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Challenges in Adiabatic Quantum Computing: Algorithms, Error Correction, and Performance Bounds

On January 28, 2007, Dr. Geordie Rose, Founder and CTO of D-Wave Systems, presented four critical problems concerning adiabatic quantum computing (AQC) during a visit to Eddie Farhi's theory group at MIT. The discussion encompassed developing a practical factoring algorithm requiring O(N) qubits, formulating passive quantum error correction under specific noise conditions, predicting asymptotic performance bounds for exact adiabatic algorithms, and exploring improved scaling for QUBO instances. This session highlighted the intersection of theoretical concepts and implementation challenges in quantum computing.

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Challenges in Adiabatic Quantum Computing: Algorithms, Error Correction, and Performance Bounds

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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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