Monte-Carlo approximation algorithms for enumeration problems
Journal of Algorithms
SIAM Journal on Computing
Complexity limitations on Quantum computation
Journal of Computer and System Sciences
Yang-Baxterizations, Universal Quantum Gates and Hamiltonians
Quantum Information Processing
A polynomial quantum algorithm for approximating the Jones polynomial
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
Quantum Information & Computation
Quantum automata, braid group and link polynomials
Quantum Information & Computation
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Motivated by the result that an ‘approximate’ evaluation of the Jones polynomial of a braid at a 5th root of unity can be used to simulate the quantum part of any algorithm in the quantum complexity class BQP, and results relating BQP to the counting class GapP, we introduce a form of additive approximation which can be used to simulate a function in BQP. We show that all functions in the classes #P and GapP have such an approximation scheme under certain natural normalizations. However, we are unable to determine whether the particular functions we are motivated by, such as the above evaluation of the Jones polynomial, can be approximated in this way. We close with some open problems motivated by this work.