AIO APEX

Logical qubits, not physical qubit counts, are the number that matters in quantum computing

Share:
Logical qubits, not physical qubit counts, are the number that matters in quantum computing

Every few months a quantum computing announcement arrives with a bigger number attached. A chip with more qubits, a processor with a higher count, a roadmap promising thousands by the end of the decade. The number is easy to report and easy to compare, which is exactly why it is misleading. A physical qubit is a noisy device that loses its quantum state within microseconds to milliseconds. A machine that can run algorithms useful for chemistry, materials or cryptography needs logical qubits: units of information protected by error correction, reliable enough to chain thousands or millions of operations together.

The gap between the two numbers is the central engineering problem of the field. Reading vendor claims well means understanding that gap and asking the questions that expose it.

Why physical qubits are not enough

Quantum states are fragile. Heat, electromagnetic noise and imperfect control pulses all introduce errors, and those errors accumulate. Without correction, a long computation becomes a random number generator. Error correction solves this by encoding one logical qubit across many physical qubits, then repeatedly measuring parity checks that reveal errors without destroying the stored information. The surface code, the most studied scheme so far, arranges physical qubits on a two-dimensional grid and uses those checks to detect and fix errors continuously.

The catch is overhead. A logical qubit built with a surface code needs a code distance d, a number that roughly sets how many errors the code can tolerate. The physical qubit count per logical qubit scales with the square of d, so a logical qubit may require several hundred to over a thousand physical qubits depending on the error rate of the hardware and the accuracy the algorithm needs. A machine with ten thousand physical qubits may therefore hold only a handful of usable logical qubits.

The threshold result that changed the conversation

The most important recent milestone was a demonstration of below-threshold error correction. The threshold is the physical error rate below which adding more qubits to a code reduces the logical error rate instead of increasing it. In late 2024, Google Quantum AI reported on its Willow chip that a surface code logical qubit's error rate fell by roughly half each time the code distance increased from 3 to 5 to 7. That scaling behaviour is what makes larger machines potentially useful, because it means more hardware can buy more reliability rather than more noise.

Several other groups have since reported small logical-qubit experiments on trapped-ion and neutral-atom platforms, using different codes and hardware. The field has moved from asking whether error correction can work at all to asking how well, how cheaply and across which architectures.

How to read a logical qubit claim

When a company announces a logical qubit result, five pieces of information decide how much it means.

The logical error rate per operation or per correction cycle. A logical qubit that survives a single cycle is not the same as one that survives a thousand. Ask for the error rate per cycle and how it was measured.

The code distance and the code used. A demonstration at distance 3 is a proof of concept. Distance 7 or above tells you whether the approach scales. Ask which code family is used, because overhead differs between codes.

The physical-to-logical ratio. Divide the physical qubit count by the number of logical qubits and check whether the number is plausible for the stated error rates. A claim of many logical qubits on modest hardware should prompt questions.

Post-selection. Some experiments discard runs in which error detection flagged a problem and report results only from the remaining runs. This can improve the apparent error rate substantially. Check whether the reported figures include discarded data, and whether the algorithm would still work if every run were kept.

Non-Clifford gates. Error correction handles some operations cheaply, but others, notably the T gate needed for universal computation, require a costly process called magic state distillation. A machine that corrects errors well on simple gates may still be very slow for the algorithms people care about. Ask what the cost of T gates is in physical qubits and time.

What this means for the next few years

The honest picture is that the field is in the phase where the building blocks are being proven, not where useful machines exist. Chemistry and materials simulations that outperform classical methods are the most-cited targets, and they require many thousands of high-quality logical qubits running for long periods. Cryptographically relevant machines are further out, and the timelines in public discussion vary widely. For planning purposes, the most useful indicators are logical error rates at larger code distances, the cost of non-Clifford operations, and demonstrations of multi-round algorithms on logical qubits rather than single-round tests.

There is also a practical implication for anyone tracking the field. Press releases that lead with qubit counts are usually easier to write than ones that lead with logical error rates, and that asymmetry is itself a signal. Treat a headline number as the start of the question, not the answer.

Actionable takeaways

  • When you see a qubit count, ask for the number of logical qubits, the code distance and the logical error rate per cycle. If none are given, the claim is not yet comparable.
  • Calculate the physical-to-logical ratio yourself and sanity-check it against the reported error rates.
  • Check whether results used post-selection, and whether the figures would hold if discarded runs were included.
  • For algorithm planning, focus on the cost of non-Clifford gates and the number of logical operations a target computation needs, not hardware size alone.
  • Follow peer-reviewed papers and the vendor's raw data releases rather than only the announcement, since the methods section often contains the caveats that the headline omits.

Physical qubits are a measure of how much hardware a lab has built. Logical qubits are a measure of how much reliable computation it can perform. Only the second number tells you when quantum computers will start solving problems that classical machines cannot, and that is the number worth tracking.

Share:
Logical Qubits vs Physical Qubits: How to Read Quantum Claims | IRCNF | AIO APEX