Better-than-classical Grover search via quantum error detection and suppression

We report better-than-classical success probabilities for a complete Grover quantum search algorithm on the largest scale demonstrated to date, of up to five qubits, using two different IBM platforms. This is enabled by error suppression via robust dynamical decoupling. Further improvements arise after the use of measurement error mitigation, but the latter is insufficient by itself for achieving better-than-classical performance. For two qubits, we demonstrate a 99.5% success probability via the use of the [[4, 2, 2]] quantum error-detection (QED) code. This constitutes a demonstration of quantum algorithmic breakeven via QED. Along the way, we introduce algorithmic error tomography (AET), a method that provides a holistic view of the errors accumulated throughout an entire quantum algorithm, filtered via the errors detected by the QED code used to encode the circuit. We demonstrate that AET provides a stringent test of an error model based on a combination of amplitude damping, dephasing, and depolarization.