Read the equation
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read p as the quantity being defined or updated by this relation.
Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
|\psi_p\rangle=\prod_{\ell=1}^{p}
e^{-i\beta_\ell\sum_{q=1}^{m}X_q}e^{-i\gamma_\ell H_C}|+\rangle^{\otimes m},
\quad p\in\{1,2\}.
\end{equation*}
Valid diagonal entries are $J(S)/\max J$; the single invalid all-in-one bitstring has cost 2. Three COBYLA starts minimize the \emph{exact penalized expectation}, with 160 evaluations per start at $p=1$ and 240 at $p=2$. Selection never uses optimal-state probability. All $p=2$ starts exhausted this budget; convergence is not asserted. After training, ten independent 256-shot batches are sampled, retaining the lowest-cost valid observed partition. Invalid shots are counted, not replaced. Uniform search uses ten batches of 256 draws from valid partitions.
\callout{\textbf{Resource accounting.} This is a dense-diagonal QAOA simulator, not an efficient QUBO encoding or a transpiled hardware circuit. Building its full cost table already performs exhaustive search. QAOA also receives noiseless expectation values during training. The comparison measures output quality at stated, unequal budgets; it does not demonstrate a speedup.}
[Context excerpt; full source linked.]Exact original notation
p=2