The DiVincenzo Criteria

Every few months a headline announces a new "quantum computer" — built from trapped ions, or superconducting loops, or single atoms, or photons. How do you tell a real contender from a physics demo? In 2000 David DiVincenzo wrote down the checklist: a short list of things any physical technology must be able to do before it deserves the name. It is the scorecard every qubit technology is graded on, and once you know its five entries you can size up any platform — read a press release and ask, calmly, "fine, but which boxes does it actually tick?"

The five core criteria

A machine is a quantum computer only if it can do all five of these. Each one sounds obvious in isolation; the trick is that a single physical system has to satisfy all of them at once.

Scalable, well-characterised qubits. A physical system holding two-level qubits whose behaviour you understand precisely — and, crucially, a way to make more of them without the engineering falling apart.
Initialise to a known state. You must be able to reset the register to a simple fiducial starting point, conventionally the all-zeros state |0\cdots0\rangle.
Long coherence times. The qubits must keep their quantum information alive much longer than it takes to operate on them — many gates' worth — before noise scrambles them.
A universal set of gates. A small kit of gates from which any quantum computation can be assembled (typically some single-qubit gates plus one entangling two-qubit gate like the CNOT).
Qubit-specific measurement. The ability to read out a chosen qubit and get a reliable classical bit at the end.

…and two more for a quantum internet

DiVincenzo added two further criteria — not needed to compute, but required to communicate quantum information between distant machines (a future "quantum internet"):

Interconvert stationary and flying qubits. Turn a computing qubit (a stationary ion or circuit) into a flying one — typically a photon — and back again.
Faithfully transmit flying qubits. Send those flying qubits between two locations without corrupting the state they carry.

Keep the split in mind: criteria 1–5 are for computation, criteria 6–7 are for networking. A stand-alone quantum computer only has to ace the first five.

The scorecard

Here is the whole checklist as one card. Step through it: the five core criteria tick off first, then a divider, then the two networking extras. This is the mental template to hold up against any hardware platform.

Worked example 1: why criterion 3 is really a ratio

Criterion 3 is easy to misread as "the qubit must last a long time." A long time compared to what? A trapped ion whose coherence lasts a full second sounds fabulous — but useless if a single gate also took a second, because you'd get to run only one operation before the state died. What matters is the ratio

N \;\approx\; \frac{T_{\text{coherence}}}{t_{\text{gate}}},

roughly the number of gates you can apply before decoherence wrecks the computation. Suppose a superconducting qubit has coherence time T_{\text{coherence}} = 100\,\mu\text{s} and a gate time t_{\text{gate}} = 20\,\text{ns}. Then

N \approx \frac{100\times 10^{-6}\,\text{s}}{20\times 10^{-9}\,\text{s}} = 5000

operations before the qubit forgets. That is the figure of merit — not the raw coherence time. Criterion 3 is properly read as coherence time ≫ gate time: a big ratio, so many gates fit inside one qubit lifetime. (Error correction needs this ratio to be very large indeed — thousands to millions.)

Worked example 2: the circuit model needs both ends

Two of the criteria — initialisation (2) and measurement (5) — look like bookkeeping, but the circuit model can't run without them. Recall the shape of every circuit:

|0\cdots0\rangle \;\xrightarrow{\;\text{gates } U\;}\; U\,|0\cdots0\rangle \;\xrightarrow{\;\text{measure}\;}\; \text{classical bits}.

The very left of the diagram is a fixed starting vector — you must be able to prepare |0\cdots0\rangle, which is exactly criterion 2. The very right is a column of meters — you must be able to read out the answer, which is exactly criterion 5. The gates in the middle are criterion 4 (a universal set), running fast enough relative to criterion 3 (coherence) to finish before the state decays, on qubits provided by criterion 1. So the abstract circuit model and the physical checklist line up piece for piece: initialise on the left, gates in the middle, measure on the right.

a technology is a quantum computer only if it meets five core criteria: (1) scalable well-characterised qubits, (2) initialisation to |0\cdots0\rangle, (3) long coherence, (4) a universal gate set, and (5) qubit-specific measurement;
criterion 3 is a ratio: coherence time \gg gate time, i.e. many gates fit inside one qubit lifetime;
the circuit model needs the two ends — initialise on the left (2), measure on the right (5);
two extra criteria enable quantum networking: (6) interconvert stationary and flying qubits, and (7) faithfully transmit them;
the criteria are the lens for comparing hardware platforms — trapped ions, superconductors, photons — each a different compromise.

The power of the checklist is that it turns a zoo of exotic physics into a single comparison table. Down the side: the seven criteria. Across the top: the candidate platforms — trapped ions, superconducting circuits, neutral atoms, photonic qubits, spins in silicon. Every real research programme is, in effect, an entry in that table, strong in some rows and weak in others. Trapped ions have gorgeous coherence and readout but are slow and fiddly to scale; superconducting qubits are fast and lithographically scalable but decohere quickly; photons fly beautifully (criteria 6–7) yet barely interact, which makes gates hard. No entry is all ticks. Reading a hardware announcement, then, is just filling in one more column of DiVincenzo's table — and asking which box the newcomer failed to tick.

It is tempting to imagine you could satisfy the criteria one at a time, as if ticking a shopping list. You can't, because the criteria fight each other. Criterion 3 wants a qubit that is exquisitely isolated from its environment, so noise can't disturb it. But criteria 4 and 5 — applying gates and reading the qubit out — require you to reach in and touch it with control fields and detectors. A qubit hidden well enough from noise is, by the same token, hard for you to talk to; the very coupling that lets you control it is a channel through which noise leaks in. Good isolation trades against strong control and readout. That is why no platform aces all five — each technology is a different negotiated compromise between staying quiet and staying controllable. When you compare trapped ions, superconducting qubits, and photonic qubits, you are really comparing where each one drew that line.