Port a finite-dimensional invariant-state identity.
Acceptance: Exact generator, Gibbs normalizer and adjoint convention.
planned; no claimed closure
Structure before circuit tricks
Low-temperature Gibbs preparation with quantitative mixing
An invariant Gibbs state does not guarantee that an implementable sampler reaches it quickly at low temperature.
research target setting:local-kms-generator
\[\rho_\beta=\frac{e^{-\beta H}}{\operatorname{Tr}(e^{-\beta H})},\quad \|\mathcal E_t(\rho)-\rho_\beta\|_1\le\epsilon\]
Frozen target and input model
For a restricted noncommuting local Hamiltonian family, prove a mixing certificate and implemented-channel error bound.
Access model: Specified Hamiltonian and KMS generator with charged simulation access, temperature, initial state and convergence norm.
- Primitivity/ergodicity or invariant-subspace restriction stated
- Spectral or functional-inequality mixing certificate supplied
- Generator implementation and statistical output contract specified
Desired result, not an achieved bound
A model-specific polynomial mixing and total-cost theorem in the promised temperature regime.
KMS detailed balance and stationarity are not polynomial mixing. Classical sampling inequalities cannot be transferred to quantum operators without a hypothesis map.
Dependency-ready execution route
Identify and prove a coercivity or mixing condition for one class.
Acceptance: An explicit rate with temperature/system-size dependence; no assumed conclusion.
planned; no claimed closure
Compose mixing with generator-simulation error.
Acceptance: A trace-norm output theorem and total implementation budget.
planned; no claimed closure
Next bounded advance: Use a finite-dimensional warm-up and then separate the high-temperature baseline from the intended low-temperature regime.
Reusable mathematics
No local transport theorem is bound to this record. Do not infer formal truth from its position in the atlas.
Lower-bound comparison contract
model-definition-pending
State the oracle and Hamiltonian class before importing hardness or mixing obstructions.
Same-model key: setting:local-kms-generator
Diagnostic examples, not proofs
- Commuting warm-up
- Small noncommuting local families
- Explicit high-temperature comparison baseline
Primary-source ledger
primary-text-checked Article abstract and Gibbs-sampler construction; Communications in Mathematical Physics 406, 67
Invariant Gibbs state and efficient mixing are different obligations. A low-temperature polynomial mixing claim needs additional model-specific evidence.
Download bounded agent / contributor packet
python3 website/scripts/research_atlas.py context --route spw-gibbs