from these identiﬁcations has a very diﬀerent ﬂavour to linear logic, indeed to any fa-miliar system of logic. 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. Appl. Q A version of linearized set theory, in which subsets of a set correspond to subspaces of a vector space, was recognized by … Cyclic structures abound, and every sequent is provable. The calculus turns out to be closely related to the linear lambda calculi used in the study of linear logic. Quantum programming languages thus need linear dependent type theory. multiplicative linear logic with quantum modalities; we then investigate in detail the relations between QMLL and quantum circuits. RAIRO-Theor. The categorical model of the quantum … This paper defines a general semantic structure for such a type theory via certain fibrations of monoidal categories. 44 (2010) 419–441 Available online at: DOI: 10.1051/ita/2010021 www.rairo-ita.org QUANTUM COHERENT SPACES AND LINEAR LOGIC Stefano Baratella1 Abstract. Quantum set theory, linear logic and the von Domarus principle. Inf. These apparent perversities are, however, no cause for alarm: the resulting equations faithfully mirror calculations in quantum … A key ingredient in the proof of this correspondence is an interactive …

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