Mahboobeh Houshmand
Mehdi Sedighi
Morteza Saheb Zamani
Skip Abstract Section
Abstract
One-way quantum computation (1WQC) is a model of universal quantum computations in which a specific highly entangled state called a cluster state allows for quantum computation by single-qubit measurements. The needed computations in this model are organized as measurement patterns. The traditional approach to obtain a measurement pattern is by translating a quantum circuit that solely consists of CZ and J(α) gates into the corresponding measurement patterns and then performing some optimizations by using techniques proposed for the 1WQC model. However, in these cases, the input of the problem is a quantum circuit, not an arbitrary unitary matrix. Therefore, in this article, we focus on the first phase—that is, decomposing a unitary matrix into CZ and J(α) gates. Two well-known quantum circuit synthesis methods, namely cosine-sine decomposition and quantum Shannon decomposition are considered and then adapted for a library of gates containing CZ and J(α), equipped with optimizations. By exploring the solution space of the combinations of these two methods in a bottom-up approach of dynamic programming, a multiobjective quantum circuit synthesis method is proposed that generates a set of quantum circuits. This approach attempts to simultaneously improve the measurement pattern cost metrics after the translation from this set of quantum circuits.
- M. Arabzadeh, M. Houshmand, M. Sedighi, and M. Saheb Zamani. 2015. Quantum-logic synthesis of Hermitian gates. ACM Journal of Emerging Technologies in Computing Systems 12, 4, Article No. 40. Google Scholar
Digital Library
- D. Bacon. 2006. Operator quantum error-correcting subsystems for self-correcting quantum memories. Physical Review A 73, 1, 012340-1--012340-13. Google ScholarCross Ref
- A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter. 1995. Elementary gates for quantum computation. Physical Review A 52, 5, 3457--3467. Google ScholarCross Ref
- S. Barz, J. Fitzsimons, E. Kashefi, and P. Walther. 2013. Experimental verification of quantum computation. Nature Physics 9, 11, 727--731.Google ScholarCross Ref
- V. Bergholm, J. J. Vartiainen, M. Möttönen, and M. M. Salomaa. 2005. Quantum circuits with uniformly controlled one-qubit gates. Physical Review A 71, 052330. Google ScholarCross Ref
- H. J. Briegel, D. E. Browne, W. Dur, R. Raussendorf, and M. Van den Nest. 2009. Measurement-based quantum computation. Nature Physics 5, 19--26.Google ScholarCross Ref
- A. Broadbent, J. Fitzsimons, and E. Kashefi. 2009. Universal blind quantum computation. In Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS’09). IEEE, Los Alamitos, CA, 517--526. Google ScholarDigital Library
- A. Broadbent and E. Kashefi. 2009. Parallelizing quantum circuits. Theoretical Computer Science 410, 26, 2489--2510. Google ScholarDigital Library
- D. Browne and H. J. Briegel. 2006. One-way quantum computation—a tutorial introduction. arXiv:quant-ph/0603226.Google Scholar
- D. Browne, E. Kashefi, M. Mhalla, and S. Perdrix. 2007. Generalized flow and determinism in measurement-based quantum computation. New Journal of Phys 9, 1--16. Google ScholarCross Ref
- S. S. Bullock and I. L. Markov. 2003. An elementary two-qubit quantum computation in 23 elementary gates. Physical Review A 68, 012318--012325. Google ScholarCross Ref
- S. S. Bullock and I. L. Markov. 2004. Asymptotically optimal circuits for arbitrary n-qubit diagonal computations. Quantum Information and Computation 4, 1, 27--47.Google ScholarDigital Library
- T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. 2009. Introduction to Algorithms. MIT Press, Cambridge, MA.Google Scholar
- G. Cybenko. 2001. Reducing quantum computations to elementary unitary operations. Computing in Science and Engineering 3, 2, 27--32. Google ScholarDigital Library
- V. Danos, E. Kashefi, and P. Panangaden. 2005. Parsimonious and robust realizations of unitary maps in the one-way model. Physical Review A 72, 5, 3824--3851. DOI:http://dx.doi.org/10.1103/PhysRevA.54.3824 Google ScholarCross Ref
- V. Danos, E. Kashefi, and P. Panangaden. 2007. The measurement calculus. Journal of ACM 54, 2, Article No. 8. Google ScholarDigital Library
