What they claim is that adding physical qubits reduce error rate of the logical qubits exponentially. For the Schor algorithm the error rate of the logical qubits must decrease exponentially with every single logical qubit added to make the system produce meaningful results.
To see how it plays out consider adding a single logical qubit. First you need to increase the number of physical qubits to accommodate the new logical qubit at the same error rate. Then multiply the number of physical qubits to accommodate for exponentially decreased error rate which would be a constant factor N ( or polynomial but let’s keep things simple) by which the number of physical qubits need to be multiplied to produce a system with one additional logical qubit with an error rate to produce meaningful results.
To attain 1024 logical qubits for Schor algorithm one would need N^1024 physical qubits. The case where N<1 would be possible if error would decrease by itself without additional error correction.
alt Hacker News
What they claim is that adding physical qubits reduce error rate of the logical qubits exponentially. For the Schor algorithm the error rate of the logical qubits must decrease exponentially with every single logical qubit added to make the system produce meaningful results.
To see how it plays out consider adding a single logical qubit. First you need to increase the number of physical qubits to accommodate the new logical qubit at the same error rate. Then multiply the number of physical qubits to accommodate for exponentially decreased error rate which would be a constant factor N ( or polynomial but let’s keep things simple) by which the number of physical qubits need to be multiplied to produce a system with one additional logical qubit with an error rate to produce meaningful results.
To attain 1024 logical qubits for Schor algorithm one would need N^1024 physical qubits. The case where N<1 would be possible if error would decrease by itself without additional error correction.