Noise Thresholds for Amplification: From Quantum Foundations to Classical Fault-Tolerant Computation
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We revisit an old question--fault-tolerant computation by noisy circuits--in a new light. More precisely, we investigate noise thresholds in fault-tolerant computation for new classes of noisy gates inspired by foundational questions in quantum mechanics. Our main technical result is that, perhaps surprisingly, noiseless XOR gates are not more helpful than noisy ones in read-once formulas that have noisy AND gates for the task of building amplifiers. We also formalize a connection between fault-tolerant computation and amplification, and highlight new directions and open questions in fault-tolerant computation with noisy circuits.
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