PACOX: A FPGA-based Pauli Composer Accelerator for Pauli String Computation

TL;DR

The paper addresses the exponential growth in Pauli-string operator spaces that hampers classical processing in hybrid quantum-classical workflows. It introduces PACOX, an FPGA-based accelerator that uses a compact binary encoding to convert Pauli-string evaluation into XOR-based index permutation and phase accumulation, enabling a parallel, pipelined architecture with a PE cluster. Key contributions include a memory design with Context Buffers and an $n$-Pauli Matrix Memory (scaling to $n=19$), a 32-PE cluster, and a single-cycle XOR-based ALU. On a Xilinx ZCU102, PACOX delivers up to 100× speedups over CPU-based methods with low power-delay product, outperforming standard software libraries like Qiskit and PennyLane for Pauli workloads.

Abstract

Pauli strings are a fundamental computational primitive in hybrid quantum-classical algorithms. However, classical computation of Pauli strings suffers from exponential complexity and quickly becomes a performance bottleneck as the number of qubits increases. To address this challenge, this paper proposes the Pauli Composer Accelerator (PACOX), the first dedicated FPGA-based accelerator for Pauli string computation. PACOX employs a compact binary encoding with XOR-based index permutation and phase accumulation. Based on this formulation, we design a parallel and pipelined processing element (PE) cluster architecture that efficiently exploits data-level parallelism on FPGA. Experimental results on a Xilinx ZCU102 FPGA show that PACOX operates at 250 MHz with a dynamic power consumption of 0.33 W, using 8,052 LUTs, 10,934 FFs, and 324 BRAMs. For Pauli strings of up to 19 qubits, PACOX achieves speedups of up to 100 times compared with state-of-the-art CPU-based methods, while requiring significantly less memory and achieving a much lower power-delay product. These results demonstrate that PACOX delivers high computational speed with superior energy efficiency for Pauli-based workloads in hybrid quantum-classical systems.

Figures (6)

• Figure 1: Dataflow and internal datapath of PEs in PACOX method.
• Figure 2: Overview hardware architecture of PACOX.
• Figure 3: Memory organization of PACOX.
• Figure 4: Micro-architecture of the (a) PE and (b) ALU.
• Figure 5: Comparison of Execution Time and PDP for random $n$-qubit Pauli strings: PACOX vs. PC paulicomposor, Algo993 fackler2019algorithm and Tree 482008 methods.