Gottesman Types for Quantum Programs


The Heisenberg representation of quantum operators provides a powerful technique for reasoning about quantum circuits, albeit those restricted to the common (non-universal) Clifford set H, S and CNOT. The Gottesman-Knill theorem showed that we can use this representation to efficiently simulate Clifford circuits. We show that Gottesman’s semantics for quantum programs can be treated as a type system, allowing us to efficiently characterize a common subset of quantum programs. We also show that it can be extended beyond the Clifford set to partially characterize a broad range of programs. We apply these types to reason about separable states and the superdense coding algorithm.

Proceedings of the 17th International Conference on Quantum Physics and Logic (QPL), Paris, France, June 2–6, 2020