An improved heuristic technique for nearest neighbor realization of quantum circuits in 2D architecture

Abstract Last couple of years has witnessed tremendous advancements in the field of quantum computing and even it has started providing technological footprints in the design industry. Though advancements in the physical implementation of quantum circuits has taken a giant leap but it has faced with several design challenges and one such design constraint is Nearest Neighbor (NN) criteria which demands the operating qubits of the quantum gates to be adjacent. Focusing on the design issue, here, we show a heuristic design technique for efficient transformation of quantum circuits to NN based designs in 2D configuration. Our entire strategy is based on initial qubit mapping policy, where we have introduced three different mapping techniques 1) Influence Index, 2) Adjacency Matrix and 3) Distance Ratio based strategy. After placing the qubits in appropriate positions, we also undertake a dynamic windowing based local reordering scheme to further reduce the SWAP requirement in the designs. At the end of the work, to check the effectiveness of our transformation algorithms, we have tested a wide range of benchmarks over our algorithms and a comparative study over state-of-the-art design techniques also has been undertaken.

[1]  Amlan Chakrabarti,et al.  2D Qubit Placement of Quantum Circuits Using LONGPATH , 2019, ACSS.

[2]  Naser Mohammadzadeh,et al.  Mapping quantum circuits on 3D nearest-neighbor architectures , 2019, Quantum Science and Technology.

[3]  Yuan Feng,et al.  Quantum Circuit Transformation Based on Simulated Annealing and Heuristic Search , 2019, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[4]  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).

[5]  O. Gühne,et al.  03 21 7 2 3 M ar 2 00 6 Scalable multi-particle entanglement of trapped ions , 2006 .

[6]  Gushu Li,et al.  Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices , 2018, ASPLOS.

[7]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[8]  Robert Wille,et al.  A Novel Approach for Nearest Neighbor Realization of 2D Quantum Circuits , 2018, 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI).

[9]  M. Lukin,et al.  Relaxation, dephasing, and quantum control of electron spins in double quantum dots , 2006, cond-mat/0602470.

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

[11]  Robert Wille,et al.  Realizing reversible circuits using a new class of quantum gates , 2012, DAC Design Automation Conference 2012.

[12]  Hafizur Rahaman,et al.  A template-based technique for efficient Clifford+T-based quantum circuit implementation , 2018, Microelectron. J..

[13]  Daniel Park,et al.  Recent advances in nuclear magnetic resonance quantum information processing , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  Aram W. Harrow,et al.  Using Spectral Graph Theory to Map Qubits onto Connectivity-limited Devices , 2019 .

[15]  Robert Wille,et al.  Look-ahead schemes for nearest neighbor optimization of 1D and 2D quantum circuits , 2016, 2016 21st Asia and South Pacific Design Automation Conference (ASP-DAC).

[16]  Alexandre Blais,et al.  Quantum information processing with circuit quantum electrodynamics , 2007 .

[17]  Kamalika Datta,et al.  Fast Qubit Placement in 2D Architecture Using Nearest Neighbor Realization , 2015, 2015 IEEE International Symposium on Nanoelectronic and Information Systems.

[18]  Robert Wille,et al.  Exact Global Reordering for Nearest Neighbor Quantum Circuits Using A ^* ∗ , 2017, RC.

[19]  Masaki Nakanishi,et al.  An efficient conversion of quantum circuits to a linear nearest neighbor architecture , 2011, Quantum Inf. Comput..

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

[21]  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.

[22]  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.

[23]  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).

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

[25]  C. Monroe,et al.  Architecture for a large-scale ion-trap quantum computer , 2002, Nature.

[26]  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.

[27]  Kamalika Datta,et al.  A Heuristic for Linear Nearest Neighbor Realization of Quantum Circuits by SWAP Gate Insertion Using $N$-Gate Lookahead , 2016, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[28]  D. Michael Miller,et al.  Transforming MCT Circuits to NCVW Circuits , 2011, RC.

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

[30]  Adriano Masone,et al.  Swap Minimization in Nearest Neighbour Quantum Circuits: An ILP Formulation , 2019 .

[31]  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.

[32]  Robert Wille,et al.  Elementary Quantum Gate Realizations for Multiple-Control Toffoli Gates , 2011, 2011 41st IEEE International Symposium on Multiple-Valued Logic.