Quantum and classical parallelism in parity algorithms for ensemble quantum computers
- University of Dortmund Department of Computer Science, 44221 Dortmund (Germany)
- University of Dortmund, Department of Physics, 44221 Dortmund (Germany)
- Memorial University of Newfoundland, Department of Computer Science, St. John's, NL, A1B 3X5 (Canada)
The determination of the parity of a string of N binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least N/2 oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor 2{sup k}, with k is a member of {l_brace}{l_brace}1,2,...,log{sub 2}(N/2{r_brace}{r_brace}, provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.
- OSTI ID:
- 20650383
- Journal Information:
- Physical Review. A, Vol. 71, Issue 3; Other Information: DOI: 10.1103/PhysRevA.71.032345; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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