Quantum learning by measurement and feedback

We investigate an approach to quantum computing in which quantum gate strengths are parametrized by quantum degrees of freedom. The capability of the quantum computer to perform desired tasks is monitored by measurements of the output and gradually improved by successive feedback modifications of the coupling strength parameters. Our proposal uses only information available in an experimental implementation and is demonstrated with simulations on search and factoring algorithms.

[1]  Barenco,et al.  Approximate quantum Fourier transform and decoherence. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[2]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[3]  Rocco A. Servedio,et al.  Improved Bounds on Quantum Learning Algorithms , 2004, Quantum Inf. Process..

[4]  Prem Kumar,et al.  Quantum algorithm design using dynamic learning , 2008, Quantum Inf. Comput..

[5]  Masahide Sasaki,et al.  Quantum learning and universal quantum matching machine , 2002 .

[6]  Lov K. Grover.  Quantum Computers Can Search Rapidly by Using Almost Any Transformation , 1998 .

[7]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[8]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[9]  G. Gerber,et al.  Photoselective adaptive femtosecond quantum control in the liquid phase , 2001, Nature.

[10]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[11]  V. Kendon,et al.  A random walk approach to quantum algorithms , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  M. Zak.  Quantum Analog Computing , 1999 .

[13]  Marcus Motzkus,et al.  Quantum control of energy flow in light harvesting , 2002, Nature.

[14]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[15]  Jeongho Bang,et al.  Quantum Learning Machine , 2008, 0803.2976.

[16]  Ujjwal Sen,et al.  Trapped ion chain as a neural network: error resistant quantum computation. , 2007, Physical review letters.

[17]  X Wang,et al.  Multibit gates for quantum computing. , 2001, Physical review letters.

[18]  Peter W. Glynn,et al.  Stochastic Simulation: Algorithms and Analysis , 2007 .

[19]  R. Brockett,et al.  Time optimal control in spin systems , 2000, quant-ph/0006114.