Quantum State Analysis and Optimal Logic Synthesis for Linear Nearest Neighbor Architecture

Abstract

Abstract: Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact. It is common to use a pair of SWAP gates to bring the control and target qubits of any quantum gate to adjacent lines and maintain correct circuit functionality. A new method to synthesize linear nearest neighbor quantum circuit was introduced on the base of the analysis of quantum state in circuit. For all 3-qubit quantum circuit, experimental results shows that our algorithm can reduce the quantum cost by approximately 30% on average compared with one recent proposed method.

CLC Number:

TP302.2

References

[1]Golubitsky O, Maslov D.A study of optimal 4-bit reversible toffoli circuits and their synthesis[J].IEEE Transactions on Computers, 2012, 61(9):1341-1353 [2]Patel Ketan N, Markov I L, Hayes J P.Optimal synthesis of linear reversible circuits[J].Quantum Information and Computation, 2008, 8(3):282-294 [3]Shende V V, Bullock S S, Markov I L.Synthesis of quantum-logic circuits[J].Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 2006, 25(6):1000-1010 [4]Shende V V, Prasad A K, Markov I L, Hayes J P.Synthesis of reversible logic circuits[J].Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 2003, 22(6):710-722 [5]Hung W N N, Song X, Yang G, et al.Optimal synthesis of multiple output Boolean functions using a set of quantum gates by symbolic reachability analysis[J].Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 2006, 25(9):1652-1663 [6]Yang G, Hung W N N, Song X, et al.Exact synthesis of 3-qubit quantum circuits from non-binary quantum gates using multiple-valued logic and group theory[C]//Proceedings of the conference on Design, Automation and Test in Europe-Volume 1. IEEE Computer Society, 2005: 434-435. [7]Maslov D, Miller D M.Comparison of the cost metrics through investigation of the relation between optimal NCV and optimal NCT three-qubit reversible circuits[J].IET Computers & Digital Techniques, 2007, 1(2):98-104 [8]Yang G, Song X, Perkowski M A, et al.Four-level realisation of 3-qubit reversible functions[J].IET Computers & Digital Techniques, 2007, 1(4):382-388 [9]Knill E, Laflamme R, Milburn G J.A scheme for efficient quantum computation with linear optics[J].Nature, 2001, 409(6816):46-52 [10]Laforest M, Simon D, Boileau J C, et al.Using error correction to determine the noise model[J].Physical Review A, 2007, 75(1):012331-012331 [11]H?ffner H, H?nsel W, Roos C F, et al.Scalable multiparticle entanglement of trapped ions[J].Nature, 2005, 438(7068):643-646 [12]Perkowski M, Lukac M, Shah D, Kameyama M.Synthesis of quantum circuits in linear nearest neighbor model using positive davio lattices[J].Facta universitatis-series: Electronics and Energetics, 2011, 24(1):71-87 [13]Saeedi M, Wille R, Drechsler R.Synthesis of quantum circuits for linear nearest neighbor architectures[J].Quantum Information Processing, 2011, 10(3):355-377 [14]AlFailakawi M, AlTerkawi L, Ahmad I, et al.Line ordering of reversible circuits for linear nearest neighbor realization[J].Quantum information processing, 2013, 12(10):3319-3339 [15]Hirata Y, Nakanishi M, Yamashita S, Nakashima Y.An efficient conversion of quantum circuits to a linear nearest neighbor architecture[J].Quantum Information & Computation, 2011, 11(1):142-166 [16]Matsuo A, Yamashita S.Changing the gate order for optimal lnn conversion[M]//Reversible Computation. Springer Berlin Heidelberg, 2012: 89-101. [17]Shafaei A, Saeedi M, Pedram M.Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures[C]//Proceedings of the 50th Annual Design Automation Conference. ACM, 2013: 41. [18]Wille R, Lye A, Drechsler R.Exact reordering of circuit lines for nearest neighbor quantum architectures[J].Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 2014, 33(12):1818-1831 [19]Lye A, Wille R, Drechsler R.Determining the minimal number of swap gates for multi-dimensional nearest neighbor quantum circuits[C]//Design Automation Conference (ASP-DAC), 2015 20th Asia and South Pacific. IEEE, 2015: 178-183. [20]Lee S, Lee S J, Kim T, et al.The cost of quantum gate primitives[J].Journal of multiple-valued logic and soft computing, 2006, 12(5):561-573