Two-way quantum computers – enhancement of 1WQC to solve NP problems
arxiv.org
arxiv.org
This is enhancement of standard one-way quantum computers (1WQC) by adding missing operation: "reversed" version (CPT symmetry analog) of state preparation (e.g. pull/push, negative/positive pressure, stimulated emission/absorption). There are many arguments it should be possible, but needs experimental confirmation.
In theory this enhancement allows to attack any NP problems, but it likely will be more difficult than Shor's factorization - so might be completely impractical (?)
There are many interesting new question - like of theoretical complexity class for such 2WQC, somewhere between NP and PSPACE?
There might appear also different approaches to NP, so maybe it would be safer to start thinking of cryptography based on PSPACE? https://en.wikipedia.org/wiki/PSPACE-complete