Quantum computation is inherently hybrid, and fast classical manipulation of qubit operators is necessary to ensure scalability in quantum software. We introduce PauliEngine, a high-performance C++ framework that provides efficient primitives for Pauli string multiplication, commutators, symbolic phase tracking, and structural transformations. Built on a binary symplectic representation and optimized bit-wise operations, PauliEngine supports both numerical and symbolic coefficients and is accessible through a Python interface. Runtime benchmarks demonstrate substantial speedups over state-of-the-art implementations. PauliEngine provides a scalable backend for operator-based quantum software tools and simulations.
Quantum computation is inherently hybrid, and fast classical manipulation of qubit operators is necessary to ensure scalability in quantum software. We introduce PauliEngine, a high-performance C++ framework that provides efficient primitives for Pauli string multiplication, commutators, symbolic phase tracking, and structural transformations. Built on a binary symplectic representation and optimized bit-wise operations, PauliEngine supports both numerical and symbolic coefficients and is accessible through a Python interface. Runtime benchmarks demonstrate substantial speedups over state-of-the-art implementations. PauliEngine provides a scalable backend for operator-based quantum software tools and simulations.
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.
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.
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 matrices and Pauli strings are widely used in quantum computing. These mathematical objects are useful to describe or manipulate the quantum state of qubits. They offer a convenient basis to express operators and observables used in different problem instances such as molecular simulation and combinatorial optimization. Therefore, it is important to have a well-rounded, versatile and efficient tool to handle a large number of Pauli strings and operators expressed in this basis. This is the objective behind the development of the PauliArray library presented in this work. This library introduces data structures to represent arrays of Pauli strings and operators as well as various methods to modify and combine them. Built using NumPy, PauliArray offers fast operations and the ability to use broadcasting to easily carry out otherwise cumbersome manipulations. Applications to the fermion-to-qubit mapping, to the estimation of expectation values and to the computation of commutators are considered to illustrate how PauliArray can simplify some relevant tasks and accomplish them faster than current libraries.
We present a new software package for efficient quantum circuit generation, designed to achieve optimal runtime performance. Despite being in an early stage of development, our implementation demonstrates significant advantages over existing tools. Using the quantum Fourier transform (QFT) as a benchmark, we show that our backend can generate circuits for systems with up to 2000 qubits faster than widely used frameworks such as Qiskit and Q#. This improvement is particularly relevant for applications where classical preprocessing time, including circuit generation, must be minimized to not diminish any potential quantum advantage - for example, in combinatorial optimization tasks. Additionally, our software provides high-level primitives for bit- and integer-level manipulations, offering a simplified interface for integration with high-level quantum programming languages.
Abstract Analysis of quantum processes, especially in the context of noise, errors, and decoherence is essential for the improvement of quantum devices. An intuitive representation of those processes modeled by quantum channels are Pauli transfer matrices. They display the action of a linear map in the n-qubit Pauli basis in a way, that is more intuitive, since Pauli strings are more tangible objects than the standard basis matrices. We set out to investigate classical algorithms that convert the various representations into Pauli transfer matrices. We propose new algorithms that make explicit use of the tensor product structure of the Pauli basis. They convert a quantum channel in a given representation (Chi or process matrix, Choi matrix, superoperator, or Kraus operators) to the corresponding Pauli transfer matrix. Moreover, the underlying principle can also be used to calculate the Pauli transfer matrix of other linear operations over n-qubit matrices such as left-, right-, and sandwich multiplication as well as forming the (anti-)commutator with a given operator. Finally, we investigate the runtime of these algorithms, derive their asymptotic scaling and demonstrate improved performance using instances with up to seven qubits.