Edgard Muñoz-Coreas
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Abstract
Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant, but the T gate is very costly to implement. As a result, reducing T-count has become an important optimization goal. Further, quantum circuits with many qubits are difficult to realize, making designs that save qubits and produce no garbage outputs desirable. In this work, we present a T-count optimized quantum square root circuit with only 2 ṡ n + 1 qubits and no garbage output. To make a fair comparison against existing work, the Bennett’s garbage removal scheme is used to remove garbage output from existing works. We determined that our proposed design achieves an average T-count savings of 43.44%, 98.95%, 41.06%, and 20.28% as well as qubit savings of 85.46%, 95.16%, 90.59%, and 86.77% compared to existing works.
- M. Amy, D. Maslov, and M. Mosca. 2014. Polynomial-time T-depth optimization of clifford+T circuits via matroid partitioning. IEEE Trans. Comput.-Aid. Des. Integr. Circ. Syst. 33, 10 (Oct. 2014), 1476--1489.Google Scholar
- M. Amy, D. Maslov, M. Mosca, and M. Roetteler. 2013. A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits. IEEE Trans. Comput.-Aid. Des. Integr. Circ. Syst. 32, 6 (June 2013), 818--830. Google ScholarDigital Library
- A. V. AnanthaLakshmi and Gnanou Florence Sudha. 2017. A novel power efficient 0.64-GFlops fused 32-bit reversible floating point arithmetic unit architecture for digital signal processing applications. Microprocess. Microsyst. 51, Suppl. C (2017), 366--385.Google ScholarCross Ref
- S Beauregard. 2003. Circuit for shor’s algorithm using 2n+3 gubits. Quant. Inf. Comput. 3, 2 (Mar. 2003), 175--185. Google ScholarDigital Library
- C. H. Bennett. 1973. Logical reversibility of computation. IBM J. Res. Dev. 17, 6 (Nov. 1973), 525--532. Google ScholarDigital Library
- M. K. Bhaskar, S. Hadfield, A. Papageorgiou, and I. Petras. 2016. Quantum algorithms and circuits for scientific computing. Quant. Inf. Comput. 16, 3--4 (Mar. 2016), 197--236. Google ScholarDigital Library
- Donny Cheung, Dmitri Maslov, Jimson Mathew, and Dhiraj K. Pradhan. 2008. Design and optimization of a quantum polynomial-time attack on elliptic curve cryptography. In Proceedings of the 3rd Workshop on the Theory of Quantum Computation, Communication, and Cryptography. Springer, Berlin, 96--104. Google ScholarDigital Library
- S. J. Devitt, A. M. Stephens, W. J. Munro, and K. Nemoto. 2013. Requirements for fault-tolerant factoring on an atom-optics quantum computer. Nat. Commun. 4, Article 2524 (Oct. 2013), 2524 pages. arxiv:quant-ph/1212.4934Google Scholar
- Dave Wecker et al. 2016. Language-Integrated Quantum Operations: LIQUi|>. Retrieved from https://www.microsoft.com/en-us/research/project/language-integrated-quantum-operations-liqui/.Google Scholar
- Peter Selinger et al. 2016. The Quipper System. Retrieved from http://www.mathstat.dal.ca/selinger/quipper/doc/.Google Scholar
- David Gosset, Vadym Kliuchnikov, Michele Mosca, and Vincent Russo. 2014. An algorithm for the T-count. Quant. Inf. Comput. 14, 15--16 (2014), 1261--1276. Google ScholarDigital Library
- S. Guodong, S. Shenghui, and X. Maozhi. 2014. Quantum algorithm for polynomial root finding problem. In Proceedings of the 2014 10th International Conference on Computational Intelligence and Security. 469--473. Google ScholarDigital Library
- Sean Hallgren. 2007. Polynomial-time quantum algorithms for pell’s equation and the principal ideal problem. J. ACM 54, 1, Article 4 (Mar. 2007), 19 pages. Google ScholarDigital Library
- IBM. 2017. Quantum Computing—IBM Q. Retrieved from https://www.research.ibm.com/ibm-q/.Google Scholar
- N. Cody Jones, Rodney Van Meter, Austin G. Fowler, Peter L. McMahon, Jungsang Kim, Thaddeus D. Ladd, and Yoshihisa Yamamoto. 2012. Layered architecture for quantum computing. Phys. Rev. X 2, 3 (Jul. 2012), 031007.Google Scholar
