Readout fidelity

At the end of a quantum program, you measure (read out) the qubits. Each qubit gives a 0 or a 1. Readout fidelity is how often that answer is correct. Its flip side is the readout error: 100% minus the fidelity. So 99% fidelity is a 1% error, often written 1E-2.

It has other names too: measurement fidelity and assignment fidelity. Trapped-ion vendors often report SPAM error instead. SPAM stands for "state preparation and measurement". It counts mistakes in setting the qubit up at the start and in reading it at the end, together.

Readout fidelity is often split into two parts, because they are rarely equal:

• P(read 0 | was 0): the chance of reading 0 when the qubit really was 0.
• P(read 1 | was 1): the chance of reading 1 when the qubit really was 1.

On superconducting chips the second one is usually lower. A qubit in state 1 can lose its energy and drop to 0 while it is being read. (That drop is the T1 process.)

An everyday example. Think of a line judge at a tennis match. The ball landed either in or out. The judge calls it. A good judge is right 99 times out of 100. Readout fidelity is the judge's accuracy.

Where the example breaks. The tennis ball landed in one clear spot before the judge looked. A qubit in superposition does not have a set answer waiting to be seen. The measurement itself picks 0 or 1, with odds set by the qubit's state. That randomness is not an error. Readout fidelity is tested only on qubits set up in a clear 0 or a clear 1. So it measures reporting mistakes, not the normal randomness of quantum results. Our lesson on measurement explains that difference.

The basic test is simple. Prepare a qubit in 0 thousands of times and measure it each time. Count how often it reads 0. Then do the same with 1. Average the two success rates. That average is the usual readout fidelity.

How the reading itself works depends on the hardware:

• Superconducting qubits are read by sending a small microwave signal to a tiny circuit (a resonator) next to the qubit. The echo comes back slightly different for 0 and for 1. This is called dispersive readout. It is fast, but a short signal is hard to tell apart cleanly.
• Trapped ions and neutral atoms are read with a laser. One state glows (gives off light) and the other stays dark. A camera or light detector counts the light. This is often very accurate, but slower.

Two extra things change the number:

• Alone or together. Reading one qubit while the others sit quiet is easier than reading all of them at once. Signals can leak between neighbours.
• Raw or mitigated. Readout error mitigation is a software fix. You measure how often each wrong answer happens, then correct your counts afterward. It improves averages over many runs. It cannot fix a single run. A mitigated figure is a different claim from a raw one, and vendors do not always say which they give.

Measurement protocols are covered in Krantz et al., 2019. Our chapter on mitigation versus correction explains the software side.

Readout figures are not directly comparable when:

1. One is raw and the other is mitigated. Software correction can make a number look far better without changing the hardware.
2. One is readout-only and the other is SPAM. SPAM also includes set-up errors, so it answers a wider question.
3. The aggregation differs. A median qubit, a mean over the chip, and a best qubit are three different numbers.
4. One qubit read alone vs all read together. Reading everything at once is harder.
5. The kind of readout differs. Reading in the middle of a program, to be used again, is harder than a final read at the end.
6. Speed differs. A slow, careful readout can score higher than a fast one. That speed has a cost in run time.

Annealing machines are a special case. They report readout error too, but they are not gate-based machines. Their number describes a different kind of result, so it does not belong in the same column. Where a vendor did not state the method, our record says so instead of guessing.

Readout errors add up across qubits. If each qubit reads right with a chance of 0.98, the chance that all of 10 qubits read right is 0.98 multiplied ten times.

• 0.98¹⁰ ≈ 0.817. So about 82% of runs read every qubit right.
• That leaves about 18% of runs, nearly one in five, with at least one wrong bit. And that is before counting any gate errors.
• At 99% per qubit: 0.99¹⁰ ≈ 0.904. Now about 10% of runs have a wrong bit.

Why the two parts matter. Use made-up numbers to see it (these belong to no real device). Say P(read 0 | was 0) = 0.99 and P(read 1 | was 1) = 0.95. The average is (0.99 + 0.95) ÷ 2 = 0.97. Now read 5 qubits:

• If the true answer is 00000: 0.99⁵ ≈ 0.951. About 95% of runs read it right.
• If the true answer is 11111: 0.95⁵ ≈ 0.774. Only about 77% read it right.

Same chip, same "97% average", but results with many 1s come out worse. A single average hides this. The simple estimate also assumes each qubit's error is independent. Real neighbours can affect each other.

On each QPU page, readout appears under "Readout". Check the unit first. Some records give fidelity (like 96%), and some give error (like 3.418E-3). Then check the method and aggregation. For example:

• Google Sycamore lists a vendor-reported mean readout error of 3.1% isolated and 3.8% simultaneous. Reading all qubits together adds error.
• Google Willow lists two vendor-reported mean figures from two chips: 0.77% ± 0.21% for repetitive readout (Chip 1, used for error correction) and 0.67% ± 0.51% for a terminal readout of all qubits (Chip 2). Different chips and different kinds of readout, so they are not a direct pair.
• IonQ Forte lists a vendor-reported SPAM fidelity of 99.5% (0.5% SPAM error), an average. SPAM includes set-up errors, so it is a wider figure than readout alone.

Also see OQC Toshiko, which lists a vendor-reported median readout fidelity of 96% with the method not stated.

Next, see how readout combines with two-qubit gate fidelity on the comparison page. The lesson on reading hardware specs shows how to put all the figures together.