[zerodensity]

Questing regarding error correction and logical qbits. From my very limited understanding logical qbits could mitigate some of the error but uses multiple physical qbits for every logical qbits. Has anyone created a quantum computer that has logical qbits? Say a small one with 16 physical 4 logical qbits quantum computer, or similar.

[cohomologo]

No, but the quantum groups are making progress towards essentially making 1 logical qubit -- a common scheme uses a square grid of physical qubits, say with size 7x7, 8x8, 9x9, etc.. as a single logical qubit. This may seem like a moving target, but it is not. There is a specific, concrete error rate on the physical qubits, below which it is known that the logical qubits on increasingly large grids get _exponentially_ more accurate. Once the engineering achieves that noise level, logical qubits in the form of NxN grids where N~10-20 will ~eventually~ follow. I won't venture to predict how long, as building and controlling these grids of qubits while keeping the error rate low isn't easy. Could be years or decades.