qkrylov

A modern C++20 framework for matrix-free Krylov methods in quantum many-body physics.

Overview

qkrylov provides a high-performance core for performing exact diagonalization and Krylov-based calculations (like Lanczos and Davidson) without explicitly constructing Hamiltonian matrices. By implementing the matrix-free action $y = Hx$, the library enables the study of much larger Hilbert spaces than traditional matrix-based methods.

Features Completed

C++20 Core: Leveraging modern C++ features for performance and safety.
Basis Abstraction: Generic basis management with support for symmetry sectors.
Supported Models:
- Spin-Half Systems: Heisenberg, transverse-field Ising, etc.
- Fermionic Systems: Spinless fermions with Jordan-Wigner phases.
- Hubbard Models: Interacting electrons with spin conservation.
- t-J Models: Doped antiferromagnets with no-double-occupancy constraint.
Matrix-Free Hamiltonian: Efficient application of operator sums (OpSum) to state vectors.
Advanced Solvers:
- Lanczos: Accurate ground-state energy and Ritz vector calculation.
- Davidson: Iterative solver for the lowest few eigenpairs.
- Dynamics: Continued Fraction Lanczos for dynamical structure factor $S(\omega)$ calculations.
Multi-Language Scaffolding: Robust Python interface via nanobind.

Build Requirements

C++20 compatible compiler (e.g., GCC 11+, Clang 13+, MSVC 19.30+)
CMake 3.20+
nanobind (install via pip install nanobind)

Quick Start

Build the library and tests

make build

Install Python package

pip install ./bindings/python

Run tests

make test
pytest bindings/python/tests/test_basic.py

C++ Example

#include <qkrylov/basis/spinhalf_basis.hpp>
#include <qkrylov/operators/opsum.hpp>
#include <qkrylov/sites/spinhalf_site.hpp>
#include <qkrylov/hamiltonian/matrix_free_hamiltonian.hpp>
#include <qkrylov/solvers/lanczos.hpp>
#include <iostream>

using namespace qkrylov;

int main() {
    int N = 4;
    auto basis = std::make_shared<SpinHalfBasis>(N);
    auto site = std::make_shared<SpinHalfSite>();

    OpSum os;
    for (int i = 0; i < N - 1; ++i) {
        // Heisenberg interaction: Sz_i Sz_{i+1} + 0.5(Sp_i Sm_{i+1} + Sm_i Sp_{i+1})
        os += {1.0, {{"Sz", i}, {"Sz", i+1}}};
        os += {0.5, {{"Sp", i}, {"Sm", i+1}}};
        os += {0.5, {{"Sm", i}, {"Sp", i+1}}};
    }

    MatrixFreeHamiltonian H(basis, site, os);
    auto result = lanczos_ground_state(H);

    std::cout << "Ground state energy: " << result.energy << std::endl;
    return 0;
}

Python Example

import qkrylov

# 4-site Heisenberg chain
N = 4
basis = qkrylov.SpinHalfBasis(N)
site = qkrylov.SpinHalfSite()

os = qkrylov.OpSum()
for i in range(N - 1):
    # Heisenberg interaction: Sz_i Sz_{i+1} + 0.5(Sp_i Sm_{i+1} + Sm_i Sp_{i+1})
    os += 1.0, "Sz", i, "Sz", i+1
    os += 0.5, "Sp", i, "Sm", i+1
    os += 0.5, "Sm", i, "Sp", i+1

H = qkrylov.MatrixFreeHamiltonian(basis, site, os)
result = qkrylov.lanczos_ground_state(H)

print(f"Ground state energy: {result.energy}")

Things To Be Done (Roadmap)

GPU Acceleration: CUDA/HIP support for Hamiltonian application.
HDF5 Integration: Efficient storage of large eigenvectors and results.
Julia Bindings: Interop via CxxWrap.jl.
Finite Temperature: Finite Temperature Lanczos Method (FTLM).

Documentation

Full documentation is available in the docs/ directory. See docs/source/tutorial.md for a comprehensive guide modeled after iTensor.

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Provenance

The following attestation bundles were made for qkrylov-0.0.6-cp311-cp311-macosx_14_0_arm64.whl:

Publisher: pypi_publish.yaml on sjp95/qkrylov

Attestations: Values shown here reflect the state when the release was signed and may no longer be current.

Statement:
- Statement type: https://in-toto.io/Statement/v1
- Predicate type: https://docs.pypi.org/attestations/publish/v1
- Subject name: qkrylov-0.0.6-cp311-cp311-macosx_14_0_arm64.whl
- Subject digest: 260b19b7e7ffcd02b8dbc7479fdb4661da87192c55495673dca298b7e8e4e043
- Sigstore transparency entry: 2417786324
- Sigstore integration time: Aug 11, 2026
Source repository:
- Permalink: sjp95/qkrylov@b07c162110bd84655d1e0ef7dedc9cc65da9d1c6
- Branch / Tag: refs/tags/v0.0.6
- Owner: https://github.com/sjp95
- Access: public
Publication detail:
- Token Issuer: https://token.actions.githubusercontent.com
- Runner Environment: github-hosted
- Publication workflow: pypi_publish.yaml@b07c162110bd84655d1e0ef7dedc9cc65da9d1c6
- Trigger Event: release

Release history Release notifications | RSS feed

0.0.7

Aug 12, 2026 9 files

This release

0.0.6 This release

Aug 11, 2026 9 files

Aug 8, 2026 9 files

Aug 8, 2026 9 files

Aug 8, 2026 8 files

Aug 5, 2026 8 files

qkrylov 0.0.6

qkrylov

Overview

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Quick Start

Build the library and tests

Install Python package

Run tests

C++ Example

Python Example

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