A genetic-algorithm-based method to find unitary transformations for any desired quantum computation and application to a one-bit oracle decision problem

We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the “genetic parameter vector” of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the often-called Deutsch problem. By numerical simulations, we can faithfully find the appropriate unitary transformations to solve the problem by using our method. We analyze the quantum algorithms identified by the found unitary transformations and generalize the variant models of the original Deutsch’s algorithm.

[1]  Franz Rothlauf,et al.  Representations for genetic and evolutionary algorithms , 2002, Studies in Fuzziness and Soft Computing.

[2]  Helmut G. Katzgraber,et al.  Genetic braid optimization: A heuristic approach to compute quasiparticle braids , 2012, ArXiv.

[3]  John J. Oh,et al.  Application of machine learning algorithms to the study of noise artifacts in gravitational-wave data , 2013, 1303.6984.

[4]  Darrell Whitley,et al.  A genetic algorithm tutorial , 1994, Statistics and Computing.

[5]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[6]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[7]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[8]  Gerber,et al.  Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses , 1998, Science.

[9]  Singlet-state creation and universal quantum computation in NMR using a genetic algorithm , 2012, 1205.4294.

[10]  Geometric manipulation of the quantum states of two-level atoms , 2004 .

[11]  H. Rosu,et al.  Genetic Algorithm Optimization of Entanglement , 2006, quant-ph/0604126.

[12]  G. D’Ariano,et al.  Optimal quantum learning of a unitary transformation , 2009, 0903.0543.

[13]  Mikio Nakahara,et al.  A quantum genetic algorithm with quantum crossover and mutation operations , 2012, Quantum Inf. Process..

[14]  Wei Chu,et al.  A new evolutionary search strategy for global optimization of high-dimensional problems , 2011, Inf. Sci..

[15]  W. Son,et al.  d-outcome measurement for a nonlocality test , 2003, quant-ph/0309193.

[16]  Jaehyun Kim,et al.  Implementing unitary operators in quantum computation , 2000 .

[17]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[18]  Haldun Aytug,et al.  Stopping Criteria for Finite Length Genetic Algorithms , 1996, INFORMS J. Comput..

[19]  George Cybenko,et al.  Reducing quantum computations to elementary unitary operations , 2001, Comput. Sci. Eng..

[20]  Majid Mohammadi,et al.  Heuristic methods to use don’t cares in automated design of reversible and quantum logic circuits , 2008, Quantum Inf. Process..

[21]  S Forrest,et al.  Genetic algorithms , 1996, CSUR.

[22]  J. Audretsch.  Entangled Systems: New Directions in Quantum Physics , 2007 .

[23]  Jeongho Bang,et al.  A strategy for quantum algorithm design assisted by machine learning , 2013, 1301.1132.

[24]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[25]  H. Rabitz,et al.  Teaching lasers to control molecules. , 1992, Physical review letters.

[26]  J. Eberly,et al.  N-Level Coherence Vector and Higher Conservation Laws in Quantum Optics and Quantum Mechanics , 1981 .

[27]  Elham Kashefi,et al.  Comparison of quantum oracles , 2002 .

[28]  Sabre Kais,et al.  Decomposition of Unitary Matrices for Finding Quantum Circuits , 2010, The Journal of chemical physics.

[29]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[30]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[31]  Daniel A. Lidar,et al.  Optimized dynamical decoupling via genetic algorithms , 2013 .

[32]  Procedures for realizing an approximate universal-NOT gate , 2012, 1208.2111.