{"id":51222613,"url":"https://github.com/mapleleaflatte03/qem-inverse-theory","last_synced_at":"2026-06-28T08:31:39.466Z","repository":{"id":358709759,"uuid":"1242716333","full_name":"mapleleaflatte03/qem-inverse-theory","owner":"mapleleaflatte03","description":"Zero-noise extrapolation as a constrained quantum inverse problem.","archived":false,"fork":false,"pushed_at":"2026-05-18T18:45:59.000Z","size":349,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"master","last_synced_at":"2026-05-18T19:40:02.340Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Python","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/mapleleaflatte03.png","metadata":{"files":{"readme":"README.md","changelog":"CHANGELOG.md","contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":"ROADMAP.md","authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2026-05-18T17:26:59.000Z","updated_at":"2026-05-18T18:46:03.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/mapleleaflatte03/qem-inverse-theory","commit_stats":null,"previous_names":["mapleleaflatte03/qem-inverse-theory"],"tags_count":1,"template":false,"template_full_name":null,"purl":"pkg:github/mapleleaflatte03/qem-inverse-theory","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mapleleaflatte03%2Fqem-inverse-theory","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mapleleaflatte03%2Fqem-inverse-theory/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mapleleaflatte03%2Fqem-inverse-theory/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mapleleaflatte03%2Fqem-inverse-theory/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/mapleleaflatte03","download_url":"https://codeload.github.com/mapleleaflatte03/qem-inverse-theory/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mapleleaflatte03%2Fqem-inverse-theory/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":34882751,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-26T15:22:16.424Z","status":"online","status_checked_at":"2026-06-28T02:00:05.809Z","response_time":54,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2026-06-28T08:31:38.776Z","updated_at":"2026-06-28T08:31:39.461Z","avatar_url":"https://github.com/mapleleaflatte03.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# qem-inverse-theory\n\n**Zero-noise extrapolation as a constrained quantum inverse problem.**\n\nWe do not propose another extrapolation curve; we study when extrapolation is physically identifiable.\n\n## Mission\n\nThis repository studies when quantum error mitigation is physically identifiable, statistically stable, and worth applying under finite-shot constraints.\n\n## Motivation\n\nStandard ZNE asks: \"Which curve fits the noisy data best?\"\n\nThis project asks: \"Under which physical and statistical assumptions is the zero-noise limit identifiable from finite noisy observations?\"\n\nThe distinction matters. Without physical constraints, ZNE is an ill-posed inverse problem: infinitely many curves pass through noisy data points but disagree at zero noise. Finite shots compound the problem by adding statistical uncertainty to already-ambiguous observations.\n\nWe study the mathematical structure of this problem: when constraints restore identifiability, when finite shots make mitigation harmful, and what structured assumptions allow escape from generic QEM lower bounds.\n\n## How this differs from `quantum-noise-optimizer`\n\n| | quantum-noise-optimizer | qem-inverse-theory |\n|---|---|---|\n| Goal | Production mitigation engine | Theoretical research |\n| Output | Mitigated expectation values | Theorems, phase diagrams, risk bounds |\n| Approach | AICc + bounded optimization | Inverse problem theory + Bayesian inference |\n| Hardware | Wukong 180 calibration | Synthetic only |\n| Claims | Empirical benchmark results | Mathematical conditions and conjectures |\n\n## Research questions\n\n1. **Identifiability**: Under what physical constraints is the zero-noise limit uniquely determined from finite noisy observations?\n2. **Stability**: How does the estimation error amplify as a function of noise strength, model complexity, and shot budget?\n3. **Help–harm boundary**: For a given circuit class and shot budget, when does ZNE reduce MSE versus amplify it?\n4. **Bayesian calibration**: Can posterior credible intervals provide reliable coverage for the zero-noise estimate?\n5. **Structured escape hatches**: Which problem structures (locality, symmetry, spectral gaps) allow mitigation to remain useful despite generic lower bounds?\n\n## Mathematical framing\n\nLet $\\lambda_1 \u003c \\lambda_2 \u003c \\cdots \u003c \\lambda_n$ be noise scale factors and $y_i = f(\\lambda_i) + \\epsilon_i$ the observed expectations with shot noise $\\epsilon_i \\sim \\mathcal{N}(0, \\sigma_i^2)$.\n\nZNE seeks $f(0)$ subject to:\n- **Physical admissibility**: $f(0) \\in [\\lambda_{\\min}(O), \\lambda_{\\max}(O)]$ for observable $O$\n- **Smoothness/structure**: $f$ belongs to some function class $\\mathcal{F}$\n- **Finite data**: only $n \\leq 7$ observations available\n\nThis is a constrained inverse problem. We study its well-posedness in the sense of Hadamard: existence, uniqueness, and continuous dependence on data.\n\n## Modules\n\n- `constraints/` — Spectral bounds, probability simplex, physical admissibility\n- `estimators/` — Unconstrained, constrained, regularized, Bayesian, model selection\n- `theory/` — Inverse problem formulation, risk bounds, identifiability, phase diagrams\n- `benchmarks/` — Synthetic response generators, shot noise, metrics\n- `plots/` — Phase diagrams, risk frontiers, coverage plots\n- `experiments/` — Runnable scripts demonstrating each research question\n\n## Out of scope\n\n- Hardware integration or SDK\n- Production-ready mitigation pipeline\n- MCP server or AI-agent tooling\n- Claims of solving QEM lower bounds\n- Peer-reviewed theorems (this is early-stage research)\n\n## Roadmap\n\n1. ✅ Scaffold: types, constraints, estimators, synthetic benchmarks\n2. 🔜 Finite-shot phase diagrams for polynomial ZNE\n3. 🔜 Bayesian GP-based ZNE with calibrated intervals\n4. 🔜 Adversarial identifiability examples\n5. 🔜 Theorem sketches → rigorous proofs\n6. 🔜 Paper draft: \"ZNE as a Constrained Quantum Inverse Problem\"\n\n## Status\n\nEarly research prototype. See [STATUS.md](STATUS.md).\n\n## Checkpoint\n\nCurrent: **v0.1-research-scaffold**\n\nVerify with:\n```bash\nbash scripts/smoke_check.sh\n```\nExpected: 41 tests pass, all safety checks green.\n\n## Current Paper Status\n\n- LaTeX skeleton exists (`paper/main.tex`) with 7 sections, 2 proven propositions\n- 4 figures reproducible via `python experiments/generate_figures.py`\n- `refs.bib` scaffold with verified DOIs for key citations\n- All results are synthetic — no hardware claims\n- Not peer-reviewed; draft is work-in-progress\n- Claim safety enforced by automated tests\n\n## Install\n\n```bash\npip install -e \".[dev]\"\npytest\n```\n\n## License\n\nMIT\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmapleleaflatte03%2Fqem-inverse-theory","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmapleleaflatte03%2Fqem-inverse-theory","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmapleleaflatte03%2Fqem-inverse-theory/lists"}