Technology Mapping of Reversible Circuits to Clifford+T Quantum Circuits

The Clifford+T quantum gate library has attracted much interest in the design of quantum circuits, particularly since the contained operations can be implemented in a fault-tolerant manner. Since fault tolerant implementations of the T gate have very high latency, synthesis and optimization are aiming at minimizing the number of T stages, referred to as the T-depth. In this paper, we present an approach to map mixed polarity multiple controlled Toffoli gates into Clifford+T quantum circuits. Our approach is based on the multiple control Toffoli mapping algorithms proposed by Barenco et al., which are given T-depth optimized Clifford+T translations. Experiments show that our approach leads to a significant T-depth reduction of 54% on average.

[1]  Dmitri Maslov,et al.  Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning , 2013, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[2]  Gerhard W. Dueck,et al.  Improved quantum cost for n-bit Toffoli gates , 2003 .

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

[4]  Robert Wille,et al.  RevLib: An Online Resource for Reversible Functions and Reversible Circuits , 2008, 38th International Symposium on Multiple Valued Logic (ismvl 2008).

[5]  Rolf Drechsler,et al.  On quantum circuits employing roots of the Pauli matrices , 2013, ArXiv.

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

[7]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[8]  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.

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

[10]  Peter Selinger,et al.  Quantum circuits of T-depth one , 2012, ArXiv.

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

[12]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[13]  Rolf Drechsler,et al.  Quantum Circuit Optimization by Hadamard Gate Reduction , 2014, RC.

[14]  Yaakov S. Weinstein,et al.  Non-fault-tolerantTgates for the [7,1,3] quantum error-correction code , 2013, 1303.4291.

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

[16]  Rolf Drechsler,et al.  Mapping NCV Circuits to Optimized Clifford+T Circuits , 2014, RC.