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Samuel J. Lomonaco, Jr. Dept. of Comp. Sci. & Electrical Engineering University of Maryland Baltimore County Baltimore, MD 21250 Email: Lomonaco@UMBC.EDU WebPage: http://www.csee.umbc.edu/~lomonaco Simons Algorithm: A Benchmork for the D-Wave Computer

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The D-Wave Computer is based on the adiabatic model. Different Models of Q. Computation Gate Model Quantum Turing Machine Measurement Based Q. Comp. Adiabatic Model Topological Q. Comp.

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Basic Quantum MechanicsIf Basic Quantum Mechanics: If is a quantum system in state is a Hamiltonian of as a function of time. Then Then evolves via Schroedingers eq Adiabatic ApproximationIf Adiabatic Approximation: If started in lowest En. State of changes slowly Then Then remains in L.E.S. of

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Adiabatic Quantum Computation Select simple Hamiltonian with easily prepared L.E.S. Design a Hamiltonian whose L.E.S. provides answer to chosen problem P. Construct a q. system with Hamiltonian Start in state Slowly change the parameter until system reaches state Measure the state

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Question ??? Question: Question: Is D-Wave Computer a Quantum Computer ??? Or is it simply computing according to the laws of classical physics ??? Aaronson & Vazirani Most likely NOT. Because system qubits decohere much faster than instruction execution time

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Question ??? But the D-Wave is based on the adiabatic approximation. So it is the decoherence of the L.E.S. that is the central issue. Key Question scale Key Question: Does the time complexity of D- Wave scale like a quantum computer, or like a classical one? Question: Question: Is D-Wave Computer a Quantum Computer ???

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Simons Algorithm But Simons quantum algorithm solves the above problem in polytime !!! Theorem Theorem: (Simon) All classical algorithms take at least exponential time to solve the above problem. Given a 2-to-1 function with unknown period, i.e., such that for all, find the period. Simons Problem: Simons Problem: Let be n-D vector space over the finite field.

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Proposed Project Run Simons algorithm on the D-Wave to see how the algorithm scales. If the above plot shows that T(n) is bounded above by a polynomial, then the D-Wave is most likely a quantum computer. If not, then the D-Wave is most likely another classical computer. Plot of Computation Time Number of qubits ??? ? ?

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Weird !

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