Mapping NCV Circuits to Optimized Clifford+T Circuits
The need to consider fault tolerance in quantum circuits has led to recent work on the optimization of circuits composed of Clifford+T gates. The primary optimization objectives are to minimize the T-count (number of T gates) and the T-depth (the number of groupings of parallel T gates). These objectives arise due to the high cost of the fault tolerant implementation of the T gate compared to Clifford gates. In this paper, we consider the mapping of a circuit composed of NOT, Controlled-NOT and square-root of NOT (NCV) gates to an equivalent circuit composed of Clifford+T gates. Our approach is heuristic and proceeds through three phases: (i) mapping a circuit of NCV gates to a Clifford+T circuit; (ii) optimization of the placement of the T gates in the Clifford+T circuit; and (iii) optimization of the subcircuits between T gate groupings. The approach takes advantage of earlier work on the optimization of NCV circuits. Examples are presented to show the approach presented here compares well with other approaches. Our approach does not add ancilla lines.
KeywordsQuantum Computation Quantum Circuit Full Adder Control Gate Circuit Level
Unable to display preview. Download preview PDF.
- 2.Amy, M., Maslov, D., Mosca, M.: Polynomial-time T-depth optimization of Clifford+T circuits via matroid partitioning, arXiv:quant-ph/1303.2042v2 (2013)Google Scholar
- 5.Buhrman, H., Cleve, R., Laurent, M., Linden, N., Schrijver, A., Unger, F.: New limits on fault-tolerant quantum computation. In: Foundations of Computer Science, vol. 27, pp. 411–419. IEEE Computer Society (2006)Google Scholar
- 6.Chakrabarti, A., Sur-Kolay, S., Chaudhury, A.: Linear nearest neighbor synthesis of reversible circuits by graph partitioning. CoRR, arXiv:1112.0564v2 (2012)Google Scholar
- 8.Khan, M.H.A.: Cost reduction in nearest neighbour based synthesis of quantum Boolean circuits. Engineering Letters 16, 1–5 (2008)Google Scholar
- 9.Lukac, M.: Quantum Inductive Learning and Quantum Logic Synthesis. BiblioLabsII (2011)Google Scholar
- 11.Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2000)Google Scholar
- 14.Selinger, P.: Quantum circuits of T-depth one. Phys. Rev. A 87, 042302 (2013)Google Scholar
- 16.Soeken, M., Miller, D.M., Drechsler, R.: Quantum circuits employing roots of the Pauli matrices. Phys. Rev. A 88, 042322 (2013)Google Scholar
- 18.Weinstein, Y.S.: Non-fault tolerant T-gates for the [7,1,3] quantum error correction code. Phys. Rev. A 87, 032320 (2013)Google Scholar
- 19.Wille, R., Große, D., Teuber, L., Dueck, G.W., Drechsler, R.: RevLib: An online resource for reversible functions and reversible circuits. In: Int’l Symp. on Multi-Valued Logic, pp. 220–225 (2008), RevLib is available at www.revlib.org