- V. Danos, E. Kashefi, P. Panangaden, and S. Perdrix. 2009. Extended measurement calculus. In Semantic Techniques in Quantum Computation, S. Gay and I. Mackie (Eds.). Cambridge University Press, Cambridge, MA, 235--310. Google ScholarCross Ref
- D. Deutsch. 1989. Quantum computational networks. Proceedings of the Royal Society A 425, 1868, 73--90. Google ScholarCross Ref
- R. Dias da Silva and E. F. Galvo. 2013. Compact quantum circuits from one-way quantum computation. Physical Review A 88, 012319. Google ScholarCross Ref
- R. Dias da Silva, E. Pius, and E. Kashefi. 2015. Global quantum circuit optimization. arXiv:1301.0351.Google Scholar
- M. Eslamy, M. Houshmand, M. Saheb Zamani, and M. Sedighi. 2016. Geometry-based signal shifting of one-way quantum computation measurement patterns. In Proceedings of the 24th Iranian Conference on Electrical Engineering (ICEE’16). Google ScholarCross Ref
- A. G. Fowler. 2011. Constructing arbitrary Steane code single logical qubit fault-tolerant gates. Quantum Information and Computation 11, 9--10, 867--873.Google Scholar
- A. G. Fowler, A. M. Stephens, and P. Groszkowski. 2009. High-threshold universal quantum computation on the surface code. Physical Review A 80, 052312-1--052312-14. Google ScholarCross Ref
- B. Giles and P. Selinger. 2013. Exact synthesis of multiqubit Clifford+T circuits. Physical Review A 87, 032332. Google ScholarCross Ref
- T. Hogg, C. Mochon, W. Polak, and E. Rieffel. 1999. Tools for quantum algorithms. International Journal of Modern Physics C 10, 1, 1347--1361. Google ScholarCross Ref
- M. Houshmand, M. Saheb Zamani, M. Sedighi, and M. Arabzadeh. 2014a. Decomposition of diagonal Hermitian quantum gates using multiple-controlled Pauli Z gates. ACM Journal of Emerging Technologies in Computing Systems 11, 3, Article No. 28. Google ScholarDigital Library
- M. Houshmand, M. Saheb Zamani, M. Sedighi, and M. H. Samavatian. 2014b. Automatic translation of quantum circuits to optimized one-way quantum computation patterns. Quantum Information Processing 13, 11, 2463--2482. Google ScholarDigital Library
- R. Jozsa. 2006. An introduction to measurement-based quantum computation. NATO Science Series, III: Computer and Systems Sciences. Quantum Information Processing—From Theory to Experiment 69, 20, 137--158.Google Scholar
- V. Kliuchnikov, D. Maslov, and M. Mosca. 2013. Fast and efficient exact synthesis of single-qubit unitaries generated by Clifford and T gates. Quantum Information and Computation 13, 7--8, 607--630.Google Scholar
- A. Konak, D. W Coit, and A. E Smith. 2006. Multi-objective optimization using genetic algorithms: A tutorial. Reliability Engineering and System Safety 91, 9, 992--1007. Google ScholarCross Ref
- Ch. Lin and A. Chakrabarti. 2014. FTQLS: Fault-tolerant quantum logic synthesis. IEEE Transactions on VLSI Systems 22, 6, 1350--1363. Google ScholarCross Ref
- M. Mhalla and S. Perdrix. 2008a. Finding optimal flows efficiently. In Proceedings of the 35th International Colloquium on Automata, Languages, and Programming (ICALP’08). 857--868.Google Scholar
- M. Mhalla and S. Perdrix. 2008b. Finding optimal flows efficiently. In Proceedings of the 35th International Colloquium on Automata, Languages, and Programming (ICALP’08). 857--868. Google ScholarDigital Library
- J. Miyazaki, M. Hajdusek, and M. Murao. 2010. Rewriting measurement-based quantum computations with generalised flow. In Automata, Languages and Programming. Lecture Notes in Computer Science, Vol. 91. Springer, 285--296.Google Scholar
- J. Miyazaki, M. Hajdusek, and M. Murao. 2015. An analysis of the trade-off between spatial and temporal resources for measurement-based quantum computation. Physical Review A 91, 052302. Google ScholarCross Ref
- M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa. 2004. Quantum circuits for general multiqubit gates. Physical Review Letters 93, 13, 130502.Google ScholarCross Ref
- N. de Beaudrap, V. Danos, and E. Kashefi. 2006. Phase map decomposition for unitaries. arXiv:quant-ph/0603266.Google Scholar
- M. A. Nielsen and I. L. Chuang. 2010. Quantum Computation and Quantum Information (10th anniversary ed.). Cambridge University Press, Cambridge, UK.Google Scholar