- Igor L. Markov and Mehdi Saeedi. 2012. Constant-optimized quantum circuits for modular multiplication and exponentiation. Quant. Inf. Comput. 12, 5--6 (2012), 361--394. Google ScholarDigital Library
- D. Michael Miller, Mathias Soeken, and Rolf Drechsler. 2014. Mapping NCV circuits to optimized clifford+T circuits. In Reversible Computation, Shigeru Yamashita and Shin-ichi Minato (Eds.). Lecture Notes in Computer Science, Vol. 8507. Springer International Publishing, Berlin, 163--175.Google ScholarCross Ref
- C. Monroe, R. Raussendorf, A. Ruthven, K. R. Brown, P. Maunz, L.-M. Duan, and J. Kim. 2014. Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects. Phys. Rev. A 89, 2 (Feb. 2014), 022317.Google ScholarCross Ref
- A. Montanaro. 2017. Quantum pattern matching fast on average. Algorithmica 77, 1 (Jan. 2017), 16--39. Google ScholarDigital Library
- E. Muñoz-Coreas and H. Thapliyal. 2017. T-count optimized design of quantum integer multiplication. ArXiv e-prints (June 2017). arxiv:quant-ph/1706.05113Google Scholar
- A. Paler and S. J. Devitt. 2015. An introduction into fault-tolerant quantum computing. In Proceedings of the 2015 52nd ACM/EDAC/IEEE Design Automation Conference (DAC’15). 1--6. Google ScholarDigital Library
- Alexandru Paler, Ilia Polian, Kae Nemoto, and Simon J. Devitt. 2017. Fault-tolerant, high-level quantum circuits: Form, compilation and description. Quant. Sci. Technol. 2, 2 (2017), 025003. http://stacks.iop.org/2058-9565/2/i=2/a=025003Google ScholarCross Ref
- I. Polian and A. G. Fowler. 2015. Design automation challenges for scalable quantum architectures. In Proceedings of the 2015 52nd ACM/EDAC/IEEE Design Automation Conference (DAC’15). 1--6. Google ScholarDigital Library
- J. Proos and C. Zalka. 2003. Shor’s discrete logarithm quantum algorithm for elliptic curves. Quant. Inf. Comput. 3, 4 (Jul. 2003), 317--344. Google ScholarDigital Library
- S. Samavi, A. Sadrabadi, and A. Fanian. 2008. Modular array structure for non-restoring square root circuit. J. Syst. Arch. 54, 10 (2008), 957--966. Google ScholarDigital Library
- S. Sultana and K. Radecka. 2011. Reversible implementation of square-root circuit. In Proceedings of the 2011 18th IEEE International Conference on Electronics, Circuits, and Systems. 141--144.Google Scholar
- Himanshu Thapliyal. 2016. Mapping of subtractor and adder-subtractor circuits on reversible quantum gates. In Transactions on Computational Science XXVII. Springer, 10--34. Google ScholarDigital Library
- Himanshu Thapliyal and Nagarajan Ranganathan. 2013. Design of efficient reversible logic-based binary and BCD adder circuits. J. Emerg. Technol. Comput. Syst. 9, 3, Article 17 (Oct. 2013), 31 pages. Google ScholarDigital Library
- W. van Dam and S. Hallgren. 2000. Efficient quantum algorithms for shifted quadratic character problems. eprint arXiv:quant-ph/0011067 (Nov. 2000). arXiv:quant-ph/0011067Google Scholar
- W. van Dam and G. Seroussi. 2002. Efficient quantum algorithms for estimating gauss sums. eprint arXiv:quant-ph/0207131 (July 2002). arXiv:quant-ph/0207131Google Scholar
- Wim van Dam and Igor E. Shparlinski. 2008. Classical and Quantum Algorithms for Exponential Congruences. Springer, Berlin, 1--10.Google Scholar
- Paul Webster, Stephen D. Bartlett, and David Poulin. 2015. Reducing the overhead for quantum computation when noise is biased. Phys. Rev. A 92, 6 (Dec. 2015), 062309.Google ScholarCross Ref
- Xinlan Zhou, Debbie W. Leung, and Isaac L. Chuang. 2000. Methodology for quantum logic gate construction. Phys. Rev. A 62, 5 (Oct. 2000), 052316.Google ScholarCross Ref
Index Terms
- T-count and Qubit Optimized Quantum Circuit Design of the Non-Restoring Square Root Algorithm
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