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The logical error rate is the probability that an error-corrected logical qubit suffers an uncorrected error during a logical operation. It is the single most important performance metric for fault-tolerant quantum computers, because it directly determines how many operations a computation can run before failing — and therefore which applications are possible.
How is it different from a physical error rate?
The physical error rate describes raw hardware: how often an individual qubit or gate fails. The best systems today operate around 10⁻³ — QuEra's neutral-atom machines have demonstrated 99.77% two-qubit gate fidelity. At that rate, a computation degrades after roughly a thousand operations.
The logical error rate describes error-corrected performance. Quantum error correction encodes each logical qubit across many physical qubits and actively detects and fixes faults, so the logical error rate can be pushed far below the physical one — to 10⁻⁶, 10⁻⁹, and beyond.
Why does the logical error rate determine what's possible?
A useful rule of thumb: a machine can reliably run about 1/p operations, where p is the logical error rate.
• 10⁻³ (physical, uncorrected): ~1,000 operations — the NISQ regime.
• 10⁻⁶: ~1 million operations — the megaquop regime. QuEra's Libra (launching 2028) targets 256 logical qubits at this level, enough for classically intractable quantum simulations in materials science.
• 10⁻⁹: ~1 billion operations — the gigaquop regime. QuEra's next-generation system targets 1,000+ logical qubits at this level, opening quantum chemistry and nuclear dynamics applications.
This is why logical metrics, not physical qubit counts, are the right way to compare quantum computers: 10,000 uncorrected physical qubits still fail after ~1,000 operations, while 256 logical qubits at 10⁻⁶ can run a million.
How do you improve the logical error rate?
Three levers, all demonstrated in peer-reviewed research:
1. Operate below threshold. When physical error rates are below the QEC threshold, increasing the code distance suppresses logical errors exponentially. QuEra and collaborators demonstrated below-threshold error correction by a factor of more than 2.
2. Use better codes. High-rate qLDPC codes deliver strong logical performance with far fewer physical qubits; QuEra's ultra-high-rate code research reaches logical memory error rates in the 10⁻¹³ regime.
3. Decode smarter. Correlated decoding across logical qubits improves logical error rates by roughly 1.5x, and neural-network decoders have shown ~17x improvements over standard bicycle-code decoders.