- E. Nikahd, M. Houshmand, M. Saheb Zamani, and M. Sedighi. 2012. OWQS: One-way quantum computation simulator. In Proceedings of the 2012 15th Euromicro Conference on Digital System Design (DSD’12). IEEE, Los Alamitos, CA, 98--104. Google ScholarDigital Library
- E. Nikahd, M. Houshmand, M. Saheb Zamani, and M. Sedighi. 2015. One-way quantum computer simulation. Microprocessors and Microsystems 39, 3, 210--222. Google ScholarDigital Library
- E. Nikahd, M. Houshmand, M. Saheb Zamani, and M. Sedighi. 2016. GOWQS: Graph-based one-way quantum computation simulator. In Proceedings of the 24th Iranian Conference on Electrical Engineering (ICEE’16). Google ScholarCross Ref
- E. Pius. 2010. Automatic Parallelisation of Quantum Circuits Using the Measurement-Based Quantum Computing Model. Master’s thesis. University of Edinburgh.Google Scholar
- R. Raussendorf. 2012. Measurement-Based Quantum Computation with Cluster States. Ph.D. Dissertation. Ludwig-Maximilians-Universitat Munich.Google Scholar
- R. Raussendorf and H. J. Briegel. 2001. A one-way quantum computer. Physical Review Letters 86, 22, 5188--5191. Google ScholarCross Ref
- M. Saeedi, M. Arabzadeh, M. Saheb Zamani, and M. Sedighi. 2011. Block-based quantum-logic synthesis. Quantum Information and Computation 11, 3--4, 262--277.Google ScholarDigital Library
- M. Saeedi and I. L. Markov. 2013. Synthesis and optimization of reversible circuits—a survey. ACM Computing Surveys 45, 2, Article No. 21. Google ScholarDigital Library
- V. V. Shende, S. S. Bullock, and I. L. Markov. 2006. Synthesis of quantum-logic circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25, 6, 1000--1010. Google ScholarDigital Library
- V. V. Shende and I. L. Markov. 2009. On the CNOT-cost of Toffoli gates. Quantum Information and Computation 9, 5--6, 461--486.Google ScholarDigital Library
- V. V. Shende, I. L. Markov, and S. S. Bullock. 2004a. Minimal universal two-qubit quantum circuits. Physical Review A 69, 062321. Google ScholarCross Ref
- V. V. Shende, I. L. Markov, and S. S. Bullock. 2004b. Smaller two-qubit circuits for quantum communication and computation. In Proceedings of the Conference on Design, Automation, and Test in Europe (DATE’04). 980--985. Google ScholarCross Ref
- G. Song and A. Klappenecker. 2003. Optimal realizations of controlled unitary gates. Quantum Information and Computation 3, 2, 139--155.Google ScholarDigital Library
- A. M. Steane. 1996. Error correcting codes in quantum theory. Physical Review Letters 77, 5, 793--797. Google ScholarCross Ref
- J. J. Vartiainen, M. Möttönen, and M. M. Salomaa. 2004. Efficient decomposition of quantum gates. Physical Review Letters 92, 177902. Google ScholarCross Ref
- F. Vatan and C. Williams. 2004. Optimal quantum circuits for general two-qubit gates. Physical Review A 69, 032315. Google ScholarCross Ref
- G. Vidal and C. M. Dawson. 2004. A universal quantum circuit for two-qubit transformations with three CNOT gates. Physical Review A 69, 010301. Google ScholarCross Ref
- P. Walther, K. J. Resch, T. Rudolph, and E. Schenck. 2005. Experimental one-way quantum computing. Nature 434, 169--176. Google ScholarCross Ref
- D. S. Wang, A. G. Fowler, and L. C. L. Hollenberg. 2011. Surface code quantum computing with error rates over 1. Physical Review A 83, 020302-1--020302-4. Google ScholarCross Ref
Index Terms
- Quantum Circuit Synthesis Targeting to Improve One-Way Quantum Computation Pattern Cost Metrics
Recommendations
Automatic translation of quantum circuits to optimized one-way quantum computation patterns
One-way quantum computation (1WQC) is a model of universal quantum computations in which a specific highly entangled state called a cluster state (or graph state) allows for quantum computation by only single-qubit measurements. The needed computations ...
Universal quantum circuit for N-qubit quantum gate: a programmable quantum gate
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the basic steps is ...
Pairwise decomposition of toffoli gates in a quantum circuit
GLSVLSI '08: Proceedings of the 18th ACM Great Lakes symposium on VLSIQuantum circuit synthesis is the procedure of automatically generating quantum circuits to represent specified functions. A common gate in quantum circuits is the reversible Toffoli gate, a type of generalized controlled NOT operation. There are ...
Comments