Qupertino: Pure MLX Array Kernels versus Hand-Tuned Metal Shaders for Quantum Circuit Simulation on Apple Silicon
Abstract
We present Qupertino, an open-source quantum circuit simulator for Apple Silicon, and use it to ask how far a simulator written purely in MLX array operations can go and what remains for hand-tuned Metal shaders. The framework ships two measured tiers. The pure tier dispatches structured gates to specialized MLX kernels: diagonal gates run as broadcast phase multiplies, controlled gates as masked half-state updates, and SWAP as an axis permutation; a paired dense-path ablation attributes a 25-33x speedup to this dispatch alone. The opt-in shader tier adds hand-written Metal kernels for every structured layer family in our benchmarks, including phase-LUT diagonals, GF(2) affine permutation gathers, fused tensor-product single-qubit layers, radix-4 QFT and Walsh-Hadamard butterflies, and basis-conjugated XX/YY Trotter layers; runtime fusion detectors route work to them while preserving circuit semantics exactly, confirmed by parity tests. In a four-way interleaved campaign on M1 Max (two warmups, ten measured repeats per cell), the shader tier is fastest by mean runtime in all 18 comparison cells against same-machine Qiskit Aer CPU and PennyLane lightning.qubit. At 25 qubits, gate-stream QFT runs in 0.0591 +/- 0.0029 s (paired 47.2x over Aer, 95.3x over PennyLane) and TFIM Trotter evolution in 0.495 +/- 0.035 s (36.2x and 67.2x). Across a 29-workload suite, the shader tier's paired speedup over pure MLX reaches 25x, with 25 of 29 workloads accelerating above parity. The framework also supports variational ansatz workloads, QAOA, QCBM, Trotter-Suzuki Hamiltonian simulation, and OpenQASM 2.0 import (unitary subset); a preliminary MPS backend reaches 150 qubits on limited-entanglement workloads. Correctness rests on 253 Python tests, independent complex128 checks, and a Trotter-error curve against exact diagonalization. State-vector memory remains exponential in qubit count.
Related
- PPVM: A Circuit Simulation Framework for Digital Twins of Quantum Processors
- Quantum circuit simulation with high-order optical tensor processing
- Quantum Simulation of Two-Dimensional Free Dirac Hamiltonian in Multimode Circuit QED
- Quantum Simulation of Electronic Structure using Quantum Density Functional Theory on a Programmable Integrated Photonic Circuit
- Quantum-circuit simulation of three-flavor neutrino oscillations: vacuum, matter, and CP diagnostics
BibTeX
@misc{kashani2026qupertino,
title = {{Qupertino: Pure MLX Array Kernels versus Hand-Tuned Metal Shaders for Quantum Circuit Simulation on Apple Silicon}},
author = {Shlomo Kashani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19147},
eprint = {2609.19147},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19147},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Qupertino: Pure MLX Array Kernels versus Hand-Tuned Metal Shaders for Quantum Circuit Simulation on Apple Silicon
AU - Shlomo Kashani
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.19147
UR - https://arxiv.org/abs/2609.19147
AB - We present Qupertino, an open-source quantum circuit simulator for Apple Silicon, and use it to ask how far a simulator written purely in MLX array operations can go and what remains for hand-tuned Metal shaders. The framework ships two measured tiers. The pure tier dispatches structured gates to specialized MLX kernels: diagonal gates run as broadcast phase multiplies, controlled gates as masked half-state updates, and SWAP as an axis permutation; a paired dense-path ablation attributes a 25-33x speedup to this dispatch alone. The opt-in shader tier adds hand-written Metal kernels for every structured layer family in our benchmarks, including phase-LUT diagonals, GF(2) affine permutation gathers, fused tensor-product single-qubit layers, radix-4 QFT and Walsh-Hadamard butterflies, and basis-conjugated XX/YY Trotter layers; runtime fusion detectors route work to them while preserving circuit semantics exactly, confirmed by parity tests. In a four-way interleaved campaign on M1 Max (two warmups, ten measured repeats per cell), the shader tier is fastest by mean runtime in all 18 comparison cells against same-machine Qiskit Aer CPU and PennyLane lightning.qubit. At 25 qubits, gate-stream QFT runs in 0.0591 +/- 0.0029 s (paired 47.2x over Aer, 95.3x over PennyLane) and TFIM Trotter evolution in 0.495 +/- 0.035 s (36.2x and 67.2x). Across a 29-workload suite, the shader tier's paired speedup over pure MLX reaches 25x, with 25 of 29 workloads accelerating above parity. The framework also supports variational ansatz workloads, QAOA, QCBM, Trotter-Suzuki Hamiltonian simulation, and OpenQASM 2.0 import (unitary subset); a preliminary MPS backend reaches 150 qubits on limited-entanglement workloads. Correctness rests on 253 Python tests, independent complex128 checks, and a Trotter-error curve against exact diagonalization. State-vector memory remains exponential in qubit count.
ER -