Quantum Information Processing

, Volume 9, Issue 4, pp 463–496 | Cite as

Binary superposed quantum decision diagrams

  • David RosenbaumEmail author


Binary superposed decision diagrams (BSQDDs) are a new type of quantum decision diagram that can be used for representing arbitrary quantum superpositions. One major advantage of BSQDDs is that they are dependent on the types of gates used in synthesis and a BSQDD can be used to efficiently generate a quantum array that will initialize the quantum superposition that the BSQDD represents. Transformation rules for BSQDDs allow BSQDDs to be reduced into simpler BSQDDs that represent the same quantum superposition. Canonical forms exist for a broad class of BSQDDs. This allows BSQDDs to be used for synthesizing quantum arrays that are capable of initializing arbitrary quantum superpositions.


Quantum initialization Quantum decision diagram Quantum array Quantum computation Quantum logic synthesis 




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abdaollahi, A., Pedram, M.: Analysis and synthesis of quantum circuits by using quantum decision diagrams. Design, Automation and Test in Europe (2006)Google Scholar
  2. 2.
    Biron, D., Biham, O., Biham, E., Grassl, M., Lidar, D.A.: Generalized grover search algorithm for arbitrary initial amplitude distribution. Quantum Comput. Quantum Commun. 1509/1999, 140–147 (1999)Google Scholar
  3. 3.
    Bryant R.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comp. C-35, 677–691 (1986)CrossRefGoogle Scholar
  4. 4.
    Ezhov A., Nifanova, A., Ventura, D.: Quantum associative memory with distributed queries. Inf. Sci. (2000)Google Scholar
  5. 5.
    Grover, L.: A fast quantum mechanical algorithm for database search. In: Annual ACM Symposium on Theory of Computing (1996)Google Scholar
  6. 6.
    Long G., Sun Y.: Efficient scheme for initializing a quantum register with an arbitrary superposed state. Phys. Rev. A. 64, 014303 (2001)CrossRefADSGoogle Scholar
  7. 7.
    Miller, D., Thornton, M.: QMDD: A decision diagram structure for reversible and quantum circuits. In: IEEE International Symposium on Multiple Valued Logic (2006)Google Scholar
  8. 8.
    Rosenbaum, D., Perkowski, M.: Superposed quantum state initialization using disjoint prime implicants. In: IEEE International Symposium on Multiple Valued Logic (2008)Google Scholar
  9. 9.
    Rosenbaum D.J., Perkowski M.A.: Extended superposed quantum state initialization using disjoint prime implicants. Phys. Rev. A. 79, 052310 (2009)CrossRefMathSciNetADSGoogle Scholar
  10. 10.
    Schulman, L., Vazirani, U.: Molecular scale heat engines and scalable quantum computation. In: Annual ACM Symposium on Theory of Computing (1999)Google Scholar
  11. 11.
    Ventura D., Martinez T.: Initializing the amplitude distribution of a quantum state. Found. Phys. Lett. 12, 547–559 (1999)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Ventura D., Martinez T.: Quantum associative memory. Inf. Sci. 124, 273–296 (2000)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Viamontes G., Markov I., Hayes J.: Graph-based simulation of quantum computation in the density matrix representation. Quantum Inf. Comput. 5, 113–130 (2004)MathSciNetGoogle Scholar
  14. 14.
    Viamontes, G., Rajagopalan, M., Markov, I., Hayes, J.: Gate-level simulation of quantum circuits. In: Conference on Asia South Pacific Design Automation (2003)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Computer SciencePortland State UniversityPortlandUSA

Personalised recommendations