- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2016
1
Complexity classes as mathematical axioms II
Shawn
Cui
University of California, SANTA BARBARA, UNITED STATES
Michael
Freedman
University of California, SANTA BARBARA, UNITED STATES
Zhenghan
Wang
University of California, SANTA BARBARA, UNITED STATES
Complexity class, Link diagram, Jones polynomial
The second author previously discussed how classical complexity separation conjectures, we call them “axioms,” have implications in three manifold topology: polynomial length strings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simpli cations of link diagrams. In this paper, we continue this theme, exploring now more subtle separation axioms for quantum complexity classes. Surprisingly, we now fi nd that similar strings of operations are unable to eff ect even linear simpli cations of the diagrams.
Manifolds and cell complexes
Computer science
Quantum theory
185
201
10.4171/QT/75
http://www.ems-ph.org/doi/10.4171/QT/75