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 consistently outperforms state-of-the-art CPU-based methods in terms of execution speed, while also 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.
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 consistently outperforms state-of-the-art CPU-based methods in terms of execution speed, while also 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.
As quantum devices become accelerators within classical HPC deployments, the efficiency of the classical partition becomes critical. Workloads such as Hamiltonian manipulation, observable backpropagation, and Pauli-based compilation reduce to bulk arithmetic on Pauli strings and sums.
We present HPC strategies for this arithmetic, demonstrated in PauLIB, a header-only C++20 library: a bit-packed binary symplectic representation reducing Pauli multiplication to a bitwise XOR and population count; a sorted, struct-of-arrays layout replacing hash maps and exposing contiguous word arrays to SIMD units and GPU warps; and deterministic OpenMP parallelism with race-free output partitioning.
These strategies deliver orders-of-magnitude higher throughput and smaller memory footprint than Qiskit and PauliEngine, plus a speedup from a CUDA outer-product kernel on an H100. Two case studies, g-sim and truncated Pauli propagation, inherit these gains and scale unchanged from a desktop Arm CPU to a 72-core HPC Arm server. PauLIB is open source with C++ and Python interfaces.
Quantum algorithms such as the Quantum Fourier Transform (QFT), Grover’s Search, the Bernstein–Vazirani (BV) algorithm, and Bell-state generation are computationally intensive to emulate on classical processors due to the exponential growth of state vectors. This work presents a fixed-point, microcoded FPGA accelerator that achieves deterministic timing, near-unit fidelity, and linear scalability up to 4 qubits. The design features a microcoded control plane with pairwise and diagonal opcodes, fixed-point complex arithmetic, and subspace-gated execution (qubit0= LSB). We benchmark QFT(2–4), BV(2–4), Grover(4), and Bell(2) at 100 MHz and compare against equivalent CPU state-vector simulations. Across all algorithms, the FPGA demonstrates consistent latency reduction: QFT: 88×–154× (98.9–99.4% faster), BV: 54×–90× (98.1–98.9% faster), Bell: 282× (99.6% faster), and Grover-4: 14.2× (93.0% faster). Fidelity is near-unit for all programs except a single BV-2 run that yields 0.875 ; QFT, Bell, BV-3, BV-4 and Grover-4 achieve 1.000. Latency scales linearly with qubit count—growing by ~1.8× per additional qubit for QFT and ~1.6× for BV—confirming the deterministic and cycle-predictable nature of the microcoded architecture. Results reflect 100 MHz RTL simulation (Verilator); we report synthesis resources and post-P&R Fmax, and express speedups normalized to 100 MHz. These results show that even a modest FPGA can outperform our CPU state-vector baseline on small-n kernels while preserving deterministic, cycle-accurate timing for small-to-medium quantum workloads through spatial parallelism and hardware-level determinism.
Efficient manipulation of Pauli-algebraic objects is a key bottleneck in the classical emulation and benchmarking of quantum algorithms for chemistry and many-body physics. This bottleneck appears in Hamiltonian construction, variational ansatz preparation, expectation-value and gradient evaluation, and real-time propagation, all of which require repeated Pauli-algebra operations. Here, we present a high-performance Pauli-algebra framework tailored to quantum many-body and quantum-chemical simulations. The framework combines compact binary symplectic encoding, canonical coefficient reduction, and grouped sparse operator representations that exploit shared bit-flip patterns among Pauli strings. The resulting Julia/C\texttt{++} implementation accelerates Pauli multiplication, Hamiltonian construction, and operator--state multiplication in sparse and symmetry-adapted many-electron spaces. Benchmarks demonstrate efficient Hamiltonian construction, large-active-space VQE and ADAPT-VQE calculations, and real-time variational dynamics on modern multicore CPU and GPU architectures. These results show that structure-aware Pauli-algebra engines provide a scalable classical backend for developing and benchmarking quantum algorithms in quantum chemistry and many-body simulation.
Practical quantum computers are still in the nascent stages of development, which makes simulation tools essential for advancing quantum algorithms. Since such a simulation involves massive parallel computations, a naive data representation can strain the memory bandwidth and limit parallelism. In this paper, we propose an FPGA-based pipelined accelerator based on the base-21 numeral system for quantum computer simulation. The representation of base-21 numbers does not require complex multipliers and adders, but only cross-bars, shifts, and customized full adders to perform the simulation, realizing higher speed. The experimental results show that our accelerator achieves 15.1-34, 009.7 × faster than CPU and GPU, and 8.4-40.7 × faster than other FPGA-based accelerators. Thus, our accelerators based on base-21 are the fastest simulator among CPU, GPU, and FPGA-based ones, providing a valuable tool for researchers developing and testing quantum algorithms.
Decomposing classical matrices into linear combinations of Pauli strings is a major bottleneck for end-to-end implementations of near-term quantum algorithms. In this work, we consider a promise version of this Pauli decomposition problem in which the matrix is guaranteed to have support on only k=poly(n) Pauli strings and is given through classical sparse query access. Existing Pauli decomposition algorithms are designed for the generic, dense problem and do not inherently take advantage of this promised sparsity, so these approaches take time that is exponential in n. We present a randomized classical algorithm that does take advantage of this sparsity and recovers the exact Pauli decomposition with success probability at least 1−δ, for any δ. Under the stated access model, the algorithm executes with query and runtime complexity that is polynomial in n, k, and log(1/δ). These results show that, even though finding the Pauli decomposition is exponentially hard for general matrices, it becomes efficiently solvable for matrices that are known to be sparse in the Pauli basis, a regime that is relevant to near-term quantum algorithms operating on structured classical input.
The drastic growth of data generation by companies such as Google and Facebook, the widespread integration of IoT devices into everyday life, advancements in artificial intelligence, and the rise of social media platforms are driving a shift from model-driven to data-driven science. This surge in data created a need for massively parallel accelerators such as graphics processing units (GPU). High Performance Computing (HPC) are required to accommodate the growing complexity of data-driven technologies. HPC demands are anticipated to reach exascale levels within this decade. Since 2004, three waves of high-performance accelerators have driven advancements in HPC: the first wave introduced Central Processing Units (CPUs) and Field Programmable Gate Arrays (FPGAs), the second wave brought General Purpose Graphics Processing Units (GPGPUs), and the third wave focused on machine learning specific GPUs. Recent research reveals that quantum processing units (QPUs) have the potential to be the fourth wave of high-performance acceleration in the near future. However, as Quantum Computing is still in its early stages, its practical and useful quantum computation is yet to be developed. In this paper, a heterogeneous CPU-GPU-QPU (HCGQ) accelerator is proposed. The accelerator is based on an input size threshold, where the CPU assigns smaller input sizes workloads to the GPU, and larger input sizes to the QPU. This dynamic workload allocation is realized entirely through software-level integration. Using the searching algorithm and deep neural networks as benchmarks, it was observed that the HCGQ accelerator outperformed standalone GPUs and QPUs in terms of speed and energy efficiency.