Operational semantics for formal tensorial calculus

With a view towards models of quantum computation, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an interpreter/simulator) is provided for this language in the form of a term rewrite systems. The linear-algebraic -calculus hereby constructed is linear in a different (yet related) sense to that, say, of the linear -calculus. These various notions of linearity are discussed in the context of quantum programming languages .

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