Fault-tolerant quantum computing requires error rates below a threshold — we're getting close

The threshold theorem in quantum error correction says that if physical qubit error rates fall below a threshold (roughly 1% for surface codes), you can concatenate error-correcting codes to arbitrarily suppress logical error rates. Below the threshold, adding more physical qubits per logical qubit makes things better. Above it, adding qubits makes things worse.

Recent results from Google, IBM, and several academic groups have pushed physical error rates into the range where fault-tolerant operation is becoming plausible for small logical qubits. The 2023 Google result showed logical error rates below physical error rates for small surface codes — crossing below the threshold in a real device for the first time.

This matters because most proposed applications of quantum computing — Shor's algorithm for factoring, quantum simulation of chemistry, optimization algorithms with proven quantum speedups — require fault-tolerant operation at scales far larger than current hardware. NISQ-era algorithms are improvised workarounds for a machine we don't quite have yet.

The open question for the field isn't whether fault-tolerant QC is physically possible — the theory is solid. It's whether the engineering path from here to a fault-tolerant machine with thousands of logical qubits is manageable, or whether there are scaling obstacles we haven't encountered yet.

Independent researchers: what aspects of the error correction literature do you find most underexplored?