Question

What is the fundamental requirement regarding the physical error rate of a system for the threshold theorem to guarantee that large-scale fault-tolerant computation is possible?

Accepted Answer

The threshold theorem states that large-scale fault-tolerant quantum computation is possible if and only if the physical error rate of the system is below a specific value known as the fault-tolerant threshold. The physical error rate refers to the probability that a single quantum operation, such as a gate or a memory storage step, results in an unintended state change or decoherence. If the physical error rate is below this threshold, the system can use quantum error correction to encode logical qubits—which are groups of physical qubits used to store information redundantly—such that the error rate of the logical qubits decreases as more physical qubits are added. The fundamental requirement is that the rate at which errors are introduced must be slower than the rate at which the error correction protocol can detect and fix them. If the physical error rate exceeds the threshold, the overhead required to correct errors increases faster than the system can manage, and the error correction process itself introduces more errors than it fixes, leading to an exponential increase in uncorrectable noise.

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What is the fundamental requirement regarding the physical error rate of a system for the threshold theorem to guarantee that large-scale fault-tolerant computation is possible?

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