Estimate

Estimation asks every candidate engine the same question about the same job: can you run this, and what would it cost?

What an estimate contains

Field	Meaning
feasible	Whether the engine can serve this request at all
peak_bytes	Peak memory the plan would need
work_units	Cost in the model's shared unit
infeasible_reason	Why not, when feasible is false

For a plan that may run on a GPU there is also a device-side record: device bytes, bytes transferred each way, and the number of kernel launches.

Why an engine may be infeasible

The reason string is part of the report, so the loser is always explained:

Reason	Example
Does not support the output	the stabilizer engine does not track global phase -- only the dense engine can produce a statevector
Does not support an operation	operation 8 (t) is not a Clifford gate
Too large to represent	checked_pow2: n = 100 exceeds the maximum of 62
Would not fit the memory budget	direct dense simulation requires 17592186044416 bytes, budget is 7752519680 bytes
Exceeds the time budget	estimated runtime … s exceeds the job's time budget of … s
Contradicted by a run	observed runtime of at least … s exceeds the job's time budget

Checked arithmetic

Cost estimates involve powers of two that overflow quickly. Every estimate uses checked arithmetic: a quantity that cannot be represented makes the candidate infeasible with a reason. It never wraps around, and it never throws an exception the caller has to catch.

How each engine estimates

Each engine computes its estimate from structural facts (qubit count, operation counts, requested outputs) without executing anything.

• Dense prices each gate at 2^(n+k) work units for a k-qubit gate on n qubits, plus initialization and the requested outputs, and needs 16·2ⁿ bytes.
• Stabilizer is polynomial in qubit count: row initialization, one pass per gate, and Gaussian elimination over GF(2) when sampling.
• Pauli propagation bounds the worst-case number of terms an observable can split into before propagating anything, and refuses an unrepresentable bound.
• MPS bounds the entanglement (Schmidt rank) rigorously from the circuit's structure. In exact mode it is feasible only if that bound fits the budget.
• Tensor network searches for a contraction order and prices the largest intermediate tensor; the search is stopped at the memory budget.

The formulas are in Cost Model.

Memory is checked before allocation

Estimation is where the memory budget is applied. A candidate whose peak bytes exceed it is infeasible here, before an allocation is ever attempted.

Estimates are not seconds

Work units rank candidates for one job against each other. Converting them to seconds requires calibration, and that conversion is only used for time budgets and CPU-versus-CUDA selection.