Multi-qubit quantum nondemolition parity feedback and stabilization over tens of rounds in a mixed-species ion crystal

Multi-qubit nondemolition parity measurements are critical for feedback-based quantum error correction, as well as a powerful building block in quantum information processing and metrological protocols. We repeatedly and... [ view full abstract ]

Multi-qubit nondemolition parity measurements are critical for feedback-based quantum error correction, as well as a powerful building block in quantum information processing and metrological protocols. We repeatedly and nondestructively measure the parity of two beryllium ions using a calcium ancilla, and apply low-latency conditional corrections to deterministically stabilize particular parity subspaces as well as the four Bell states.

The ancilla is also used to sympathetically recool the beryllium ions, which allows us to re-initialize the system without collapsing the entangled beryllium state. The phases of future qubit gates are calculated and set in real-time based on the Stark shifts caused by the sequence of gates applied so far, which varies due to the conditional feedback. This facilitates repeated beryllium parity measurements in either the $sigma_z sigma_z$ and $sigma_x sigma_x$ bases. Based on the outcomes, the parity is swapped using $I sigma_z$ or $I sigma_x$ operations, thereby stabilizing a chosen parity subspace.

A similar approach is used to stabilize the four Bell states, by measuring and correcting both parity bases in a feedback round. The stabilized subspaces and Bell states decay an order of magnitude more slowly than in the unstabilized case. The primary decay mechanism in the stabilized cases arises from population leakage out of the beryllium hyperfine qubit subspace. The Bell states retain coherence for more than 50 rounds of measurement and feedback.

The experiment demonstrates all the basic primitives of a quantum hardware system and its attendant classical control, suited to larger-scale stabilization and feedback experiments including quantum error correction and other quantum feedback algorithms.