Optimizing Quantum Circuits by One-Way Quantum Computation Model Based on Pattern Geometries
Subject Areas : electrical and computer engineering
M.
Eslamy
1
M.
Saheb Zamani
2
(Amirkabir University of Technology)
M.
Sedighi
3
M.
Houshmand
4
(دانشگاه آزاد اسلامی، واحد مشهد)
Abstract :
A fundamentally quantum model of computation based on quantum entanglement and quantum measurement is called one-way quantum computation model (1WQC). Computations are shown by measurement patterns (or simply patterns) in this model where an initial highly entangled state called a graph state is used to perform universal quantum computations. This graph together with the set of its input and output qubits is called the geometry of the pattern. Moreover, some optimization techniques have been introduced to simplify patterns. Previously, the 1WQC model has been applied to optimize quantum circuits. An approach for parallelizing quantum circuits has been proposed which takes a quantum circuit and then produces the corresponding pattern after performing the proposed optimization techniques for this model. Then it translates the optimized 1WQC patterns back to quantum circuits to parallelize the initial quantum circuit by using a set of rewriting rules. To improve previous works, in this paper, a new automatic approach is proposed to optimize patterns based on their geometries instead of using rewriting rules by applying optimization techniques simultaneously. Moreover, the optimized pattern is translated back to a quantum circuit and then this circuit is simplified by decreasing the number of auxiliary qubits. Results show that the quantum circuit cost metrics of the proposed approach is improved as compared to the previous ones.
[1] M. Nakahara and T. Ohmi, Quantum Computing: From Linear Algebra to Physical Realizations, Taylor & Francis, 2008.
[2] M. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2011.
[3] G. Benenti, G. Strini, and G. Casati, Principles of Quantum Computation and Information, World Scientific, 2004.
[4] P. W. Shor, "Algorithms for quantum computation: discrete logarithms and factoring," in Proc. Foundations of Computer Science, Proc. of the 35th Annual Symp. on Foundations of Computer Science, pp. 124-134, Nov. 1994.
[5] L. K. Grover, "A fast quantum mechanical algorithm for database search," in Proc. of ACM Symp. on Theory of Computing, pp. 183-191, 22-24 May 1996.
[6] R. Landauer, "Irreversibility and heat generation in the computing process," IBM J. of Research and Development, vol. 5, no. 3, pp. 183-191, Jul. 1961.
[7] R. Jozsa, "An introduction to measurement based quantum computation," NATO Science Series, III: Computer and Systems Sciences. Quantum Information Processing-from Theory to Experiment, vol. 199, pp. 137-158, Nov. 2006.
[8] H. Briegel, et al., "Measurement-based quantum computation," Natur Physics, vol. 5, no. 1, pp. 19-26, Jan. 2009.
[9] D. Gottesman and I. L. Chuang, "Quantum teleportation is a universal computational primitive," arXiv preprint quant-ph/9908010, 1999.
[10] R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Physical Review Letters, vol. 86, no. 22, p. 5188, May 2001.
[11] D. E. Browne and H. J. Briegel, One-Way Quantum Computation - A Tutorial Introduction, 2nd Ed., 2006.
[12] M. Hein, et al., "Entanglement in graph states and its applications," arXiv preprint quant-ph/0602096, Feb. 2006.
[13] M. Mhalla and S. Perdrix, "Finding optimal flows efficiently," Automata, Languages, and Programming, Springer, vol. 5125, pp. 857-868, 2008.
[14] A. Broadbent and E. Kashefi, "Parallelizing quantum circuits," Theoretical Computer Science, vol. 410, no. 26, pp. 2489-2510, Jun. 2009.
[15] E. Pius, Automatic Parallelisation of Quantum Circuits Using the Measurement Based Quantum Computing Model, M.Sc. in High Performance Computing, University of Edinburgh, p. 65, 2010.
[16] R. D. Da Silva and E. F. Galvao, "Compact quantum circuits from one-way quantum computation," Physical Review A, vol. 88, no. 1, p. 012319, Jul. 2013.
[17] D. McMahon, Quantum Computing Explained, John Wiley & Sons, 2007.
[18] A. U. Khalid, Z. Zilic, and K. Radecka, "FPGA emulation of quantum circuits," in Proc. IEEE Int. Conf. Computer Design: VLSI in Computers and Processors, ICCD'04, pp. 310-315, Oct. 2004.
[19] V. Danos, E. Kashefi, and P. Panangaden, "The measurement calculus," J. of the ACM, vol. 54, no. 2, p. 8, Apr. 2007.
[20] V. Danos, E. Kashefi, P. Panangaden, and S. Perdrix, "Extended measurement calculus," in S. J. Gay and I. Mackie, eds., Semantic Techniques in Quantum Computation, Ch. 7, pp. 235-310, Cambridge University Press, 2009.
[21] D. E. Browne, E. Kashefi, M. Mhalla, and S. Perdrix, "Generalized flow and determinism in measurement-based quantum computation," New J. of Physics, vol. 9, no. 8, 16 pp., Aug. 2007.
[22] V. Danos, E. Kashefi, and P. Panangaden, "Parsimonious and robust realizations of unitary maps in the one-way model," Physical Review A, vol. 72, no. 6, p. 064301, Dec. 2005.
[23] S. S. Bullock and I. L. Markov, "Arbitrary two-qubit computation in 23 elementary gates," Physical Review A, vol. 68, no. 1, pp. 324-329, Jul. 2003.
[24] S. S. Bullock and I. L. Markov, "Smaller circuits for arbitrary n-qubit diagonal computations," arXiv preprint quant-ph/0303039, 2003.
[25] N. D. Beaudrap, "Finding flows in the one-way measurement model," Physical Review A, vol. 77, no. 2, 8 pp., Feb. 2008.
[26] V. Danos and E. Kashefi, "Determinism in the one-way model," Physical Review A, vol. 74, no. 5, p. 052310, Nov. 2006.
[27] R. D. da Silva, E. Pius, and E. Kashefi, "Global quantum circuit optimization," arXiv Preprint arXiv: 1301.0351, 2013.
[28] M. Houshmand, M. Saheb Zamani, M. Sedighi, and M. H.n Samavatian, "Automatic translation of quantum circuits to optimized one-way quantum computation patterns," Quantum Information Processing, vol. 13, no. 11, pp. 24632482, Nov. 2014.