BQP^(Time Travel)

Well I’ve done it. I’ve gone completely crazy. The proof? Today I submitted a paper on what happens to quantum computation when you have access to a time machine. But of course physicists don’t like to say time machine, so the title of the paper is “Quantum Computational Complexity in the Presence of Closed Timelike Curves.” It can be found on my publication page and will appear on the arXiv monday.
Click below for the abstract

ABSTRACT
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D {bf 44}, 3197(1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve NP-complete problems with only a polynomial number of quantum gates.