Quantum arrows in Haskell. (English) Zbl 1279.68047
Selinger, Peter (ed.), Proceedings of the 4th international workshop on quantum programming languages (QPL 2006), Oxford, UK, 17–19 July 2006. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 210, 139-152 (2008).
Summary: We argue that a realistic model for quantum computations should be general with respect to measurements, and complete with respect to the information flow between the quantum and classical worlds. We discuss two alternative models for general and complete quantum computations based on probability distributions of quantum state vectors and on density matrices with classical outputs. We show that both models can be structured using a generalization of monads called arrows.
For the entire collection see [Zbl 1276.68031].
For the entire collection see [Zbl 1276.68031].
MSC:
| 68N18 | Functional programming and lambda calculus |
| 68N15 | Theory of programming languages |
| 81P68 | Quantum computation |
References:
| [1] | Altenkirch, T.; Grattage, J., A functional quantum programming language, (Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science. Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science, LICS 2005 (2005), IEEE Computer Society Press), 249-258 |
| [2] | Altenkirch, T.; Reus, B., Monadic presentations of lambda terms using generalized inductive types, Computer Science Logic (1999) · Zbl 0944.03011 |
| [3] | Bennett, C. H.; Brassard, G.; Crepeau, C.; Jozsa, R.; Peres, A.; Wootters, W., Teleporting an unknown quantum state via dual classical and EPR channels, Phys. Rev. Lett., 1895-1899 (1993) · Zbl 1051.81505 |
| [4] | Gay, S.J. and R. Nagarajan, Communicating quantum processesProceedings of the 32nd ACM Symposium on Principles of Programming Languages; Gay, S.J. and R. Nagarajan, Communicating quantum processesProceedings of the 32nd ACM Symposium on Principles of Programming Languages · Zbl 1369.68207 |
| [5] | Hughes, J., Generalising monads to arrows, Science of Computer Programming, 37, 67-111 (2000) · Zbl 0954.68034 |
| [6] | Kashefi, E.; Panangaden, P.; Danos, V., The measurement calculus (2004) |
| [7] | Moggi, E., Computational lambda-calculus and monads, (Proceedings of the Fourth Annual Symposium on Logic in computer science (1989), IEEE Computer Society Press), 14-23 · Zbl 0716.03007 |
| [8] | Moggi, E., Notions of computation and monads, Information and Computation, 93, 55-92 (1991) · Zbl 0723.68073 |
| [9] | Nielsen, M. A., Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state, Phys. Lett. A, 308, 2-3, 96-100 (2003) · Zbl 1008.81009 |
| [10] | Paterson, R., A new notation for arrowsInternational Conference on Functional Programming; Paterson, R., A new notation for arrowsInternational Conference on Functional Programming · Zbl 1323.68147 |
| [11] | Raussendorf, R.; Browne, D.; Briegel, H., Measurement-based quantum computation with cluster states, Phys. Rev. A, 68 (2003) |
| [12] | Unruh, D., Quantum programs with classical output streams, Proceedings of the 3rd International Workshop on Quantum Programming Languages. Proceedings of the 3rd International Workshop on Quantum Programming Languages, (QPL 2005). Proceedings of the 3rd International Workshop on Quantum Programming Languages. Proceedings of the 3rd International Workshop on Quantum Programming Languages, (QPL 2005), Electronic Notes in Theoretical Computer Science, 170, 165-184 (2006) · Zbl 1277.68047 |
| [13] | Vizzotto, J. K.; Altenkirch, T.; Sabry, A., Structuring quantum effects: Superoperators as arrows, Mathematical Structures in Computer Science, special issue on Quantum Programming Languages, 16, 453-468 (2006) · Zbl 1122.68062 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
