We introduce a minimal language combining higher-order com putation and linear algebra. Roughly, this is nothing else tha n t eÎ»calculus together with the possibility to make arbitrary li nearâ€¦ (More)

We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to staticallyâ€¦ (More)

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can beâ€¦ (More)

We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higherorder computation and linear algebra.â€¦ (More)

The Linear-Algebraic Î»-Calculus [2] extends the Î»-calculus with the possibility of making arbitrary linear combinations of terms Î±.t + Î².u. Since one can express fixed points over sums in thisâ€¦ (More)

There have been several non-axiomatic approaches taken to define quantum cellular automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work weâ€¦ (More)

With a view towards models of quantum computation and/or the int rpretation of linear logic, we define a functional language wh ere all functions are linear operators by construction. A small stepâ€¦ (More)

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 anâ€¦ (More)