Manuscript Em03-C@1 · Em03-C-v1.tex · section · 47dd71ec

A joint apparatus ledger

Resources, attainable tolerances, and semantic scope › A joint apparatus ledger · lines 2483–2568

The construction uses two oscillator memories, not two qubits. Initial extraction-domain dimensions are $K_{i} + 1$ ; the modeled maximum leakage-domain dimensions are $J_{i} + 1$ . Capture itself is not restricted to finite occupation support.

With $s_{lab}$ spectator qubits, the retained register and pointer occupancy is $2 B_{reg} + s_{lab}$ . If the finite joint noise bath $D$ is stored in the laboratory, its qubit embedding must also be counted. Fresh reset registers and their peak overlap with retained registers are additional preparation resources, not silently included in this number.

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Resource	Declared quantity
Resource	Declared quantity
Shared capture	One effective temporal port; window $4 L$ ; two compact orthonormal tests; vector $λ (t)$ ; memory mixing $Ω (t)$ ; bounds (eq:capturebounds).
Memories	Two oscillators; joint preparation $σ_{c}$ ; storage duration $T_{s}$ , rate $κ_{s}$ ; initial cutoffs $K_{i}$ ; maximum controlled leakage levels $J_{i}$ .
Extraction	$K_{1} + K_{2}$ selective pulse components; duration $T_{E}$ ; finite-rank exact generator; joint bounded deviation $Δ H_{E}$ ; register preparation $σ_{Q}$ .
Phase-sensitive controls	At most $B_{reg}$ single-qubit rotations per setting; fixed phase convention; rotation error integrals $γ_{s}$ .
Readout	$B_{reg}$ pointer qubits; $B_{reg}$ ideal controlled-NOT copies; duration $T_{R}$ ; joint finite bath and generator $G_{s}$ ; full matrix $W_{s}$ .
Reset and readiness	Fresh independent preparation systems; joint errors $p_{c}, p_{Q}, p_{A}$ ; readiness failure probability $r_{F}$ ; visible failure output.
Repeated tests	A sufficient, not optimized, schedule has $n (d^{2} - 1)$ preparations for tomography. Different Pauli strings can share bases, but such reuse is not needed by the proved schedule.
Classical records	Setting, both raw words, both declared decoded values, all failure flags, and trial identifier. No failed trial is removed.
Spectators	Stored throughout the sequence; all modeled coupling errors are included in the named joint generators. Additional decoherence requires an additional complete comparison.
References	Retained in correctness statements; not laboratory memory.
Energy and work	Oscillator free energies, control phase references, cooling, bath delivery, and reset work require separately supplied physical models. No thermodynamic optimum is claimed.

The preparations can be represented by replacement through swaps with fresh systems in the stated states, discarding old apparatus states into the preparation environment. This supplies complete preparation channels. It does not prove cooling costs or independence in a reused experimental device.