Adiabatic path access and resource model

An adiabatic path access instance consists of a finite path model (Finite adiabatic path model), its exact initial preparation circuit $A_0$ and cost $C_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}}$, a finite term count $r$, and a uniform description $H(s)={\sum }_{j=1}^r{c}_j(s)H_j,$ where the $H_j$ are stated finite-dimensional self-adjoint operators and the real coefficient functions $c_j$ have explicit rational binary inputs, uniform evaluation procedures, certified value errors and certified first-derivative bound $M_1\ge {\sup }_s\mathrm{\parallel }{H}^{\mathrm{\prime }}(s)\mathrm{\parallel }$. The access declaration provides, for every allowed time code $u$, either the exact term operation $e^{-iu{H}_j}$ as a named oracle with its query charge, or a full-list uniform circuit family $V_j(u)$ with a certified bound $\mathrm{\parallel }{V}_j(u)-e^{-iu{H}_j}\mathrm{\parallel }\le {\eta }_j(u)$. Each inverse or controlled call is available only when separately declared. This is the finite term-list access interface of Hamiltonian simulation error and resources and Term-list Hamiltonian access.

The resource record lists separately: $C_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}}$; the term count $r$; all term-oracle queries; controlled and inverse calls; gate, clean-ancilla and dirty-ancilla counts; coefficient-precision bits; full circuit-description bits; uniform generator time; and the continuous evolution time $T$. If a physical energy-normalized action is used, it also records $T{\sup }_s\mathrm{\parallel }H(s)\mathrm{\parallel }$. A missing coordinate is unavailable, not zero. No arbitrary matrix description or spectral projector supplies an initial preparation, term exponential, controlled call, inverse, coefficient evaluator, or circuit generator for free.