds for toroidal mosaic numbers
Quantum Information Processing
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It is known that evaluating a certain approximation to the Jones polynomial for the plat closure of a braid is a BQP-complete problem. That is, this problem exactly captures the power of the quantum circuit model[13, 3, 1]. The one clean qubit model is a model of quantum computation in which all but one qubit starts in the maximally mixed state. One clean qubit computers are believed to be strictly weaker than standard quantum computers, but still capable of solving some classically intractable problems [21]. Here we show that evaluating a certain approximation to the Jones polynomial at a fifth root of unity for the trace closure of a braid is a complete problem for the one clean qubit complexity class. That is, a one clean qubit computer can approximate these Jones polynomials in time polynomial in both the number of strands and number of crossings, and the problem of simulating a one clean qubit computer is reducible to approximating the Jones polynomial of the trace closure of a braid.