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method-polyopt

Compute certified lower bounds for quantum observables via the moment-SOS hierarchy.

60|92|Updated Apr 30, 2026
Search Tags:#optimization#certification#quantum#hamiltonian#npa#semidefinite
One-click install
npx skills add https://github.com/QuantumBFS/quantum.harness --skill method-polyopt
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: method-polyopt
Source: https://github.com/QuantumBFS/quantum.harness/tree/main/skills/method-polyopt
Command: npx skills add https://github.com/QuantumBFS/quantum.harness --skill method-polyopt

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes references (resource) components.

What problem does it solve?

This skill provides a rigorous, certified lower bound on ground-state energies and other quantum observables, addressing the inherent uncertainty in variational or stochastic methods.

Core Features & Use Cases

  • Certified Bounds: Computes provable lower bounds on ground-state energies and Bell inequality violations using the moment-SOS (NPA) hierarchy.
  • Observable Certification: Provides two-sided bounds on observables by leveraging energy-window constraints.
  • Use Case: When you have a variational energy estimate from DMRG or QMC, use this skill to compute a rigorous lower bound, creating a certified bracket that traps the true ground-state energy.

Quick Start

Invoke the method-polyopt skill to begin the classification of your Hamiltonian and select the appropriate structured solver for your quantum system.

Frequently Asked Questions about method-polyopt

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I get a certified lower bound for a quantum ground-state energy?▼

Observable certification in quantum many-body systems is achieved by computing two-sided bounds on observables using moment-SOS energy-window constraints. This allows you to rigorously certify observable values alongside ground-state energy calculations.

What is the best way to verify variational energy estimates from DMRG or QMC?▼

To apply the moment-SOS hierarchy to your Hamiltonian, you begin by classifying the Hamiltonian structure to select the appropriate solver. The method supports structured symmetry reduction and correlative sparsity to optimize the semidefinite program.

Does the NPA hierarchy work for Bell inequality maximization?▼

The moment-SOS hierarchy handles non-commutative polynomial optimization by leveraging structured symmetry reduction and correlative sparsity. These features make the semidefinite program tractable for complex quantum many-body systems.

Can I use semidefinite programming for quantum observable certification?▼

Exact rational certification of solver bounds is achieved by solving the moment-SOS hierarchy with rational arithmetic. This ensures the computed lower bounds for ground-state energies and Bell inequalities are mathematically rigorous and provably correct.

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