Encodability criteria for quantum based systems. (English) Zbl 1499.68234
Mousavi, Mohammad Reza (ed.) et al., Formal techniques for distributed objects, components, and systems. 42nd IFIP WG 6.1 international conference, FORTE 2022, held as part of the 17th international federated conference on distributed computing techniques, DisCoTec 2022, Lucca, Italy, June 13–17, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13273, 151-169 (2022).
Summary: Quantum based systems are a relatively new research area for that different modelling languages including process calculi are currently under development. Encodings are often used to compare process calculi. Quality criteria are used then to rule out trivial or meaningless encodings. In this new context of quantum based systems, it is necessary to analyse the applicability of these quality criteria and to potentially extend or adapt them. As a first step, we test the suitability of classical criteria for encodings between quantum based languages and discuss new criteria.
Concretely, we present an encoding, from a sublanguage of CQP into qCCS. We show that this encoding satisfies compositionality, name invariance (for channel and qubit names), operational correspondence, divergence reflection, success sensitiveness, and that it preserves the size of quantum registers. Then we show that there is no encoding from qCCS into CQP (or its sublanguage) that is compositional, operationally corresponding, and success sensitive.
For the entire collection see [Zbl 1492.68025].
Concretely, we present an encoding, from a sublanguage of CQP into qCCS. We show that this encoding satisfies compositionality, name invariance (for channel and qubit names), operational correspondence, divergence reflection, success sensitiveness, and that it preserves the size of quantum registers. Then we show that there is no encoding from qCCS into CQP (or its sublanguage) that is compositional, operationally corresponding, and success sensitive.
For the entire collection see [Zbl 1492.68025].
MSC:
| 68Q85 | Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) |
| 81P68 | Quantum computation |
References:
| [1] | Bennett, C.H., Brassard, G., Crépeau, C., Richard, J., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895-1899 (1993). doi:10.1103/PhysRevLett.70.1895 · Zbl 1051.81505 |
| [2] | Bisping, B., Nestmann, U., Peters, K.: Coupled similarity: the first 32 years. Acta Informatica, 439-463 (2019). doi:10.1007/s00236-019-00356-4 · Zbl 1476.68166 |
| [3] | Feng, Y., Duan, R., Ying, M.: Bisimulation for quantum processes. ACM Trans. Program. Lang. Syst. 34(4) (2012). doi:10.1145/2400676.2400680 · Zbl 1284.68425 |
| [4] | Gay, SJ, Quantum programming languages: survey and bibliography, Mathe. Struct. Comput. Sci., 16, 4, 581-600 (2006) · Zbl 1122.68021 · doi:10.1017/S0960129506005378 |
| [5] | Gay, S.J., Nagarajan, R.: Communicating quantum processes. In: Proceedings of SIGPLAN-SIGACT (ACM), pp. 145-157 (2005). doi:10.1145/1040305.1040318 · Zbl 1369.68207 |
| [6] | Gorla, D., Towards a unified approach to encodability and separation results for process calculi, Inf. Comput., 208, 9, 1031-1053 (2010) · Zbl 1209.68336 · doi:10.1016/j.ic.2010.05.002 |
| [7] | Gruska, J.: Quantum computing. In: Wiley Encyclopedia of Computer Science and Engineering. Wiley (2008). doi:10.1002/9780470050118.ecse720 · Zbl 1036.81007 |
| [8] | Jorrand, P., Lalire, M.: Toward a quantum process algebra. In: Proceedings of CF, pp. 111-119 (2004). doi:10.1145/977091.977108 |
| [9] | Kouzapas, D.; Pérez, JA; Yoshida, N.; Thiemann, P., On the relative expressiveness of higher-order session processes, Programming Languages and Systems, 446-475 (2016), Heidelberg: Springer, Heidelberg · Zbl 1335.68174 · doi:10.1007/978-3-662-49498-1_18 |
| [10] | Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information (10th Anniversary edition). Cambridge University Press, Cambridge (2010) · Zbl 1288.81001 |
| [11] | Peters, K.: Comparing process calculi using encodings. In: Proceedings of EXPRESS/SOS. EPCTS, vol. 300, pp. 19-38 (2019). doi:10.4204/EPTCS.300.2 · Zbl 1543.68249 |
| [12] | Peters, K., van Glabbeek, R.: Analysing and comparing encodability criteria. In: Crafa, S., Gebler, D. (eds.) Proceedings of EXPRESS/SOS. EPTCS, vol. 190, pp. 46-60 (2015). doi:10.4204/EPTCS.190.4 · Zbl 1476.68181 |
| [13] | Peters, K.; Nestmann, U.; Goltz, U.; Felleisen, M.; Gardner, P., On distributability in process calculi, Programming Languages and Systems, 310-329 (2013), Heidelberg: Springer, Heidelberg · Zbl 1381.68215 · doi:10.1007/978-3-642-37036-6_18 |
| [14] | Plotkin, GD, A structural approach to operational semantics, Log. Algebraic Methods Program., 60-61, 17-139 (2004) · Zbl 1082.68062 |
| [15] | de Riedmatten, H., Marcikic, I., Tittel, W., Zbinden, H., Collins, D., Gisin, N.: Long distance quantum teleportation in a quantum relay configuration. Phys. Rev. Lett. 92, 047904 (2004) · Zbl 1068.81527 |
| [16] | Rieffel, EG; Polak, W., An introduction to quantum computing for non-physicists, ACM Comput. Surv., 32, 3, 300-335 (2000) · doi:10.1145/367701.367709 |
| [17] | Schmitt, A., Peters, K., Deng, Y.: Encodability criteria for quantum based systems (technical report). Technical report, TU Darmstadt, Germany (2022). doi:10.48550/ARXIV.2204.06068. https://arxiv.org/abs/2204.06068 |
| [18] | Ying, M., Feng, Y., Duan, R., Ji, Z.: An algebra of quantum processes. ACM Trans. Comput. Log. 10(3), 19:1-19:36 (2009). doi:10.1145/1507244.1507249 · Zbl 1351.68187 |
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.
