A Controlled Study of Memory Hierarchy Transitions in Quantum Circuit Simulation on Apple M4 Pro Unified Memory Architecture

TL;DR

This study analyzes quantum circuit simulation performance on Apple M4 Pro UMA, revealing memory-bound behavior, a significant qubit transition discontinuity, and that irregular memory access patterns outperform streaming bandwidth predictions.

Contribution

It provides a detailed hardware-characterization framework for quantum simulation workloads on UMA, highlighting the impact of memory access patterns and a notable qubit transition discontinuity.

Findings

All gate implementations are memory-bound with low arithmetic intensity.

A reproducible 4.46× timing discontinuity occurs at 28→29 qubits.

Irregular memory access patterns outperform streaming bandwidth predictions.

Abstract

State-vector quantum circuit simulation is memory-bandwidth bound, yet the interaction between memory hierarchy, access pattern, and hardware parallelism remains incompletely characterized. We address this using the Apple M4 Pro Unified Memory Architecture (UMA), where CPU and GPU share identical physical LPDDR5X DRAM ($\sim$224 GB/s STREAM bandwidth for both), eliminating memory-technology and interconnect confounds. Using a thermally isolated, multi-trial methodology across 11 simulation backends on GHZ and QFT circuits from 3 to 30 qubits, we make three central contributions. First, a Roofline analysis confirms all gate implementations have arithmetic intensity $\leq$0.38 FLOP/byte, well below the ridge point for any plausible peak compute on modern hardware, establishing structural memory-boundedness. Second, we identify a reproducible 4.46$\times$ timing discontinuity at the 28$\rightarrow$29 qubit transition, confirmed under thermally isolated conditions and cross-validated across GHZ and QFT circuits; tensordot backends exhibit the full discontinuity while direct-index backends maintain $\sim$2$\times$ per-qubit scaling throughout. Third, despite STREAM predicting only 1.85$\times$ GPU speedup (MLX CPU 119.9 GB/s vs. MLX GPU 221.9 GB/s), all three algorithm classes exceed this prediction: tensordot 3.1--4.1$\times$, flat-index 3.5--5.9$\times$, and direct-index 6--10$\times$, demonstrating that peak streaming bandwidth does not predict simulation speedup for non-contiguous memory access patterns, with the gap widening as access irregularity increases. These findings provide a hardware-characterization framework for quantum simulation workloads on UMA.