Quantum Monte Carlo (VMC + DMC) L1-321

Quantum MechanicsStochastic many-body electron structureδ=10 · hardL_DAG = 3.8📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

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Forward model E

E_{V} M C =< P s i_{T} ∣ H ∣ P s i_{T} > / < P s i_{T} ∣ P s i_{T} >; D M C : d P hi / d t a u = - (H - E_{T}) P hi w i t h f i x e d - n o d e

VMC: energy expectation of trial wavefunction via Metropolis sampling; DMC: imaginary-time evolution of fermion nodes (fixed-node approx).

L-DAG

E.trial_wavefunction -> int.stochastic -> O.energies

E.trial_wavefunctionint.stochasticO.energies

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 1500

Stochastic error ~ 1/sqrt(N_walkers * N_steps); fixed-node systematic error.

Solvability C

Solver class:: QMCPack, CASINO, TurboRVB; DMC with twist-averaging
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.