Communicating quantum processes
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A lambda calculus for quantum computation with classical control
Mathematical Structures in Computer Science
Types and typechecking for Communicating Quantum Processes
Mathematical Structures in Computer Science
Structuring quantum effects: superoperators as arrows
Mathematical Structures in Computer Science
Quantum programming languages: survey and bibliography
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science
Journal of the ACM (JACM)
An Algebra of Pure Quantum Programming
Electronic Notes in Theoretical Computer Science (ENTCS)
A Quantum Game Semantics for the Measurement Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Quantum Data and Control Made Easier
Electronic Notes in Theoretical Computer Science (ENTCS)
Linear-algebraic λ-calculus: higher-order, encodings, and confluence.
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
A review of procedures to evolve quantum algorithms
Genetic Programming and Evolvable Machines
On a measurement-free quantum lambda calculus with classical control
Mathematical Structures in Computer Science
The Arrow Calculus as a Quantum Programming Language
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Reasoning about Entanglement and Separability in Quantum Higher-Order Functions
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
Quantum implicit computational complexity
Theoretical Computer Science
On Reversible Combinatory Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
A linear-non-linear model for a computational call-by-value lambda calculus
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
On the completeness of quantum computation models
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Measurements and Confluence in Quantum Lambda Calculi With Explicit Qubits
Electronic Notes in Theoretical Computer Science (ENTCS)
Confluence Results for a Quantum Lambda Calculus with Measurements
Electronic Notes in Theoretical Computer Science (ENTCS)
The search for structure in quantum computation
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Linearity and recursion in a typed Lambda-calculus
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
Problems of adiabatic quantum program design
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A lambda calculus for quantum computation with classical control
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Quantum predicative programming
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Taming non-compositionality using new binders
UC'07 Proceedings of the 6th international conference on Unconventional Computation
Quipper: a scalable quantum programming language
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
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The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine and continues to be of enormous benefit in the classical theory of computation. We propose that quantum computation, like its classical counterpart, may benefit from a version of the lambda calculus suitable for expressing and reasoning about quantum algorithms. In this paper we develop a quantum lambda calculus as an alternative model of quantum computation, which combines some of the benefits of both the quantum Turing machine and the quantum circuit models. The calculus turns out to be closely related to the linear lambda calculi used in the study of linear logic. We set up a computational model and an equational proof system for this calculus, and we argue that it is equivalent to the quantum Turing machine.