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CS-116-A1 · revision r1 · on CS-116

OpenAI claim summary for CS-116

Literature report · LLM-generated · unknown ·

Literature report. The underlying work is credited to its authors. Automated screening checks form, honesty and scope, not correctness. Status at unsolvedmath.com: open. Claims here do not change the source status.

Claim: literature report

Summary of a claim published in openai/math; not a claim by this platform.

The theorem determines the limiting optimal QAOA energy for the Gaussian zero-field SK model when n tends to infinity before depth p. This supplies an analytical performance result for that model and order of limits, but not a general account of QAOA/RQAOA in the resource-limited NISQ regime. This entry records partial support; complete coverage of the question is not established by this catalogue.

Limitations: The linked openai/math material has not been examined or verified by the platform.

Manuscript

Contents
  1. Analytical Performance Theory for QAOA and RQAOA
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Result 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

Analytical Performance Theory for QAOA and RQAOA

OpenAI's claim

OpenAI presents a mathematical result relevant to this question in the selected manuscript. QAOA is claimed to approach the SK ground-energy density when system size goes to infinity before depth, using deterministic disorder-independent angles but no effective depth bound.

Mathematical statement of the claimed result

Result 1.
For independent standard Gaussian $J_{ij}$, set $C_{n,J}=n^{-1/2}\sum_{i<j}J_{ij}Z_iZ_j$ and $B_n=\sum_iX_i$, with Pauli operators. A depth-$p$ QAOA state is \[ \psi_{n,p,J}=e^{-i\beta_pB_n}e^{-i\gamma_pC_{n,J}}\cdots e^{-i\beta_1B_n}e^{-i\gamma_1C_{n,J}}|+\rangle^{\otimes n}. \] For deterministic parameters, put $v_p(\gamma,\beta)=\lim_n n^{-1}\mathbb E\langle\psi,C_{n,J}\psi\rangle$ and $Q_p=\sup_{\gamma,\beta\in\mathbb R^p}v_p$. The claim is \[ \lim_{p\to\infty}Q_p=P_*,\qquad P_*=\lim_n n^{-1}\mathbb E\max_{\sigma\in\{\pm1\}^n} n^{-1/2}\sum_{i<j}J_{ij}\sigma_i\sigma_j. \] For each accuracy $\varepsilon>0$, one finite depth and parameter vector, independent of both instance and size, achieves $v_p\ge P_*-\varepsilon$. The size limit is taken first.

Outline of the argument

Fixed circuit words have an exact limiting tree calculus. A nearly optimal bounded classical formula is compiled with seeded controls, then longitudinal seeds are removed; the ordinary cost-and-mixer word retains the limiting expected energy in the thermodynamic-first order.

Formal verification

For family 281, the selected value identities express the SK ground energy through an admissible Parisi minimizer and diffusion, without asserting QAOA circuit convergence. A distinct full-support statement covers integrable zero-temperature minimizers. The listed Comparator files are SKFullSupport.lean, SKValue.lean. The inventory does not supply a named declaration for these Comparator entries. This site has not executed the Lean code. The scope descriptions do not certify the remaining manuscript arguments.

Status caveat

OpenAI attributes these manuscripts to work by an internal model. Its release cautions that arguments without formalization can contain mistakes. This catalogue has not independently checked the proofs; the labels report the mathematical claims attributed to OpenAI.

Sources