Swap Minimization in Nearest Neighbour Quantum Circuits: An ILP Formulation

Quantum computing (QC) represents a great challenge for both academia and private companies and it is currently pursuing the development of quantum algorithms and physical realizations of quantum computers. Quantum algorithms exploit the concept of quantum bit (qubit). They are implemented by designing circuits which consider an ideal quantum computer where no interaction restriction between qubits is imposed. However, physical realizations of quantum computers are subject to several technological constraints and adjacency between interacting qubits is one of the most common one. To this end, additional gates, referred to as swap, can be added to a quantum circuit to make it nearest neighbour compliant. These additional gates have a cost in terms of reliability of the quantum system, hence their number should be minimized. In this paper we first give some hints about this cutting edge topic. Then we provide a review of the literature solving approaches for the swap minimization problem in quantum circuits and propose an integer linear programming formulation for it. We conclude with some preliminary results on small test instances and future work perspectives.

[1]  Alireza Shafaei,et al.  Qubit placement to minimize communication overhead in 2D quantum architectures , 2014, 2014 19th Asia and South Pacific Design Automation Conference (ASP-DAC).

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

[3]  Robert Wille,et al.  Compiling SU(4) quantum circuits to IBM QX architectures , 2018, ASP-DAC.

[4]  Robert Wille,et al.  Synthesis of quantum circuits for linear nearest neighbor architectures , 2011, Quantum Inf. Process..

[5]  Robert Wille,et al.  Determining the minimal number of swap gates for multi-dimensional nearest neighbor quantum circuits , 2015, The 20th Asia and South Pacific Design Automation Conference.

[6]  Xiaoyu Song,et al.  Quantum Circuit Synthesis using a New Quantum Logic Gate Library of NCV Quantum Gates , 2016, International Journal of Theoretical Physics.

[7]  Pedro Chamorro-Posada,et al.  Equivalent Quantum Circuits , 2011, 1110.2998.

[8]  Robert Wille,et al.  Exact Reordering of Circuit Lines for Nearest Neighbor Quantum Architectures , 2014, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[9]  Anupam Chattopadhyay,et al.  Depth-Optimal Quantum Circuit Placement for Arbitrary Topologies , 2017, ArXiv.

[10]  Robert Wille,et al.  Optimal SWAP gate insertion for nearest neighbor quantum circuits , 2014, 2014 19th Asia and South Pacific Design Automation Conference (ASP-DAC).

[11]  Imtiaz Ahmad,et al.  Line ordering of reversible circuits for linear nearest neighbor realization , 2013, Quantum Information Processing.

[12]  Kamalika Datta,et al.  A New Heuristic for $N$ -Dimensional Nearest Neighbor Realization of a Quantum Circuit , 2018, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[13]  Mozammel H. A. Khan,et al.  Cost Reduction in Nearest Neighbour Based Synthesis of Quantum Boolean Circuits , 2008, Eng. Lett..

[14]  Yang Liu,et al.  Multi-strategy based quantum cost reduction of linear nearest-neighbor quantum circuit , 2018, Quantum Inf. Process..

[15]  Rachel Courtland,et al.  Google aims for quantum computing supremacy [News] , 2017 .

[16]  Susmita Sur-Kolay,et al.  Nearest Neighbour based Synthesis of Quantum Boolean Circuits , 2007, Eng. Lett..

[17]  Tibérius O. Bonates,et al.  Minimum Linear Arrangements , 2017, Electron. Notes Discret. Math..

[18]  Robert Wille,et al.  An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures , 2017, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[19]  Alireza Shafaei,et al.  Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures , 2013, 2013 50th ACM/EDAC/IEEE Design Automation Conference (DAC).

[20]  Imtiaz Ahmad,et al.  Harmony-search algorithm for 2D nearest neighbor quantum circuits realization , 2016, Expert Syst. Appl..