Experimental Observation of Encoding-Decoding Phase Transition on Superconducting Quantum Processor

Using a superconducting quantum processor, we experimentally observe random encoding-decoding circuits, in which a random encoding operation is applied to logical and ancillary qubits, followed by a corresponding decoding unitary and measurement of the ancillas. As an error detection protocol, observation of the trivial syndrome on the ancilla qubits indicates that no detectable error has occured on the logical state. However, as previously theoretically derived and numerically tested, this protocol works, in the thermodynamic limit, so long as single-qubit error strengths fall below a critical threshold, at which a phase transition occurs in both the initial/post-selected final state fidelity as well as the entanglement entropy of the final logical state. We experimentally implement this protocol on circuits of 8 to 24 qubits and directly observe, and model, phase transitions in both fidelity and entanglement entropy.