The Study of Simulation Technique of Quantum Compute and Quantum Fourier Transform

For discussing the solving methods of NP problems in classical computers and studying the circuit model which is the most representative in quantum computing to simulate the compute processes, this article discussed how to simulate the quantum Fourier transform by using the quantum logic gates, implemented the quantum Fourier transform and constructed the quantum information and compute simulation platform. The experiment introduced the quantum register structure to be the storage medium, which is better than the form of matrix in space. The operation processes adopted the bit manipulation to avoid the mass time for matrix multiplications. The results presented the changes of quantum amplitudes and probabilities of quantum states according to the quantum effect and compared with the approximate quantum Fourier transform. The experimental platform provided a groundwork for the further simulations of other important quantum algorithms and quantum circuits.

[1]  D. Deutsch Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  Barenco,et al.  Conditional Quantum Dynamics and Logic Gates. , 1995, Physical review letters.

[3]  R. Feynman Quantum mechanical computers , 1986 .

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

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

[6]  L M Vandersypen,et al.  Experimental realization of an order-finding algorithm with an NMR quantum computer. , 2000, Physical review letters.

[7]  Ioannis Karafyllidis,et al.  Quantum computer simulator based on the circuit model of quantum computation , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  D. Coppersmith An approximate Fourier transform useful in quantum factoring , 2002, quant-ph/0201067.

[10]  Ioannis Karafyllidis,et al.  Visualization of the Quantum Fourier Transform Using a Quantum Computer Simulator , 2003, Quantum Inf. Process..

[11]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

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

[13]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[14]  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.

[15]  Michele Mosca,et al.  The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer , 1998, QCQC.