Physics – Quantum Physics
Scientific paper
2011-01-27
Physics
Quantum Physics
23 pages, 2 figures
Scientific paper
We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising result that we prove: a quantum finite automaton with just two states can be sensitive to arbitrarily small changes in a coin's bias. This contrasts with classical probabilistic finite automata, whose sensitivity to changes in a coin's bias is bounded by a classic 1970 result of Hellman and Cover. Despite this finding, we are able to bound the power of advice coins for space-bounded classical and quantum computation. We define the classes BPPSPACE/coin and BQPSPACE/coin, of languages decidable by classical and quantum polynomial-space machines with advice coins. Our main theorem is that both classes coincide with PSPACE/poly. Proving this result turns out to require substantial machinery. We use an algorithm due to Neff for finding roots of polynomials in NC; a result from algebraic geometry that lower-bounds the separation of a polynomial's roots; and a result on fixed-points of superoperators due to Aaronson and Watrous, originally proved in the context of quantum computing with closed timelike curves.
Aaronson Scott
Drucker Andrew
No associations
LandOfFree
Advice Coins for Classical and Quantum Computation 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 Advice Coins for Classical and Quantum Computation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Advice Coins for Classical and Quantum Computation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-546012