paulie-algebra

paulie-algebra is a skill for Claude Code, Codex from xi-zhao/OpenQuantum. It costs 47 tokens per session (862 once invoked), scanned A, original, MIT.

A local analyzer for the Lie algebra generated by selected Pauli operators such as X, Y, and Z strings. It calculates the real vector-space dimension, classifies the resulting algebra where supported, and can enumerate the Pauli closure or compare it with dense matrices.

In plain words
What is it for?
Use it to study commutation structure, explicit closures, dimensions, and conditions for generating the full special-unitary algebra under the stated ideal-control assumptions. A Lie algebra describes operations generated by combining infinitesimal controls and their commutators.
Why use it?
It answers whether ideal independent controls generate a larger set of quantum operations without confusing Lie-space dimension with ordinary Pauli-generator rank. The result does not prove that a finite circuit, pulse sequence, or real device can perform every operation.

Skill for Claude CodeCodex

Written for no agent in particular: nothing here depends on one. Also seen: installed under .agents/ (shared by several agents).

Good fit Use it to study commutation structure, explicit closures, dimensions, and conditions for generating the full special-unitary algebra under the stated ideal-control assumptions. A Lie algebra describes operations generated by combining infinitesimal controls and their commutators.

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Install with agentmods
npx agentmods add skills/xi-zhao/openquantum/paulie-algebra
Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

Any agent
npx skills add xi-zhao/OpenQuantum --skill paulie-algebra
Clone the repo
git clone --depth 1 https://github.com/xi-zhao/OpenQuantum

Made for: Claude Code, Codex.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for paulie-algebra

README.md
[![agentmods](https://agentmods.dev/badge/skills/xi-zhao/openquantum/paulie-algebra/github.svg)](https://agentmods.dev/skills/xi-zhao/openquantum/paulie-algebra)
Your own site
<a href="https://agentmods.dev/skills/xi-zhao/openquantum/paulie-algebra"><img src="https://agentmods.dev/badge/skills/xi-zhao/openquantum/paulie-algebra/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

agentmods 80×15 button for paulie-algebra

Your own site · 80×15
<a href="https://agentmods.dev/skills/xi-zhao/openquantum/paulie-algebra"><img src="https://agentmods.dev/badge/skills/xi-zhao/openquantum/paulie-algebra.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 47 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 862 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00047 $0.00862
Opus 5.5 $0.00019 $0.00345
Sonnet 5.5 $0.00009 $0.00172
Haiku 4.5 $0.00005 $0.00086

Measured 4d ago against content hash c357b98859b5, method: parsed. Prices are Anthropic first-party input rates as of 2026-10-07, from the pricing page.

Security

Grade A, and why

paulie-algebra scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 4d ago.

The scan reads SKILL.md. This mod also ships 3 executable files (mcp/bridge.py, mcp/contracts.mjs, mcp/server.mjs), listed below but not scanned — reading those needs a real analyzer, not pattern matching.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

.agents/skills/paulie-algebra/SKILL.md · 35 lines

What it actually says

PauLie 量子电路代数

原生 SDK 路径

本能力同时支持 Paulie 的原生公开 API。用户需要 Pauli 表达式、代数运算与库公开分析接口 时,由 Agent 在固定依赖环境中编写和运行任务代码,不限于下文便捷 Tool 的预设模型。

使用 node scripts/sdk-access.mjs inspect paulie-algebra 定位环境,按完整 SDK 工作流执行。模块导航:paulie;导航不是 API 白名单。

下文关于模型、门集、输入与预算的限制描述便捷 Tool 的合同;原生 SDK 另受上游版本、可选依赖、宿主资源与用户授权约束。已禁用或被拒绝的动作不能借代码路径绕过。执行状态和科研验收分别报告。

当用户需要研究 Pauli 门生成元的代数闭包、对易结构或理想独立控制下的 su(2^n) 生成条件时,调用 Harness 注册的 paulie_local.analyze_paulie_algebra。

  • generators 为 不同且非恒等的 I/X/Y/Z 字符串。每个字符串必须恰好含 numQubits 个字符;不接受 Pauli 项之和或系数绑定的 Hamiltonian。
  • 明确假设每个 iP 都有独立实控制系数。计算的是实 Lie 线性空间维数,不是 Pauli 二进制生成秩;例如 XI、IX、XX 两两对易,实线性维数为 3。
  • 主动作先返回上游分类与精确维数;closureMode=full 枚举显式 Pauli 闭包,skip 不枚举,auto 仅在维数不超过 4096 时枚举。独立矩阵参考由 referenceMode 单独选择;spanResidualTarget 明确残差覆盖 closure 或 generators。超出 JavaScript 精确整数范围的维数返回十进制字符串。
  • classification 保留上游同构命名,如 so(3) 与 su(2)、so(6) 与 su(4)。当前独立验证的是表示空间与维数,不是完整抽象代数分类证明。
  • generatesFullSpecialUnitary 只对应上述独立理想控制假设,不自动证明有限深 ansatz 的表达能力、可训练性、脉冲可达性或真实硬件可控性。
  • 当前 L1,scientificValidation=not_evaluated;依赖须显式准备;计算可能写本地缓存。版本和案例见接入说明。

独立参考使用 referenceMode=auto|required|skip:auto 按默认阈值选择参考,required 使用调用方资源尝试所请求规模,skip 跳过。未执行时 reference.status=not_run,参考值和差异为 null;尝试后失败会返回错误。

量子位数、控制生成元和显式闭包的执行方式由调用方选择,适配器不额外设置人工规模上限。具体资源配置见本地计算说明。

依赖准备

运行前执行 node scripts/setup-paper-tools.mjs paulie-algebra。缺失、旧锁和已安装环境的处理见共同准备说明;Tool 不自动安装或升级依赖。

Files

What ships with it

5 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 4d ago Changed · +11 lines c357b98859b5
  2. 22d ago Changed · +4 lines 4f251b957fd6
  3. 1mo ago First seen · 20 lines · 47 tokens per session scan A 57fddf76330f

Subscribe to this mod's changes

paulie-algebra is a skill published in the GitHub repository xi-zhao/OpenQuantum (75 stars, last pushed yesterday), licensed MIT. It adds 47 tokens to every session and 862 once invoked, about $0.0002 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-15.

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