2. 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

3. 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.

4. 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

5. 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

6. 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

7. 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 ???

8. 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.

9. 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 ??? ? ?

10. Weird !