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Samuel J. Lomonaco, Jr. Dept. of Comp. Sci. & Electrical Engineering

Simon ’ s Algorithm: A Benchmork for the D-Wave Computer. 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.

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Samuel J. Lomonaco, Jr. Dept. of Comp. Sci. & Electrical Engineering

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

  2. Different Models of Q. Computation Quantum Turing Machine Gate Model Measurement Based Q. Comp. Adiabatic Model Topological Q. Comp. TheD-Wave Computer is based on theadiabatic model.

  3. BasicQuantumMechanics: If • is a quantum system in state • is a Hamiltonian of as a function of time . Then evolves via Schroedinger’s eq AdiabaticApproximation: If • started in lowest En. State of • changes slowly Then remains in L.E.S. of

  4. 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

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

  6. Question ??? Question: Is D-Wave Computer a Quantum Computer ??? 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: Does the time complexity of D-Wave scale like a quantum computer, or like a classical one?

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

  8. Proposed Project Run Simon’s algorithm on the D-Wave to see how the algorithm scales. ? Plot of ? ? ComputationTime ? ? Numberof qubits 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.

  9. Weird !

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