Reversible Pebble Games for Reducing Qubits in Hierarchical Quantum Circuit Synthesis

Hierarchical reversible logic synthesis can find quantum circuits for large combinational functions. The price for a better scalability compared to functional synthesis approaches is the requirement for many additional qubits to store temporary results of the hierarchical input representation. However, implementing a quantum circuit with large number of qubits is a major hurdle. In this paper, we demonstrate and establish how reversible pebble games can be used to reduce the number of stored temporary results, thereby reducing the qubit count. Our proposed algorithm can be constrained with number of qubits, which is aimed to meet. Experimental studies show that the qubit count can be significantly reduced (by up to 63.2%) compared to the state-of-the-art algorithms, at the cost of additional gate count.

[1]  Robert Wille,et al.  Integrated Synthesis of Linear Nearest Neighbor Ancilla-Free MCT Circuits , 2016, 2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL).

[2]  Giovanni De Micheli,et al.  A best-fit mapping algorithm to facilitate ESOP-decomposition in Clifford+T quantum network synthesis , 2018, 2018 23rd Asia and South Pacific Design Automation Conference (ASP-DAC).

[3]  Siu Man Chan.  Just a Pebble Game , 2013, 2013 IEEE Conference on Computational Complexity.

[4]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[5]  Malay K. Ganai,et al.  Robust Boolean reasoning for equivalence checking and functional property verification , 2002, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[6]  Giovanni De Micheli,et al.  Logic Synthesis for Quantum Computing , 2017, ArXiv.

[7]  Ravi Sethi,et al.  Complete register allocation problems , 1973, SIAM J. Comput..

[8]  John Preskill,et al.  Quantum computing and the entanglement frontier , 2012, 1203.5813.

[9]  Giovanni De Micheli,et al.  Hierarchical reversible logic synthesis using LUTs , 2017, 2017 54th ACM/EDAC/IEEE Design Automation Conference (DAC).

[10]  Jason Cong,et al.  DAOmap: a depth-optimal area optimization mapping algorithm for FPGA designs , 2004, ICCAD 2004.

[11]  Mikhail I. Dyakonov,et al.  Is Fault-Tolerant Quantum Computation Really Possible? , 2006, quant-ph/0610117.

[12]  Giovanni De Micheli,et al.  Majority-Inverter Graph: A New Paradigm for Logic Optimization , 2016, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[13]  John A. Gunnels,et al.  Breaking the 49-Qubit Barrier in the Simulation of Quantum Circuits , 2017, 1710.05867.

[14]  M. Mosca,et al.  A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits , 2012, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[15]  Charles H. Bennett.  Time/Space Trade-Offs for Reversible Computation , 1989, SIAM J. Comput..

[16]  Matthew Amy.  Algorithms for the Optimization of Quantum Circuits , 2013 .

[17]  Rolf Drechsler,et al.  Ancilla-free synthesis of large reversible functions using binary decision diagrams , 2016, J. Symb. Comput..

[18]  Robert Wille,et al.  Trading off circuit lines and gate costs in the synthesis of reversible logic , 2014, Integr..

[19]  Martin Rötteler,et al.  Reversible circuit compilation with space constraints , 2015, ArXiv.

[20]  Robert K. Brayton,et al.  Mapping into LUT structures , 2012, 2012 Design, Automation & Test in Europe Conference & Exhibition (DATE).

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

[22]  Mathias Soeken,et al.  Unlocking efficiency and scalability of reversible logic synthesis using conventional logic synthesis , 2016, 2016 53nd ACM/EDAC/IEEE Design Automation Conference (DAC).

[23]  Alireza Shafaei,et al.  Reversible logic synthesis of k-input, m-output lookup tables , 2013, 2013 Design, Automation & Test in Europe Conference & Exhibition (DATE).

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