Practice vocabulary for fault-tolerant quantum computing: FTQC, fault-tolerant threshold, transversal gates, the quantum threshold theorem, and the roadmap to fault tolerance.
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What is 'fault-tolerant quantum computing' (FTQC)?
Fault-tolerant quantum computing (FTQC) combines quantum error correction with careful circuit design to perform reliable computations despite physical qubit noise. 'Fault-tolerant' specifically means errors introduced during error correction itself do not cascade — syndrome measurements, corrections, and logical gate operations are all designed so that one physical error causes at most one logical error. Current NISQ devices are not fault-tolerant; FTQC is the target for practical quantum advantage.
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What is the 'fault-tolerant threshold' (error threshold) in quantum error correction?
The fault-tolerant threshold is a critical error rate below which scaling up the error-correcting code (increasing code distance) reduces the logical error rate exponentially. Above the threshold, adding more physical qubits introduces more errors than the code can correct — the situation worsens. The surface code threshold is ~1% per physical gate. Current best superconducting gates are ~0.1–0.5%, below threshold — meaning error correction will help as devices scale.
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What is a 'transversal gate' in fault-tolerant quantum computing?
Transversal gates apply the same single-qubit physical gate to each physical qubit in the code block in parallel — no qubit in block A interacts with more than one qubit in block B. This prevents error spreading (if one physical qubit has an error, it cannot infect others during the gate). The Clifford group gates (H, S, CNOT) are transversal in many codes. Non-Clifford gates (like T) are generally not transversal, which is why T gates are expensive in FTQC.
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What does the 'quantum threshold theorem' state?
The quantum threshold theorem (proved independently by Aharonov & Ben-Or; Knill, Laflamme & Zurek; Kitaev — all circa 1996–1998) is foundational: it guarantees that fault-tolerant quantum computing is scalable. If physical error rates are below the threshold, the logical error rate can be suppressed to any desired level by concatenating or increasing code distance — with only polylogarithmic overhead. This theorem is what makes fault-tolerant quantum computing theoretically achievable.
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In the industry roadmap to fault-tolerant quantum computing, what are the key milestones?
Industry roadmaps (IBM, Google, Microsoft, IonQ) describe a progression: NISQ era (current — 100s to low 1000s of noisy physical qubits, no error correction); early QEC (demonstrating below-threshold logical qubits, limited error-corrected circuits); early FTQC (10s of logical qubits, running meaningful error-corrected algorithms); utility-scale FTQC (1000+ logical qubits, tractable quantum advantage in chemistry, optimisation, cryptanalysis). Timelines range from 2028 to mid-2030s across different organisations.