A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
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
A Lambda Calculus for Quantum Computation
SIAM Journal on Computing
Towards a quantum programming language
Mathematical Structures in Computer Science
A Functional Quantum Programming Language
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A lambda calculus for quantum computation with classical control
Mathematical Structures in Computer Science
Quantum programming languages: survey and bibliography
Mathematical Structures in Computer Science
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In this paper we define nQML, a functional quantum programming language that follows the ''quantum data and control'' paradigm. In comparison to Altenkirch and Grattage's QML, the control constructs of nQML are simpler and can implement quantum algorithms more directly and naturally. We avoid the unnecessary complexities of a linear type system by using types that carry the address of qubits in the quantum state. We provide a denotational semantics over density matrices and unitary transformations, inspired by Selinger's semantics for QPL. Our semantics leads naturally to an interpreter for nQML, written in Haskell. We also explore the extension of nQML with polymorphic higher-order functions.