Two-Qubit Stabilizer Circuits with Recovery I: Existence

Understanding how a stabilizer circuit responds to different input is important to formulating an effective strategy for resource management. In this paper, we further investigate the many ways of using stabilizer operations to generate a single qubit output from a two-qubit state. In particular, by restricting the input to certain product states, we discover probabilistic operations capable of transforming stabilizer circuit outputs back into stabilizer circuit inputs. These secondary operations are ideally suited for recovery purposes and require only one extra resource ancilla to succeed. As a result of reusing qubits in this manner, we present an alternative to the original state preparation process that can lower the overall costs of executing any two-qubit stabilizer procedure involving non-stabilizer resources.