Transmon or Trapped Ion? What the Price List Tells You

Two hardware modalities dominate commercially available quantum computing: superconducting transmon qubits and trapped ions. Comparisons of the two usually proceed through physics. It is more informative to proceed through the price list, because the commercial terms encode the engineering trade-off more honestly than any specification sheet.

Here are two devices available through the same cloud aggregator, at the same per-task fee:

                              Rigetti Cepheus-1-108Q   IonQ Forte-1
Modality                      Superconducting          Trapped ion
Qubits                                    108                   36
Shots per task                     1 - 10,000          100 - 5,000
Per task                                $0.30                $0.30
Per shot                            $0.000425                $0.08
1,000-shot experiment                  $0.725               $80.30

The per-shot prices differ by a factor of 188. That single number contains most of what distinguishes the two technologies, and it is worth unpacking rather than treating as a vendor pricing decision.

Why the superconducting shot is cheap

A transmon is a lithographically fabricated circuit: a Josephson junction shunted by a capacitor, cooled to around 15 millikelvin, addressed with microwave pulses. Because it is fabricated rather than assembled, adding qubits is a layout problem rather than a physics problem, which is why superconducting devices reached three-digit qubit counts first.

Gate times are the decisive economic property. Single-qubit gates take tens of nanoseconds and two-qubit gates a few hundred, so a circuit executes in microseconds and a 10,000-shot experiment completes in well under a second of device time. Shots are cheap because they are fast.

The costs sit elsewhere. Coherence times are on the order of a hundred microseconds, which bounds useful circuit depth to a few thousand gates before the state has decayed. Connectivity is fixed by the chip layout, typically nearest-neighbour on a lattice, so a two-qubit gate between distant qubits compiles into a chain of SWAPs and the effective depth grows during routing. And every qubit needs its own control lines into a dilution refrigerator, which is where the scaling difficulty ultimately concentrates.

Why the trapped-ion shot is expensive

A trapped-ion qubit is a single atomic ion held in an electromagnetic trap and manipulated with lasers. The qubits are identical because they are atoms, which removes an entire category of calibration work that superconducting devices require.

The physical advantages are substantial. Coherence times run to seconds rather than microseconds, a factor of roughly ten thousand. All-to-all connectivity is available because ions in a shared trap couple through collective motional modes, so any pair can interact directly and no SWAP chains are needed. Two-qubit gate fidelity is the best available on any platform.

The cost is speed. Gates are driven by laser pulses on microsecond to millisecond timescales, three to four orders of magnitude slower than microwave gates on a transmon. A circuit that takes a superconducting device microseconds takes a trapped-ion device milliseconds, and device time is what the per-shot price is buying. The 188x price ratio is, to a first approximation, the gate-speed ratio.

Scaling is the other constraint. Ions in a single trap interact through shared motional modes, and adding ions makes those modes progressively harder to control, which is why commercial trapped-ion devices sit in the tens of qubits while superconducting devices are in the hundreds.

What the error rates say

Representative depolarizing error rates by device class, the figures our noisy simulator uses to preview hardware behaviour:

                    1-qubit gate   2-qubit gate
Superconducting            0.001           0.01
Trapped ion               0.0005          0.005

Trapped ions are roughly twice as good on both, and the two-qubit figure is the one that matters: it is an order of magnitude worse than the single-qubit figure on both platforms, so two-qubit gate count is the quantity that predicts whether a circuit returns signal.

A rough estimate makes the consequence concrete. Circuit fidelity falls off approximately as (1 - e)^g for g two-qubit gates at error rate e, so a 100-gate circuit retains about 37% fidelity at e = 0.01 and about 61% at e = 0.005. At 300 gates the same estimate gives 5% and 22%. The gap widens with depth, which is the practical meaning of a factor-of-two fidelity advantage.

This is also where the connectivity difference stops being an abstraction. If a circuit's logical two-qubit gates are between arbitrary pairs, a nearest-neighbour device inserts SWAPs, each of which is three CNOTs. A circuit with 100 logical two-qubit gates can become several hundred physical ones after routing, on the platform that already has the higher error rate per gate. All-to-all connectivity removes that multiplier entirely.

Choosing between them

The decision is usually settled by three questions, in this order.

• How many qubits does the circuit need? Above 36, the trapped-ion device is not an option and the question is closed. This is the most common deciding factor and the least discussed.
• How deep is the circuit in two-qubit gates, after routing? Shallow circuits run acceptably on either. Deep circuits, or circuits with non-local connectivity, favour trapped ions by enough to justify the price difference. Compare transpiled depth against submitted depth before deciding; the growth is invisible otherwise.
• How many shots does the result need? At 188x per shot, a statistics-hungry experiment on trapped-ion hardware becomes expensive quickly. A 5,000-shot task, the IonQ maximum, costs $400.30. The same task on the superconducting device costs $2.425.

Note also the lower shot bound. IonQ rejects any task under 100 shots, so the single-shot smoke test that works against every simulator and against the Rigetti device fails against Forte-1. Discovering this after a queue wait is avoidable by reading the device's shot range first.

The step most people skip

Both devices cost real money and both have queues measured in minutes to hours. Neither is the right place to discover that an ansatz was misconstructed or that an observable had the wrong Pauli string length.

Simulation answers those questions for a fraction of a cent and returns in seconds. A noisy simulator using the error rates above will additionally show whether the circuit survives realistic gate noise, and if it does not, no amount of hardware time will change that. The remaining question, which platform, is then answered by the three criteria above rather than by trial.

The full arithmetic of hardware versus simulation, including what variational workloads cost once the iteration count is included, is in What does it cost to rent a quantum computer?. The constraints each platform imposes before a job is accepted are in Why your circuit was rejected.