Physics – Quantum Physics
Scientific paper
2008-08-19
Physics
Quantum Physics
15 pages
Scientific paper
10.1098/rspa.2008.0350
While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to nontrivial insights in general relativity, quantum information, and other areas. In this paper we show that if CTCs existed, then quantum computers would be no more powerful than classical computers: both would have the (extremely large) power of the complexity class PSPACE, consisting of all problems solvable by a conventional computer using a polynomial amount of memory. This solves an open problem proposed by one of us in 2005, and gives an essentially complete understanding of computational complexity in the presence of CTCs. Following the work of Deutsch, we treat a CTC as simply a region of spacetime where a "causal consistency" condition is imposed, meaning that Nature has to produce a (probabilistic or quantum) fixed-point of some evolution operator. Our conclusion is then a consequence of the following theorem: given any quantum circuit (not necessarily unitary), a fixed-point of the circuit can be (implicitly) computed in polynomial space. This theorem might have independent applications in quantum information.
Aaronson Scott
Watrous John
No associations
LandOfFree
Closed Timelike Curves Make Quantum and Classical Computing Equivalent does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Closed Timelike Curves Make Quantum and Classical Computing Equivalent, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Closed Timelike Curves Make Quantum and Classical Computing Equivalent will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-608640