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Four problems

Four problems. Visit with Eddie Farhi’s theory group, MIT, Cambridge, MA January 28 th , 2007 @ 3:00PM EST Dr. Geordie Rose Founder and Chief Technology Officer. Problem #1: A practical adiabatic factoring algorithm.

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Four problems

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  1. Four problems Visit with Eddie Farhi’s theory group, MIT, Cambridge, MA January 28th, 2007 @ 3:00PM EST Dr. Geordie Rose Founder and Chief Technology Officer

  2. Problem #1: A practical adiabatic factoring algorithm Find an adiabatic algorithm for factoring an N-bit number that requires O(N) qubits and at most O(N3) time. Assume that the AQC hardware has Hamiltonian where ∆(t) must be non-negative and each physical qubit can be connected to a maximum of 10 other physical qubits, but the other parameters are arbitrary

  3. Problem #2: Passive quantum error correction Given a noise spectral density S(w) which is peaked at low frequencies and ohmic at high frequencies, a temperature T, and the AQC Hamiltonian in problem #1, find a threshold for S(w) and T under which an AQC can operate without changing the scaling of the algorithm being run

  4. Problem #3: Predicting performance Provide lower and upper bounds on the asymptotic scaling of exact adiabatic algorithms run on the system defined in problem #2 on at least one practically relevant QUBO instance class (machine learning with non-Mercer kernels; coding theory; image matching; lattice protein folding; generation of phylogenetic trees; lots of other very interesting problems) QUBO = Quadratic Unconstrained Binary Optimization; xi=[0,1], h,J  

  5. Problem #4: Harder but better version of #3 Provide lower and upper bounds on the asymptotic scaling of adiabatic algorithms run on the system defined in problem #2 on at least one practically relevant QUBO instance class for a -approximation algorithm

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