L1 ⚛ L1-321 ⊙ Testnet

Quantum Monte Carlo (VMC + DMC)

Quantum Mechanics · Stochastic many-body electron structure

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⬇ L1-321.md

# ⚛ L1 Principle — Quantum Monte Carlo (VMC + DMC) **ID:** `L1-321` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Mechanics — *Stochastic many-body electron structure* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** many body wavefunction > **📡 Carrier:** electron · **🌫 Noise:** poisson > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41554080 --- ## 🧠 1. Introduction **Quantum Monte Carlo (VMC + DMC)** is a **nonlinear inverse problem** whose unknown lives in **many body wavefunction** space, within the **Stochastic many-body electron structure** sub-domain of **Quantum Mechanics**. Measurements consist of electrons collected by an electron detector via a **energy benchmark** sensing mechanism. The forward operator applies, in order: E · trial wavefunction operator; int · stochastic operator; O · energies operator. Observations are corrupted by Poisson counting noise. Stochastic error ~ 1/sqrt(N_walkers * N_steps); fixed-node systematic error. ## ⚙ 2. Forward Model Physical chain: **x** → E · trial wavefunction → int · stochastic → O · energies → **y** (detector). ``` y = `O.energies` `int.stochastic` `E.trial_wavefunction` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.trial_wavefunction` | E · trial wavefunction operator | | `int.stochastic` | Int · stochastic operator | | `O.energies` | O · energies operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Mechanics | | Sub domain | Stochastic many-body electron structure | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | many_body_wavefunction | | Noise model | poisson | | Integration axis | imaginary_time | | Difficulty delta | 10 | | L dag | 3.8 | ## 📡 4. Measurement Model Stochastic error ~ 1/sqrt(N_walkers * N_steps); fixed-node systematic error. | Metric | Value | |---|---| | Metric | energy_error_mHa | | Secondary | density_L2_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `quantum_monte_carlo` · **Forward operator:** `qmc_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Method | — | DMC | | N steps | — | 100000 | | N walkers | — | 1000 | | N electrons | — | 20 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Method | — | VMC, DMC, AFQMC | | N steps | — | 1000 – 100000000.0 | | N walkers | — | 100 – 1000000 | | N electrons | — | 2 – 1000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** E error <= 0.5 mHa | Metric | Range | |---|---| | Energy error mha | 0.1 – 50 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **energy_error_mHa**, with κ = `1500` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xaa13a8fdf1754fc484d9ba3afe9e0466a5bd877eb82dc17fdd2024344c6f2d80` - **Chain tx hash:** `0xc44ddf8bae284e89c21786da1c8448328f8d46ea0aee9be4ee173b6af3d43c8a` - **Chain block:** `41554080` --- ## File Mapping This bundle consists of: `L1-321.md`, `L1-321.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-321.md` | Source of truth — edit this | Human or LLM | | `L1-321.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-321`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-321.md).
Regenerate L1-321.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-321-001 Quantum Monte Carlo (VMC + DMC) Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-321",
  "chain_block": 41554080,
  "chain_hash": "0xaa13a8fdf1754fc484d9ba3afe9e0466a5bd877eb82dc17fdd2024344c6f2d80",
  "chain_tx_hash": "0xc44ddf8bae284e89c21786da1c8448328f8d46ea0aee9be4ee173b6af3d43c8a",
  "domain": "Quantum Mechanics",
  "hardness_fn": {
    "delta": 10,
    "kappa": 1500,
    "metric": "energy_error_mHa",
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    "regime": "Stochastic error ~ 1/sqrt(N_walkers * N_steps); fixed-node systematic error.",
    "secondary": "density_L2_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "electron",
    "difficulty_delta": 10,
    "domain": "Quantum Mechanics",
    "integration_axis": "imaginary_time",
    "noise_model": "poisson",
    "primitives": [
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      "int.stochastic",
      "O.energies"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "energy_benchmark",
    "solution_space": "many_body_wavefunction",
    "sub_domain": "Stochastic many-body electron structure",
    "title": "Quantum Monte Carlo (VMC + DMC)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "qmc_forward"
    ],
    "allowed_omega_dimensions": [
      "N_walkers",
      "N_steps",
      "N_electrons",
      "method"
    ],
    "allowed_problem_classes": [
      "quantum_monte_carlo"
    ],
    "center_spec": {
      "epsilon_fn_center": "E error \u003c= 0.5 mHa",
      "forward_operator": "qmc_forward",
      "input_format": "measurement_only",
      "omega": {
        "N_electrons": 20,
        "N_steps": 100000,
        "N_walkers": 1000,
        "method": "DMC"
      },
      "problem_class": "quantum_monte_carlo"
    },
    "epsilon_bounds": {
      "energy_error_mHa": [
        0.1,
        50
      ]
    },
    "omega_bounds": {
      "N_electrons": [
        2,
        1000
      ],
      "N_steps": [
        1000,
        100000000.0
      ],
      "N_walkers": [
        100,
        1000000
      ],
      "method": [
        "VMC",
        "DMC",
        "AFQMC"
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Stochastic many-body electron structure",
  "title": "Quantum Monte Carlo (VMC + DMC)"
}

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