Use cases & realizations

Use cases & fit

Platforms: all-to-all-small-register circular-nearest-neighbor-small-register superconducting-small-register trapped-ion-all-to-all solid-state-spin-register

Tasks: single-qubit-error-correction small-register-logical-gate-benchmarking flag-fault-tolerance-experiments magic-state-distillation

Physical realizations

• liquid-state NMR registers demonstrated

  Early experiments implemented a five-qubit correction benchmark and later encoded identity, NOT, and Hadamard processes with deliberately inserted single-qubit faults. These ensemble-control demonstrations do not constitute repeated scalable fault-tolerant memory.

  References: knill2001benchmark, zhang2012encoded

• superconducting five-qubit register demonstrated

  Encoded states were prepared, all stabilizers were measured, inserted single-qubit errors were identified, logical Paulis were applied, and the input was decoded. The reported fidelities belong to that finite circuit.

  References: gong2021experimental

• diamond nuclear-spin processor demonstrated

  Repeated-measurement encoding, fault-tolerant logical single-qubit Clifford operations, and flagged stabilizer measurements were executed on a seven-qubit processor containing five data and two ancillary spins.

  References: abobeih2022fault

• trapped-ion QCCD processor demonstrated

  Two five-qubit blocks were coupled by a nontransversal logical CNOT with runtime decoding, flagging, and pieceable fault-tolerance primitives. The protocol is not evidence for a transversal inter-block CNOT.

  References: ryananderson2022entangling