Superdense coding circuit sending classical bits x and y from Alice to Bob and its program annotated with types at each step
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. DOI 10.4204/EPTCS.340.14
Robert Rand, Aarthi Sundaram, Kartik Singhal, Brad Lackey
