Hybrid Logical-Physical Qubit Interaction as a Post Selection Oracle

We demonstrate a property of the quantum 5-qubit stabilizer code that enables the interaction between qubits of different logical layers, and conduct a full density-matrix simulation of an interaction between a logical and a physical qubit. We use the logical qubit as an ancilla and find under which circumstances it gives an advantage over the bare physical ancilla approach, changing the circuit depth and noise level with decoherence processes at play. We use it as a post selection oracle for quantum phase estimation to detect errors propagating from the sensor qubit. Finally, we use our simulation to give noise thresholds both for computation and for sensing a signal using quantum phase estimation that are well within the capabilities of today's hardware.