stabrank

Tools for stabilizer-rank bounds on quantum magic states.

stabrank is an open-source Python package with a C++ core for computing, certifying, and formally verifying stabilizer-rank decompositions of quantum magic states.

Built and maintained by the Unitary Foundation.

The library was developed to support the paper Stabilizer-rank bounds for qutrit magic-state orbits and packages the underlying search-and-verify toolchain as a reusable resource. It exposes three independent search modes — a simulated-annealing decomposition search for upper-bound witnesses, an exhaustive k-tuple enumeration over the canonical-form stabilizer-state dictionary for lower-bound certificates, and an enumeration over the symplectic quotient of the two-qutrit Clifford group for injection-gadget existence — and pairs each with a stand-alone verifier so that no result depends on trusting the search heuristic.

What can it do?

• Find stabilizer decompositions of arbitrary qubit and qutrit target states via a multi-chain simulated-annealing engine, with Pauli, Clifford, and single-state perturbation moves and a C++ kernel.
• Certify small-m tight values by exhaustive k-tuple enumeration over the qutrit stabilizer-state dictionary at m = 1, 2, 3 (dictionary sizes 12, 414, 41,580); per-orbit JSON certificates record the witnessing tuple or the minimum-residual non-spanning tuple.
• Verify every closed-form decomposition independently. The seven qutrit identities are checked at three levels: numerical re-check at machine precision, exact rational re-check in SymPy where available, and machine-checked Lean 4 + mathlib formalizations under lean_proofs/.
• Search the two-qutrit Clifford group $\mathrm{Cl}(2, 3)$ for injection gadgets via a reduction to the 51,840-element symplectic quotient $\mathrm{Sp}(4, \mathbb F_3)$.
• Diagnose with discrete-Wigner / mana routines and an exhaustive $F_{\max}$ solver tractable at $n \le 4$.

State of the art

Best-known stabilizer-rank values and upper bounds across the qubit and qutrit Clifford-inequivalent magic-state orbits, with citations and provenance, are catalogued on the project page:

https://unitaryfoundation.github.io/stabrank/#soa

Installation

stabrank requires Python 3.12–3.14. Pre-built wheels are published on PyPI for Linux, macOS, and Windows:

pip install stabrank

Or with uv:

uv pip install stabrank

To build from source (e.g.\ for development), clone the repo and install in editable mode; the C++ core is compiled at install time via scikit-build-core and nanobind:

git clone https://github.com/unitaryfoundation/stabrank.git
cd stabrank
uv venv
uv pip install -e .

A working C++ toolchain is required (clang or g++); on macOS the Xcode command-line tools are sufficient.

Quick start

A two-term decomposition of $|\mathbb{S}\rangle^{\otimes 2}$ via the simulated-annealing engine:

import numpy as np
from stabrank.target_functions import qutrit_strange_state
from stabrank.stabrank_core import run_sa_pauli_expansion

target = qutrit_strange_state(2)              # 9-dim |S>^2
n, p, chi = 2, 3, 2

initial_basis = [
    np.ones(p**n, dtype=complex) / np.sqrt(p**n)
    for _ in range(chi)
]

_, basis, coeffs, residual, *_ = run_sa_pauli_expansion(
    target=target,
    n_orig=n,
    p_prime=p,
    k_subset_size=chi,
    initial_basis=initial_basis,
    num_chains=16,
    early_exit_threshold=1e-12,
)

print(f"|S>^2 ≈ sum of {chi} stabilizer states, residual = {residual:.2e}")

For more involved workflows — the Norrell $m = 4$ decomposition, the exhaustive $k$-triple search at $m = 3$, and the gadget existence check on $\mathrm{Sp}(4, \mathbb F_3)$ — see the public API surface in the stabrank package and the test suite under tests/.

Citation

If you use stabrank in your work, please cite the arXiv preprint:

@misc{labib2026stabilizer,
      title={Stabilizer rank bounds for magic-state orbits}, 
      author={Farrokh Labib and Vincent Russo},
      year={2026},
      eprint={2605.28586},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2605.28586}, 
}

Funding

This work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing under Award Number DE-SC0025336.

This material is also based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center.

This work is partly supported by the European Union through the QLASS project (EU Horizon Europe grant agreement 101135876). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union. Neither the European Union nor the granting authority can be held responsible for them.

Development

The test suite runs under pytest. pytest is declared as an optional test extra (it is not a runtime dependency of the library), so run it via uv with the extra enabled:

uv run --extra test python -m pytest -q tests

License

Apache-2.0