Fault-Tolerant Threshold Theorem | Scalable Quantum Computation
Quick Technical Answer:
The Fault-Tolerant Threshold Theorem proves that if physical gate and measurement error rates remain below a critical threshold p_th (~1% for surface codes), arbitrary quantum computations can be executed with arbitrarily low logical error rates.
Formula / Unitary:
p_L \propto \left( \frac{p}{p_{\text{th}}} \right)^{(d+1)/2}, \quad p < p_{\text{th}} \implies p_L \to 0 \text{ as } d \to \infty
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Frequently Asked Questions
What is the physical error rate of current quantum hardware compared to the threshold?
Leading superconducting qubits and trapped ions achieve 2-qubit gate error rates around 0.1% to 0.5%, placing them just below the ~1% threshold required for exponential error suppression.