Practice vocabulary for physical qubits, logical qubits, qubit overhead, code distance, and the fundamentals of quantum error correction encoding.
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What is a 'physical qubit' in quantum computing?
A physical qubit is the real hardware unit: a Josephson junction in a superconducting chip (IBM, Google), a trapped ytterbium ion (IonQ, Quantinuum), a photon (PsiQuantum), or a nitrogen-vacancy centre (diamond). Physical qubits are noisy — current error rates range from ~0.1% (best trapped ion) to ~0.5% (superconducting) per two-qubit gate. This noise necessitates quantum error correction.
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What is a 'logical qubit' and why is it needed?
A logical qubit is a fault-tolerant qubit built by entangling many physical qubits in an error-correcting code. The code distributes quantum information across the ensemble so that errors on individual physical qubits can be detected and corrected without measuring (and collapsing) the logical state. The goal of fault-tolerant quantum computing is to build enough logical qubits of sufficient quality to run algorithms like Shor's or quantum chemistry simulations.
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What is 'qubit overhead' in quantum error correction?
Qubit overhead quantifies the physical-to-logical ratio in an error correction code. For the surface code at code distance d=31 (targeting logical error rates suitable for Shor's algorithm on RSA-2048), estimates suggest ~1,000 physical qubits per logical qubit and millions of physical qubits total. This is why scaling to fault-tolerant quantum computing requires millions of physical qubits — far beyond current processors of ~1,000–2,000 physical qubits.
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What is 'code distance' in a quantum error correcting code?
Code distance d is the weight of the minimum-weight error that would cause an uncorrectable logical failure. A distance-3 code corrects 1 error; distance-5 corrects 2; distance-d corrects ⌊(d-1)/2⌋ errors. Higher distance codes require more physical qubits (a distance-d surface code uses d² physical qubits per logical qubit) but provide exponentially lower logical error rates as d increases, provided physical error rates are below threshold.
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Why does fault-tolerant quantum computing require so many physical qubits per logical qubit?
Quantum information cannot be copied (no-cloning theorem), so classical repetition cannot be used. Instead, QEC encodes one logical qubit across many entangled physical qubits using codes like the surface code. Regular 'syndrome measurements' detect errors without disturbing the logical state, and classical decoding algorithms (minimum-weight perfect matching) determine corrections. The overhead is the price of reliable quantum computation — until physical error rates improve dramatically, many physical qubits are needed per logical one.