Manuscript Em03-B@2 · Em03-B-v2.tex · section · c1a0977d

What the model counts

Resource ledger, reset model, and verification requirements › What the model counts · lines 2000–2080

The capture memory is an oscillator, not one qubit. The extraction input control-domain dimension is $K + 1$ . With the finite leakage model it is $J + 1$ , and these dimensions must not be confused.

The capture state itself need not have finite occupation support. Its geometric tail is priced by the extraction comparison. The control Hamiltonian is defined on the full oscillator and acts identically outside its specified finite domain, except for the explicitly bounded perturbation when included.

Let $s$ be the number of laboratory spectator qubits. The construction uses $b_{N}$ register qubits and $b_{N}$ pointer qubits. Allocating both blocks before readout gives peak laboratory qubit occupancy

2 b_{N} + s .

External references are retained in correctness specifications but are not laboratory storage.

{}1.15

Component	Explicit resource or boundary
Component	Explicit resource or boundary
Capture	Window duration $4 L$ ; coefficient $λ (t)$ ; integrated coupling $- lo g (1 - τ)$ ; peak rate and derivatives obtained from (eq:captcontrol). A hardware bandwidth restriction must be checked against this actual coefficient.
Memory	One oscillator; initial mean $m_{0}$ ; storage time $T_{s}$ ; storage rate $κ_{s}$ ; control input dimension $K + 1$ ; maximum modeled leakage domain $J + 1$ .
Extraction	$K$ simultaneous number-selective pulse components; duration $T_{E}$ ; amplitude and envelope-derivative limits; frequency modulation through $K Ω_{c}$ ; deviation integral $I_{E}$ . No oscillator drive or ancillary control qubit is concealed.
Register	$b_{N}$ qubits, independently initialized with error $p_{Q}$ . The Hamiltonian operates directly on their binary basis; a separate unpriced encoding unitary is unnecessary.
Pointer readout	$b_{N}$ pointer qubits; copy duration $T_{R}$ ; computational readout; damping time $T_{D}$ ; assignment matrix $W$ ; pointer preparation $p_{A}$ . The aggregate ideal copy uses $b_{N}$ controlled-NOT operations.
Spectators	Storage through the capture, storage, extraction, and readout intervals. The only modeled error is the stated spectator-coupling budget; additional decoherence must be added as a separate complete channel.
Classical output	Raw words and decoded values, together with all failure labels. Classical storage is not counted as quantum slots.
Preparation and reset	Fresh bath systems, their specified states, reset duration, and readiness probability. Independence across shots must be justified before invoking this one-shot model repeatedly.
Energy and work	If memory energy is $Ω_{c} N_{c}$ , its pre-extraction mean is $Ω_{c} ν_{c}$ . Control norm and duration are specified. A thermodynamic work or reset-cost theorem is not asserted.

Displayed formulas in this passage

unlabeled · line 2017
$2 b_{N} + s .$