improved Lanczos iteration and introduced numba usage leading to significant speedup

.github/workflows/ci.yml

@@ -23,14 +23,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        runs-on:
-          [
-            ubuntu-24.04,
-            ubuntu-24.04-arm,
-            macos-15-intel,
-            macos-14,
-            windows-2022,
-          ]
+        runs-on: [ubuntu-24.04, ubuntu-24.04-arm, macos-15, windows-2025]
     uses: munich-quantum-toolkit/workflows/.github/workflows/reusable-python-tests.yml@d6314c45667c131055a0389afc110e8dedc6da3f # v1.17.11
     with:
       runs-on: ${{ matrix.runs-on }}

.pre-commit-config.yaml

@@ -66,7 +66,7 @@ repos:
       - id: ty-check
         name: ty check
         entry: uv run ty check
-        language: unsupported
+        language: system
         require_serial: true
         types_or: [python, pyi, jupyter]
         exclude: ^(docs/)

CHANGELOG.md

@@ -11,7 +11,9 @@ This project adheres to [Semantic Versioning], with the exception that minor rel
 
 ### Changed
 
-- Changed Pauli summation to use finite state machine construction ([`#308`]) ([**@aaronleesander**])
+- 👷‍♂️ Stop testing on x86 macOS systems ([#310]) ([**@aaronleesander**])
+- ⚡️ Improve Lanczos iteration and use numba for significant speedup ([#310]) ([**@aaronleesander**])
+- ♻️ Change Pauli summation to use finite state machine construction ([#308]) ([**@aaronleesander**])
 - 🔧 Replace `mypy` with `ty` ([#304]) ([**@denialhaag**])
 
 ## [0.3.3] - 2026-01-12
@@ -61,6 +63,7 @@ _📚 Refer to the [GitHub Release Notes](https://github.com/munich-quantum-tool
 
 <!-- PR links -->
 
+[#310]: https://github.com/munich-quantum-toolkit/yaqs/pull/310
 [#308]: https://github.com/munich-quantum-toolkit/yaqs/pull/308
 [#304]: https://github.com/munich-quantum-toolkit/yaqs/pull/304
 [#298]: https://github.com/munich-quantum-toolkit/yaqs/pull/298

UPGRADING.md

@@ -4,6 +4,11 @@ This document describes breaking changes and how to upgrade. For a complete list
 
 ## [Unreleased]
 
+### End of support for x86 macOS systems
+
+Starting with this release, we can no longer guarantee support for x86 macOS systems.
+x86 macOS systems are no longer tested in our CI and we can no longer guarantee that MQT YAQS installs and runs correctly on them.
+
 ## [0.3.2]
 
 ### End of support for Python 3.9
@@ -14,5 +19,5 @@ As a result, MQT YAQS is no longer tested under Python 3.9 and requires Python 3
 
 <!-- Version links -->
 
-[unreleased]: https://github.com/munich-quantum-toolkit/yaqs/compare/v0.3.2...HEAD
+[Unreleased]: https://github.com/munich-quantum-toolkit/yaqs/compare/v0.3.3...HEAD
 [0.3.2]: https://github.com/munich-quantum-toolkit/yaqs/compare/v0.3.1...v0.3.2

noxfile.py

@@ -67,6 +67,8 @@ def _run_tests(
     if "--cov" in session.posargs:
         # try to use the lighter-weight `sys.monitoring` coverage core
         env["COVERAGE_CORE"] = "sysmon"
+        # disable Numba JIT coverage
+        env["NUMBA_DISABLE_JIT"] = "1"
 
     session.run(
         "uv",
@@ -89,7 +91,7 @@ def tests(session: nox.Session) -> None:
     _run_tests(session)
 
