Search for New Quantum Algorithms

Abstract

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching data sources, Gathering and maintaining the data needed, and completing and reviewing the collection of information. SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)DARPA AFRL-IF-RS-TR-2006-180 DISTRIBUTION AVAILABILITY STATEMENTApproved for public release; distribution unlimited. PA# 06-356 SUPPLEMENTARY NOTES ABSTRACTThe first objective of this effort, searching for new quantum algorithms, created six new quantum hidden subgroup algorithms. The second objective, improving the theoretical understanding of existing quantum algorithms, produced three new systematic procedures. Also, application of combinatorial group theory led to substantial progress in the understanding and analysis of nonabelian quantum hidden subgroup algorithms. Additionally, methods and techniques of quantum topology have been used to obtain new results in quantum computing including discovery of a relationship between quantum entanglement and topological linking. The last objective, analyzing issues associated with algorithm implementation proposed distributed quantum computing (DQC) as a fast track to scalable quantum computing with technology available within the next five years. A universal set of DQC primitives has been created and used to transform the quantum Fourier transform and the Shor algorithm into DQC. The additional computational overhead needed for DQC algorithms is insignificant and DQC is found to simplify the decoherence problem. SUBJECT TERMSquantum algorithms, quantum hidden subgroup algorithms, hidden subgroups, distributed quantum computation, distributed algorithms, Shor's algorithm, Grover's algorithm, non-abelian quantum hidden subgroup algorithms, decoherence, quantum computer architectures, topological quantum computation, quantum gates, anyonic computation SECURITY

Electro-Optical and Optical Components for Processor to Processor Interconnects

“…And, decoherence problems which typically plague quantum systems are reduced using such a scheme. AFRL has sponsored theoretical work on distributed quantum computing 16 .Our quantum computing team planned research on small optical quantum "subprocessor" circuits interconnected with classical channels to test the overall concept in simulation and then in hardware. Techniques to translate existing quantum algorithms into efficient distributed algorithms which would then be run on the DQC would also be investigated.…”

Models of quantum computation and quantum programming languages

“…Taking into account research efforts focused on discovering new quantum algorithms it is surprising that for the last ten years no similar results have been obtained [19,20]. One should note that there is no proof that quantum computers can actually solve NP-complete problems in polynomial time [21,22].…”

“…One should note that the development of quantum algorithms is still a very lively area of research [20,32]. General introduction to quantum algorithms can be found in [33].…”