  Finding a denotational semantics for higher order quantum computation is a
long-standing problem in the semantics of quantum programming languages. Most
past approaches to this problem fell short in one way or another, either
limiting the language to an unusably small finitary fragment, or giving up
important features of quantum physics such as entanglement. In this paper, we
propose a denotational semantics for a quantum lambda calculus with recursion
and an infinite data type, using constructions from quantitative semantics of
linear logic.