 
-@nox.session(python=PYTHON_ALL_VERSIONS, reuse_venv=True, venv_backend="uv", default=True)
+@nox.session(python=PYTHON_ALL_VERSIONS, reuse_venv=True, venv_backend="uv")
 def minimums(session: nox.Session) -> None:
     """Test the minimum versions of dependencies."""
     with preserve_lockfile():

pyproject.toml

@@ -49,6 +49,8 @@ dependencies = [
     "qiskit>=1.3.0; python_version >= '3.13'",
     "opt-einsum>=3.4.0",
     "tqdm>=4.67.1",
+    "numba>=0.61.0",
+    "numba>=0.63.0; python_version >= '3.14'",
 ]
 
 [project.urls]

src/mqt/yaqs/core/methods/lanczos_numba.py

@@ -0,0 +1,100 @@
+# Copyright (c) 2025 - 2026 Chair for Design Automation, TUM
+# All rights reserved.
+#
+# SPDX-License-Identifier: MIT
+#
+# Licensed under the MIT License
+
+"""Numba-accelerated Lanczos methods."""
+
+from __future__ import annotations
+
+import numpy as np
+from numba import jit
+
+
+@jit(nopython=True, cache=True, fastmath=True)
+def orthogonalize_step(
+    v: np.ndarray,
+    w: np.ndarray,
+    j: int,
+    alpha: np.ndarray,
+    beta: np.ndarray,
+) -> float:
+    """Perform the orthogonalization step of the Lanczos iteration.
+
+    Computes alpha[j] = <v_j, w>, orthogonalizes w against v_j and v_{j-1},
+    and computes the norm beta[j] = ||w||.
+
+    Args:
+        v: (N, m) matrix of Lanczos vectors. Columns should be contiguous (F-order) for best performance.
+        w: (N,) candidate vector. Modified in-place.
+        j: Current iteration index.
+        alpha: (m,) diagonal elements.
+        beta: (m-1,) off-diagonal elements.
+
+    Returns:
+        float: The norm of the orthogonalized vector (beta[j]), or 0.0 if not computed.
+    """
+    # Note: v[:, j] creates a view. If v is F-ordered, this view is contiguous.
+    vj = v[:, j]
+
+    # 1. alpha_j = <v_j, w>
+    aj = np.vdot(vj, w).real
+    alpha[j] = aj
+
+    # 2. w <- w - aj * vj
+    w_len = w.size
+    for i in range(w_len):
+        w[i] -= aj * vj[i]
+
+    # 3. Orthogonalize against v_{j-1} if applicable
+    if j > 0:
+        v_prev = v[:, j - 1]
+        b_prev = beta[j - 1]
+        for i in range(w_len):
+            w[i] -= b_prev * v_prev[i]
+
+    # 4. Compute norm
+    norm_sq = 0.0
+    for i in range(w_len):
+        val = w[i]
+        norm_sq += val.real * val.real + val.imag * val.imag
+
+    bj = np.sqrt(norm_sq)
+
+    if j < len(beta):
+        beta[j] = bj
+
+    return bj
+
+
+@jit(nopython=True, cache=True, fastmath=True)
+def normalize_and_store(v: np.ndarray, w: np.ndarray, j: int, bj: float) -> None:
+    """Normalize a Lanczos vector and store it in the Lanczos basis matrix.
+
+    This helper function completes the Lanczos iteration by normalizing the
+    candidate vector `w` by the computed norm `bj` and storing the result
+    as the next Lanczos vector in column `j+1` of the basis matrix `v`.
+
+    If `bj` is zero (indicating loss of orthogonality or convergence), the
+    normalization is skipped and the column remains unchanged.
+
+    Args:
+        v: (N, m) matrix of Lanczos vectors. Column `j+1` will be overwritten.
+            Should be F-ordered for optimal memory access.
+        w: (N,) candidate vector to normalize. Not modified.
+        j: Current iteration index. The normalized vector is stored in `v[:, j+1]`.
+        bj: Normalization factor (the computed norm of `w` after orthogonalization).
+            If `bj <= 0`, normalization is skipped.
+
+    Note:
+        Modifies `v` in-place.
+    """
+    if bj > 0:
+        inv_bj = 1.0 / bj
+
+        # explicit loop
+        w_len = w.size
+        for i in range(w_len):
+            v[i, j + 1] = w[i] * inv_bj