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What is a logical qubit, and why do quantum computers need them?

By PhotonDispatch Staff · Published · Last updated

Short answer: A logical qubit is a qubit built out of many physical qubits. The quantum information is spread across the group in a pattern, called an error-correcting code, so that errors on individual physical qubits can be detected and fixed without reading out, and destroying, the information itself.

Physical qubits, whether superconducting circuits, trapped ions or neutral atoms, are fragile. Heat, stray fields and imperfect control pulses flip or blur their states, and today's best hardware still makes errors far more often than long, useful algorithms are expected to tolerate. A logical qubit is the field's answer: rather than waiting for perfect hardware, it adds redundancy.

The idea can't simply copy classical backup. The no-cloning theorem says an unknown quantum state cannot be copied, and measuring a qubit directly collapses it. Error-correcting codes get around this by measuring only joint properties of groups of qubits, called stabilizers or parity checks. Those checks reveal whether, and roughly where, an error happened, but say nothing about the encoded value, as Daniel Gottesman's widely used introduction to the subject explains.

The most studied design is the surface code, in which physical qubits sit on a two-dimensional grid and neighbouring groups are checked over and over in rounds. Austin Fowler and colleagues' 2012 review describes how logical qubits are formed on such a grid and how operations between them are carried out. The size of a surface-code logical qubit is set by its code distance, d: a distance-d code needs on the order of 2d² physical qubits including the measurement helpers, and can correct any combination of fewer than about d/2 errors.

Bigger is only better if the hardware is good enough. Below a hardware error rate called the threshold, each step up in code distance makes the logical qubit more reliable; above it, adding qubits makes things worse. In a paper published in Nature in December 2024, Google Quantum AI reported a 101-qubit distance-7 surface-code memory on its Willow processor with an error rate of 0.143% per error-correction cycle, and said the logical error rate fell by a factor of 2.14 each time the distance grew by two. The team also reported that the logical memory outlived its best physical qubit by a factor of 2.4.

Other hardware approaches use the same concept. A Harvard-led team reported in Nature in 2023 a neutral-atom processor that ran circuits with up to 48 logical qubits using a small error-detecting code, and improved a logical two-qubit gate by moving from a distance-3 to a distance-7 surface code.

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