Quantum capacity is the ability to complete a specified workload under its quality, timing, and evidence requirements. A qubit count alone cannot express it. A job may fit on the device but exceed its usable duration, require unsupported controls, saturate the decoder, or need more repetitions than the reservation can accommodate. Scheduling connects those constraints to the commitments made to users.
Begin with a workload envelope: required operations, acceptable failure or estimation uncertainty, expected duration, resource footprint, and the conditions under which execution may be interrupted. Keep this separate from the machine inventory. The inventory describes what is available; the envelope describes what a particular job needs.
Shots are an acquisition budget
The captured Aer baseline accepts after 5,000 shots in each of three bases, consuming 15,000 shots. Its degraded-readout counterpart rejects after 200 per basis, consuming 600. A scheduler should not assume either observed stopping point will occur on every run. It needs both the declared maximum and the policy for releasing unused capacity.
The approved precision gate cannot accept before 5,000 per basis. Consequently a budget of 1,000 per basis can support early rejection, but cannot support acceptance under this rule. The captured budget scenario demonstrates that outcome: it completes with an inconclusive decision. This limitation is predictable before spending the first shot.
A constructed cost illustration assigns one accounting unit per shot and 300 units of preparation overhead per experiment. Baseline then costs 15,300 units and degraded readout 900. These units are not a provider's prices. A real budget must identify charges for reservation time, retries, compilation, classical compute, calibration, and retained artifacts, according to the applicable service terms.
When mitigation increases the necessary number of samples, include that change before admission. A cheaper circuit per execution may be more expensive per useful estimate. Error Mitigation and Verification shows why dividing out readout attenuation also enlarges uncertainty.
A logical-resource planning calculation
The teaching fixture contains a hypothetical capacity model, not a hardware forecast. Assume each logical patch costs approximately 2d² physical qubits. Request A needs 100 patches plus 40,000 fixed overhead qubits; B needs 60 patches plus 30,000. Available capacity is 230,000. These assumed overheads do not model any particular machine’s routing, factories, or control resources.
| Distance d | Qubits per patch | Request A | Request B | Combined | Both fit? |
|---|---|---|---|---|---|
| 21 | 882 | 128,200 | 82,920 | 211,120 | yes |
| 25 | 1,250 | 165,000 | 105,000 | 270,000 | no |
| 29 | 1,682 | 208,200 | 130,920 | 339,120 | no |
Suppose A operates its 100 patches for 10⁸ cycles each. For illustration only, assume a per-patch-cycle failure bound
p_L(d) = 0.1 × (0.001/0.01)^((d+1)/2).A union bound over the 10¹⁰ patch-cycles gives modeled workload bounds of 0.01, 0.0001, and 0.000001 at distances 21, 25, and 29 respectively. The union bound does not require independent failure events, but every per-location bound and the complete set of relevant failure mechanisms must be justified. This toy calculation omits other logical operations and failures. A fitted expression is not evidence that a real processor attains those numbers.
If A requires its modeled bound to be at most 0.0001, distance 21 is inadequate despite allowing both jobs to fit. Distance 25 meets the illustrative requirement, but A and B no longer fit together at that distance. The scheduler must change timing, capacity, or an explicitly negotiable requirement. Silently lowering distance would violate the admission contract.
Scheduling must preserve meaning
Capacity has a time dimension. Two individually admissible jobs may overlap beyond available resources. A reservation needs room for dependencies and validation, not merely the circuit's estimated execution time. Dispatching near the end of a window may leave too little time to finish a useful experiment.
Checkpoint classical preprocessing, optimizer state, completed shot batches, and evidence where the runtime supports those boundaries. An arbitrary unknown quantum state cannot be saved as a reusable classical checkpoint. Cancellation also does not guarantee that a dispatched device operation immediately stops. Declare non-preemptible execution windows and safe abort boundaries before promising resumability.
Report queue delay, acquisition duration, evidence completion, and wasted or excluded work separately. A job that fails quickly can consume little machine time yet substantial scientific effort. A scientifically rejected result can still be a useful and correctly delivered outcome. The scheduling objective should reflect the intended service, rather than maximizing occupancy at the expense of trustworthy results.
Exercise and worked answer
Under the hypothetical model, A requires a workload bound no larger than 0.0001, while both requests are planned at distance 25. Can they run concurrently on 230,000 qubits? Would lowering A to distance 21 solve the problem correctly? Separately, how many extra shots are needed to resume the captured interrupted Bell run from 200 to 5,000 per basis?
Worked answer: At distance 25 the requests need 270,000 qubits, exceeding capacity by 40,000. Each fits individually, so sequential admission is possible if all other requirements hold. Lowering A to distance 21 gives a modeled failure bound 0.01, violating its requirement. With B at distance 25, the combined 233,200 qubits still exceed capacity by 3,200. The Bell continuation needs (5,000−200)×3=14,400 additional shots. Preserve its existing 600 shots and provenance. That is a classical experiment continuation, not restoration of an unknown quantum state.