Compiling Permutations for Superconducting QPUs

In this paper we consider the compilation of quantum state permutations into quantum gates for physical quantum computers. A sequence of generic single-target gates, which realize the input permutation, are extracted using a decomposition based reversible logic synthesis algorithm. We present a compilation algorithm that translates single-target gates into a quantum circuit composed of the elementary quantum gate sets that are supported by IBM’s 5-qubit and 16-qubit, and Rigetti’s 8-qubit and 19-qubit superconducting transmon QPUs. Compared to generic state-of-the-art compilation techniques, our technique improves gate volume and gate depth by up to 59% and 53%, respectively.

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

[2]  Dmitri Maslov,et al.  On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization , 2015, ArXiv.

[3]  Alexis De Vos,et al.  Young subgroups for reversible computers , 2008, Adv. Math. Commun..

[4]  Jens Siewert,et al.  Programmable networks for quantum algorithms. , 2003, Physical review letters.

[5]  Margaret Martonosi,et al.  Programming languages and compiler design for realistic quantum hardware , 2017, Nature.

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

[7]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[8]  Alán Aspuru-Guzik,et al.  Efficient quantum circuits for diagonal unitaries without ancillas , 2013, 1306.3991.

[9]  Igor L. Markov,et al.  Synthesis and optimization of reversible circuits—a survey , 2011, CSUR.

[10]  Michele Mosca,et al.  On the CNOT-complexity of CNOT-PHASE circuits , 2017, 1712.01859.

[11]  Blake R. Johnson,et al.  Unsupervised Machine Learning on a Hybrid Quantum Computer , 2017, 1712.05771.

[12]  Dmitri Maslov,et al.  Complete 3-Qubit Grover search on a programmable quantum computer , 2017, Nature Communications.

[13]  Stefan Frehse,et al.  RevKit: A Toolkit for Reversible Circuit Design , 2012, J. Multiple Valued Log. Soft Comput..

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

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