Abstract
We extend quantum process calculus in order to describe linear optical elements. In all previous work on quantum process calculus a qubit was considered as the information encoded within a 2 dimensional Hilbert space describing the internal states of a localised particle, most often realised as polarisation information of a single photon. We extend quantum process calculus by allowing multiple particles as information carriers, described by Fock states. We also consider the transfer of information from one particular qubit realisation (polarisation) to another (path encoding), and describe post-selection. This allows us for the first time to describe linear optical quantum computing (LOQC) in terms of quantum process calculus. We illustrate this approach by presenting a model of an LOQC CNOT gate.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2000)
Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)
O’Brien, J.L., Pryde, G.J., White, A.G., Ralph, T.C., Branning, D.: Demonstration of an all-optical quantum controlled-not gate. Nature 426, 264 (2003)
Politi, A., Cryan, M.J., Rarity, J.G., Yu, S., O’Brien, J.L.: Silica-on-silicon waveguide quantum circuits. Science 320, 646 (2008)
Gay, S.J., Nagarajan, R.: Communicating Quantum Processes. In: Proceedings of the 32nd Annual ACM Symposium on Principles of Programming Languages, pp. 145–157. ACM (2005)
Jorrand, P., Lalire, M.: Toward a quantum process algebra. In: CF 2004: Proceedings of the 1st Conference on Computing Frontiers, pp. 111–119. ACM Press (2004)
Feng, Y., Duan, R., Ji, Z., Ying, M.: Probabilistic bisimilarities between quantum processes arXiv:cs.LO/0601014 (2006)
Milner, R.: Communication and Concurrency. Prentice-Hall (1989)
Myers, C.R., Laflamme, R.: Linear optics quantum computation: an overview arXiv: quant-ph/0512104v1 (2005)
Ralph, T.C., Lanford, N.K., Bell, T.B., White, A.G.: Linear optical controlled-not gate in the coincidence basis. Physical Review Letters A 65, 62324–1 (2002)
Milner, R.: Communicating and Mobile Systems: the Pi-Calculus. Cambridge University Press (1999)
Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, I. Information and Computation 100(1), 1–40 (1992)
Gay, S.J., Nagarajan, R.: Types and Typechecking for Communicating Quantum Processes. Mathematical Structures in Computer Science 16(3), 375–406 (2006)
Davidson, T.A.S.: Formal Verification Techniques using Quantum Process Calculus. PhD thesis, University of Warwick (2011)
Davidson, T.A.S., Gay, S.J., Nagarajan, R., Puthoor, I.V.: Analysis of a quantum error correcting code using quantum process calculus. EPTCS 95, 67–80 (2011)
Wright, A.K., Felleisen, M.: A syntactic approach to type soundness. Information and Computation 115(1), 38–94 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Franke-Arnold, S., Gay, S.J., Puthoor, I.V. (2013). Quantum Process Calculus for Linear Optical Quantum Computing. In: Dueck, G.W., Miller, D.M. (eds) Reversible Computation. RC 2013. Lecture Notes in Computer Science, vol 7948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38986-3_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-38986-3_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38985-6
Online ISBN: 978-3-642-38986-3
eBook Packages: Computer ScienceComputer Science (R0)