Síntese de Operadores Unitários Baseada em Gramáticas
Resumo
Algoritmos quânticos propõem uma vantagem computacional no tempo de resolução de uma gama de problemas. Nesse cenário, a compilação de software quântico consiste na tradução dessas rotinas de alto nível em portas de baixo nível, e define uma etapa crucial diante da série de limitações enfrentadas pelos dispositivos quânticos atuais. A síntese de operadores quânticos baseia-se em decomposições matriciais recursivas, o que torna possível a sua reescrita através do uso de gramáticas formais. Esse trabalho propõe o uso de regras gramaticais no processo de síntese de unitários, visando otimizar a construção da árvore sintática relativa ao circuito, poupando portas CNOT.Referências
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Bergholm, V., Vartiainen, J. J., Möttönen, M., and Salomaa, M. M. (2005). Quantum circuits with uniformly controlled one-qubit gates. Physical Review A, 71(5).
Bullock, S. S. and Markov, I. L. (2004). Asymptotically optimal circuits for arbitrary n-qubit diagonal comutations. Quantum Inf. Comput., 4(1):27–47.
Callison, A. and Chancellor, N. (2022). Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond. Physical Review A, 106(1).
de Carvalho, J. A., Batista, C., de Veras, T., Araujo, I., and da Silva, A. J. (2025). Quantum multiplexer simplification for state preparation. ACM Transactions on Quantum Computing, 6(4):1–12.
Harrow, A. W., Hassidim, A., and Lloyd, S. (2009). Quantum algorithm for linear systems of equations. Physical Review Letters, 103(15).
Kim, Y., Eddins, A., Anand, S., Wei, K. X., Van Den Berg, E., Rosenblatt, S., Nayfeh, H., Wu, Y., Zaletel, M., Temme, K., et al. (2023). Evidence for the utility of quantum computing before fault tolerance. Nature, 618(7965):500–505.
Krol, A. M. and Al-Ars, Z. (2024). Beyond quantum shannon: Circuit construction for general n-qubit gates based on block zxz-decomposition.
Malvetti, E., Iten, R., and Colbeck, R. (2021). Quantum circuits for sparse isometries. Quantum, 5:412.
Nielsen, M. A. and Chuang, I. L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press.
Parr, T. (2009). Language implementation patterns: create your own domain-specific and general programming languages. The Pragmatic Bookshelf.
Plesch, M. and Brukner, Č. (2011). Quantum-state preparation with universal gate decompositions. Physical Review A, 83(3).
Preskill, J. (2018). Quantum computing in the nisq era and beyond. Quantum, 2:79.
Puschel, M., Moura, J. M., Johnson, J. R., Padua, D., Veloso, M. M., Singer, B. W., Xiong, J., Franchetti, F., Gacic, A., Voronenko, Y., et al. (2005). Spiral: Code generation for dsp transforms. Proceedings of the IEEE, 93(2):232–275.
Shende, V., Bullock, S., and Markov, I. (2006). Synthesis of quantum-logic circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 25(6):1000–1010.
Shende, V. V., Markov, I. L., and Bullock, S. S. (2004). Minimal universal two-qubit controlled-not-based circuits. Physical Review A, 69(6).
Bergholm, V., Vartiainen, J. J., Möttönen, M., and Salomaa, M. M. (2005). Quantum circuits with uniformly controlled one-qubit gates. Physical Review A, 71(5).
Bullock, S. S. and Markov, I. L. (2004). Asymptotically optimal circuits for arbitrary n-qubit diagonal comutations. Quantum Inf. Comput., 4(1):27–47.
Callison, A. and Chancellor, N. (2022). Hybrid quantum-classical algorithms in the noisy intermediate-scale quantum era and beyond. Physical Review A, 106(1).
de Carvalho, J. A., Batista, C., de Veras, T., Araujo, I., and da Silva, A. J. (2025). Quantum multiplexer simplification for state preparation. ACM Transactions on Quantum Computing, 6(4):1–12.
Harrow, A. W., Hassidim, A., and Lloyd, S. (2009). Quantum algorithm for linear systems of equations. Physical Review Letters, 103(15).
Kim, Y., Eddins, A., Anand, S., Wei, K. X., Van Den Berg, E., Rosenblatt, S., Nayfeh, H., Wu, Y., Zaletel, M., Temme, K., et al. (2023). Evidence for the utility of quantum computing before fault tolerance. Nature, 618(7965):500–505.
Krol, A. M. and Al-Ars, Z. (2024). Beyond quantum shannon: Circuit construction for general n-qubit gates based on block zxz-decomposition.
Malvetti, E., Iten, R., and Colbeck, R. (2021). Quantum circuits for sparse isometries. Quantum, 5:412.
Nielsen, M. A. and Chuang, I. L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press.
Parr, T. (2009). Language implementation patterns: create your own domain-specific and general programming languages. The Pragmatic Bookshelf.
Plesch, M. and Brukner, Č. (2011). Quantum-state preparation with universal gate decompositions. Physical Review A, 83(3).
Preskill, J. (2018). Quantum computing in the nisq era and beyond. Quantum, 2:79.
Puschel, M., Moura, J. M., Johnson, J. R., Padua, D., Veloso, M. M., Singer, B. W., Xiong, J., Franchetti, F., Gacic, A., Voronenko, Y., et al. (2005). Spiral: Code generation for dsp transforms. Proceedings of the IEEE, 93(2):232–275.
Shende, V., Bullock, S., and Markov, I. (2006). Synthesis of quantum-logic circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 25(6):1000–1010.
Shende, V. V., Markov, I. L., and Bullock, S. S. (2004). Minimal universal two-qubit controlled-not-based circuits. Physical Review A, 69(6).
Publicado
19/07/2026
Como Citar
CARVALHO, José Alex de; SILVA, Adenilton José da.
Síntese de Operadores Unitários Baseada em Gramáticas. In: SIMPÓSIO BRASILEIRO DE COMPUTAÇÃO E COMUNICAÇÃO QUÂNTICAS (SBCCQ), 1. , 2026, Gramado/RS.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 155-163.
DOI: https://doi.org/10.5753/sbccq.2026.23563.
