Complexity Classes as Mathematical Axioms II
Shawn X. Cui, Michael H. Freedman, Zhenghan Wang
TL;DR
This paper explores how certain quantum complexity class separation axioms, viewed as mathematical axioms, impose limitations on diagram simplifications, showing they cannot achieve even linear reductions.
Contribution
It extends previous work by analyzing more subtle quantum complexity separation axioms and demonstrating their constraints on diagram simplification.
Findings
Quantum axioms prevent exponential diagram simplifications
Similar strings cannot achieve linear diagram reductions
Extends classical complexity topology connections
Abstract
The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simplifications of link diagrams. In this paper, we continue this theme, exploring now more subtle separation axioms for quantum complexity classes. Surprisingly, we now find that similar strings are unable to effect even linear simplifications of the diagrams.
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