We study a measurement-free, untyped λ–calculus with quantum data and classical control. This work stems from previous proposals by Selinger and Valiron and by Van Tonder. We focus on operational and expressiveness issues, rather than (denotational) semantics. We prove sub ject reduction, confluence and a standardization theorem. Moreover, we prove the computational equivalence of the proposed calculus with a suitable class of quantum circuit families.
On a Measurement-Free Quantum Lambda Calculus with Classical Control
MASINI, Andrea;ZORZI, Margherita
2009-01-01
Abstract
We study a measurement-free, untyped λ–calculus with quantum data and classical control. This work stems from previous proposals by Selinger and Valiron and by Van Tonder. We focus on operational and expressiveness issues, rather than (denotational) semantics. We prove sub ject reduction, confluence and a standardization theorem. Moreover, we prove the computational equivalence of the proposed calculus with a suitable class of quantum circuit families.
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