Appendix G: Hardware Reference

What the physical devices are, what they cost, and which numbers are worth trusting. Every measured figure here came from this book's own runs against real calibration data; anything else is labelled.

The modalities

★ The trade is speed against connectivity. Superconducting gates are ~1,000× faster and pay for it in routing: Chapter 39 measured a 14-qubit circuit spanning 49 to 112 two-qubit gates purely from routing overhead. Trapped ions have no routing overhead and cost 28× per shot.

Measured device characteristics

From a real 133-qubit heavy-hex device (Chapter 39):

   dt (time resolution)          4e-09 s
   cz  (two-qubit)               68.0 - 184.0 ns
   sx  (single-qubit)            32.0 -  64.0 ns
   rz  (virtual)                       0.0 ns
   measure                          1,560.0 ns
   reset                     1,600.0 - 1,848.0 ns

From a 127-qubit ECR-based device:

   dt                            2.22e-10 s
   ecr                          341.3 - 881.8 ns
   sx                                  56.9 ns
   measure                          1,216.0 ns

Error rates and coherence, same 133-qubit device:

   cz  (two-qubit)   min 1.79e-03   median 3.66e-03   max 1.00e+00
   sx  (one-qubit)   min 1.13e-04   median 2.44e-04   max 1.00e+00
   T1                min 15.2 µs    median 174.9 µs   max 483.0 µs
   T2                similar spread

⚠️ Some links have error 1.00 — they are dead. And T1 varies by a factor of 32 across one chip. Which physical qubits you are assigned is a first-order determinant of your result, and the platform assigns them at execution time.

Reading calibration data

target = backend.target
target.dt                                     # time resolution, seconds
target["cz"][(0, 1)].error                    # link error rate
target["cz"][(0, 1)].duration                 # seconds
target["measure"][(0,)].error                 # readout error
target.qubit_properties[0].t1                 # seconds
target.qubit_properties[0].t2
backend.coupling_map.neighbors(3)             # DIRECTED

⚠️ coupling_map.neighbors() is directed. Chapter 29 treated it as undirected and 29 qubits appeared to have no neighbours at all. Use coupling_map.graph.neighbors_undirected() or union both directions.

Topologies

Heavy-hex (IBM) — degree ≤ 3, chosen to suppress crosstalk and frequency collisions. The cost is routing: any circuit needing rich connectivity pays in SWAPs.

Grid (Google) — degree 4, denser than heavy-hex.

All-to-all (trapped ion) — no routing at all. A circuit's two-qubit gate count is what you wrote.

Reconfigurable (neutral atom) — atoms can be physically moved between operations.

Timing and coherence

A circuit must finish inside coherence. The budget:

$$\text{circuit duration} \ll \min(T_1, T_2)$$

Chapter 39's measured durations for 4,096 shots:

★ On shallow circuits, readout dominates. Measurement alone is 1,560 ns — longer than the entire Bell circuit's gate sequence.

Pricing

Published list rates change. The structure is what is durable.

A per-shot and a per-minute price cannot be compared without the circuit duration — the duration is the conversion factor.

Chapter 39 priced one 18,456,984-shot VQE run — 31.2 seconds of device time:

   per-minute    $     50      ($    2 per device-second)
   per-shot      $  7,432      ($  238 per device-second)   149x
   trapped ion   $185,542      ($5,948 per device-second) 3,718x

You are not paying for device time. You are paying for access.

Metrics, and what each hides

⚠️ Chapter 30 measured one chip supporting quoted two-qubit errors from 0.00750 to 0.07205 — a factor of 9.6 — depending on which statistic you pick. Never accept a device fidelity without asking which one. Best-link, median, and mean are three different marketing claims.

Choosing a backend

A written decision procedure, before you see results (Chapter 12):

1. Does the circuit fit? Qubits, and the connectivity it actually needs.
2. Does it fit in coherence? Duration against $T_1$, $T_2$.
3. Are the qubits you would get any good? Check the specific links, not the chip average.
4. What is the queue? Chapter 39: this dominates wall clock by 4–6 orders of magnitude.
5. What does it cost? Shots × duration × rate card — knowable before you run.
6. Can you reproduce it? Record the nine fields in Chapter 39 §39.8.

See also: Chapter 12 (running on hardware), 29 (hardware-aware programming), 30 (benchmarking), 31 (timing), 39 (platforms and cost).