Measurement-Free Quantum Error Correction and Synonyms

Error correction with quantum-feedback
Coherent error correction

Randomized Benchmarking

"average gate infidelity r(D) due to a noise process D can be accessed experimentally via randomized benchmarking" ^[zhao]

Diamond Distance

Analytic tool for obtaining an estimation of noise threshold.

While on the other hand, the error thresholds are usually obtain using rigorous bounds via the diamond distance D(D)

For noise process $\mathcal{D}$ of different nature, "The diamond distance scales as D(D) ∝ r(D) for stochastic Pauli noise, but scales differently as D(D) ∝ √r(D) for the coherent noise". ^[zhao]

"(i) qubits are disposed in a planar array, only requiring local measurement operations; and (ii) early estimates based on stochastic error models indicated a very large threshold value, pc ≈ 11% [4], for the single-qubit error probability p. For p < pc, the probability of successful encoding tends to 1 as the number of physical qubits is increased." : Fidelity threshold of the surface code beyond single-qubit error models

Coherent error source

"systematic control noise, cross-talk, global external fields, and unwanted qubit–qubit interactions" Greenbaum

Topological code

A code whose codewords form the ground-state or low-energy subspace of a (typically geometrically local) code Hamiltonian realizing a topological phase. A topological phase may be bosonic or fermionic, i.e., constructed out of underlying subsystems whose operators commute or anti-commute with each other, respectively. Unless otherwise noted, the phases discussed are bosonic.

3D Color Code

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes: Three-dimensional color code thresholds via statistical-mechanical mapping