Qubit count

A qubit is the basic unit of a quantum computer, like a bit in a normal one. Qubit count is how many a processor has. It is the headline number in almost every announcement. But the word "qubit" hides several different things:

• Physical qubits are the actual hardware parts: tiny circuits, trapped ions, atoms or particles of light.
• Logical qubits are error-protected qubits built from many physical qubits working together. Today's machines have few or none of these.
• Fabricated vs working. A chip may be built with more qubits than actually work.
• Computational vs helper parts. Some chips have extra elements, like couplers, that link qubits but do not hold data.
• Sites vs atoms. A neutral-atom machine has spots for atoms. Not every spot is filled on every run.

An everyday example. Think of a piano. Counting the keys tells you its range. It does not tell you if it is in tune, or if some keys stick. It also does not tell you which keys you can press together. Qubit count is the number of keys. Fidelity is the tuning. Connectivity (which qubits can act on each other directly) is which keys you can reach at once.

Where the example breaks. Piano keys are independent. Each makes its own sound. Qubits are useful because they can be linked (entangled) so they act as one system. Errors can also spread from one qubit to its neighbours. So adding qubits can make a chip harder to control, not just bigger.

To describe n qubits fully, a normal computer must track 2ⁿ numbers, called amplitudes. Each extra qubit doubles that. Ten qubits need 1,024 numbers. Twenty need 1,048,576. Thirty need 1,073,741,824.

That growth is the reason quantum computers are interesting. It is also why our Lab simulator has an honest size limit. But the doubling only helps if the qubits are good enough to use together. A large count with high error rates cannot run a deep circuit on all of those qubits and still give a clear answer.

Counting sounds simple, but each vendor chooses what to count:

• Some count every qubit on the chip. Others count only the ones users can program.
• IonQ also leads with "algorithmic qubits" (#AQ). That is a score from running a set of test programs, not a count of hardware parts.
• Annealing machines, like D-Wave's, count qubits that solve one kind of problem (finding low-energy states). They do not run gate-based programs. Their qubits are also linked in a fixed pattern.
• Analog machines count atoms that are driven together by one shared signal. They are not gate-model qubits at all.

Counts can also change over time on one product line, as individual machines are built or retuned. That is why our records say which specific machine or system a count describes, where the vendor says.

For how many physical qubits one logical qubit may need, see Fowler et al., 2012 and our chapter on physical versus logical qubits.

Often, no. Gate-model, annealing and analog counts live on different scales. Thousands of annealing qubits and about a hundred gate-model qubits solve different kinds of problems. One cannot be ranked above the other. QPU137 lists non-gate machines separately for exactly this reason, and leaves them out of gate-level comparisons.

Even within gate-model machines, counts are not directly comparable when:

1. Connectivity differs. On some chips each qubit touches only two or three neighbours. On others every qubit can act on every other. The same circuit needs more extra gates (SWAPs) on the first kind.
2. Gate quality differs. A chip whose gates fail more often cannot use a large count for deep circuits.
3. One count is physical and one is logical. A logical qubit may use dozens or hundreds of physical ones.
4. One is fabricated and one is working. Check which the record says.

The honest test is to run your own circuit on both layouts. Compare two processors to see the cost of each layout for the same program.

Say your program needs 100 two-qubit gates after compiling. Compare two made-up machines (these numbers belong to no real device):

• Machine A has 1,000 qubits and 99.0% two-qubit fidelity. Chance that all 100 gates work: 0.99¹⁰⁰ ≈ 0.366, about 37%.
• Machine B has 50 qubits and 99.9% fidelity. Chance: 0.999¹⁰⁰ ≈ 0.905, about 90%.

If your program fits in 50 qubits, the smaller machine is far more likely to give a clean answer. The extra 950 qubits do nothing for you. (This is a rough rule of thumb that ignores other errors. See two-qubit fidelity for its limits.)

The cost of error correction. One common design, the rotated surface code, uses d² data qubits plus d² − 1 helper qubits per logical qubit. Here d is the code's size (its distance). Bigger d protects better. So the total is 2d² − 1:

• d = 3: 2 × 9 − 1 = 17 physical qubits for one logical qubit.
• d = 7: 2 × 49 − 1 = 97 physical qubits for one logical qubit.

So a chip with around a hundred physical qubits holds about one logical qubit at d = 7. Physical count and useful count are very different things.

On every QPU page, the count appears under "Qubit count", with the vendor's own wording. Read that wording carefully. It often says what kind of count it is:

• Google Sycamore: vendor-reported "54 fabricated; 53 functional". One qubit did not work.
• IQM Garnet: vendor-reported "20 computational qubits (+30 tunable coupler qubits, 50 total on chip)". Only 20 hold data.
• IBM Condor: vendor-reported 1121 qubits. Our record also shows that IBM did not disclose its two-qubit gate fidelity, T1/T2 or readout fidelity. A count with no quality figures cannot tell you what the chip can run.

For machines that are not gate-based, see D-Wave Advantage2 (annealing, vendor-reported "4,400+") and QuEra Aquila (analog, a vendor-reported maximum of 256 filled sites). Their counts measure different things from gate-model qubits.

To judge a machine properly, read its count together with two-qubit fidelity and coherence time. The lesson on reading hardware specs walks through a full spec sheet.