quantum-computingQupertino: Pure MLX Array Kernels versus Hand-Tuned Metal Shaders for Quantum Circuit Simulation on Apple Silicon
--> Quantum Physics arXiv:2609.19147 (quant-ph) [Submitted on 9 Jul 2026] Title:Qupertino: Pure MLX Array Kernels versus Hand-Tuned Metal Shaders for Quantum Circuit Simulation on Apple Silicon Authors:Shlomo Kashani View a PDF of the paper titled Qupertino: Pure MLX Array Kernels versus Hand-Tuned Metal Shaders for Quantum Circuit Simulation on Apple Silicon, by Shlomo Kashani View PDF HTML (experimental) 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 this http URL. 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 Hamiltoni
