linear-systems

name	linear-systems
description	A set of quantum algorithms for solving linear systems of equations and related Fourier/signal-processing subroutines. This skill includes UnitaryLab implementations and educational resources for AQC, HHL, LCU, QFT, the basic single-qubit QSP demo, QSVT-QLSA, and VQLS.

Quantum Linear Systems Algorithms

Purpose

This file routes requests for quantum linear algebra algorithms and related Fourier or signal-processing subroutines.

Use this category when the user asks to solve linear systems, compare quantum linear-system solvers, build QFT/basic QSP components, or use QSVT-style linear algebra workflows.

Routing Rules

• If the user asks about adiabatic quantum computation for linear systems, a discrete adiabatic QLSP, five-ancilla block-encoding evolution, or AQC post-selection:
  • Read ./aqc/SKILL.md
• If the user asks for the HHL algorithm, phase-estimation-based linear solving, or textbook quantum linear systems:
  • Read ./hhl/SKILL.md
• If the user asks about Linear Combination of Unitaries, block construction from weighted unitaries, or LCU-based solving:
  • Read ./lcu/SKILL.md
• If the user asks about the Quantum Fourier Transform, inverse QFT, Fourier basis changes, or QFT as a subroutine:
  • Read ./quantum-fourier-transform/SKILL.md
• If the user asks about basic Quantum Signal Processing, single-qubit QSP demos, scalar polynomial transformations, phase-factor optimization, or QSP circuits for approximating functions such as cos(t*x):
  • Read ./quantum-signal-processing/SKILL.md
• If the user asks for QSP-based Hamiltonian simulation, QSP-HS, block-encoding a Hamiltonian, or approximating time evolution e^{-iHt}:
  • Route to ../hamiltonian-simulation/qsp/SKILL.md instead of this linear-systems QSP demo.
• If the user asks about QSVT-based quantum linear-system solving or singular-value transformation:
  • Read ./qsvt-qlsa/SKILL.md
• If the user asks for a variational linear-system solver or NISQ-style Ax=b workflow:
  • Read ./vqls/SKILL.md

Available Leaf Skills

1. AQC discrete adiabatic linear solver: ./aqc/SKILL.md
2. HHL Algorithm: ./hhl/SKILL.md
3. LCU: ./lcu/SKILL.md
4. Quantum Fourier Transform: ./quantum-fourier-transform/SKILL.md
5. Basic Quantum Signal Processing demo: ./quantum-signal-processing/SKILL.md
6. QSVT QLSA: ./qsvt-qlsa/SKILL.md
7. VQLS: ./vqls/SKILL.md

Response Contract

1. Decide whether the task is solving a linear system or using a supporting transform/subroutine.
2. Read the matching leaf skill before writing code or commands.
3. Keep solver-specific assumptions, parameters, and examples in the leaf skill.