Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
MPC '00 Proceedings of the 5th International Conference on Mathematics of Program Construction
Towards a quantum programming language
Mathematical Structures in Computer Science
Communicating quantum processes
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Computation and Quantum Information: 10th Anniversary Edition
On a measurement-free quantum lambda calculus with classical control
Mathematical Structures in Computer Science
Reasoning about Entanglement and Separability in Quantum Higher-Order Functions
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
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As a first step toward a notion of quantum data structures, we introduce a typing system for reflecting entanglement and separability. This is presented in the context of classically controlled quantum computation where a classical program controls a sequence of quantum operations, i.e. unitary transformations and measurements acting on a quantum memory. Abstract models for such quantum computations are the Quantum Random Access Machine (QRAM [E. Knill, Conventions for Quantum Pseudocode, LANL report LAUR-96-2724, 1996]) and the Classically-Controlled Quantum Turing Machine (CQTM [S. Perdrix, Ph. Jorrand, Classically-Controlled Quantum Computation, arXiv:quant-ph/0407008, to appear in Mathematical Structures in Computer Science]). Several quantum programming languages follow this model [S. Bettelli, T. Calarco, L. Serafini, Toward an architecture for quantum programming, Eur. Phys. J. D 25 (2) (2003) 181-200, S.J. Gay, R. Nagarajan, Communicating quantum processes, Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Jens Palsberg and Martin Abadi (Eds.), POPL 2005, January 12-14, 2005, pp. 145-157, M. Lalire, Ph. Jorrand, A process algebraic approach to concurrent and distributed quantum computation: operational semantics, Proceedings of the 2nd International Workshop on Quantum Programming Languages, 2004, pp. 109-126, J.W. Sanders, P. Zuliani, Quantum Programming, Mathematics of Program Construction, Springer LNCS 1837, 80-99, 2000, P. Selinger, Towards a Quantum Programming Language, Mathematical Structures in Computer Science 14 (4) (2004) 527-586]. Among them, the functional language defined by Valiron [B. Valiron, Quantum Typing, Proceedings of the 2nd International Workshop on Quantum Programming Languages, 2004, pp. 163-178] is the basis for the language developed in this paper. This is work in progress.