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
Mathematics of Quantum Computation and Quantum Technology
Mathematics of Quantum Computation and Quantum Technology
Quantum Information Processing
Estimating Jones polynomials is a complete problem for one clean qubit
Quantum Information & Computation
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In this paper, we construct mosaic representations of knots on the torus, rather than in the plane. This consists of a particular choice of the ambient group $$\mathbb{A }$$, as well as different Definitions of contiguous and suitably connected. We present conditions under which mosaic numbers might decrease by this projection, and present a tool (called waste) to measure this reduction. We show that the order of edge identification in construction of the torus sometimes yields different resultant knots from a given mosaic when reversed. Additionally, in the Appendix we give the catalog of all torus $$2$$-mosaics.