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QiliSim: A C++ Quantum Simulator for Digital/Analog Workflows

Luke Mortimer, D. Babal, Vyron Vasileiadis, Natàlia Padilla

Published Sep 14, 2026• 0 citations
Publisher

Abstract

This work presents QiliSim, the native C++ simulation backend of QiliSDK, an open-source Python framework for digital and analog quantum computing. QiliSim supports quantum circuits, Hamiltonian time evolution, and analog-digital quantum reservoirs through a common interface, allowing users to test quantum algorithms before executing them on quantum hardware. The simulator provides statevector and density-matrix methods for digital workloads, alongside fixed-step and adaptive Runge–Kutta integrators, Krylov-subspace methods, and direct matrix exponentiation for analog evolution. Monte Carlo trajectories, mid-circuit measurements, and Kraus and Lindbladian noise models support the simulation of noisy quantum systems. Numerical methods and execution settings are selected through structured configuration objects, allowing the same quantum program to run with different simulation strategies without modifying its definition. The poster includes a circuit simulation example and performance comparisons for digital circuit sampling and quantum annealing. The reported benchmarks show competitive CPU performance against Qiskit Aer and Cirq for small to medium circuits, and faster execution than QuTiP and CUDA-Q dynamics for the tested annealing task at a target fidelity of 99%.

DOI
10.5281/zenodo.23471614

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This work presents QiliSim, the native C++ simulation backend of QiliSDK, an open-source Python framework for digital and analog quantum computing. QiliSim supports quantum circuits, Hamiltonian time evolution, and analog-digital quantum reservoirs through a common interface, allowing users to test quantum algorithms before executing them on quantum hardware. The simulator provides statevector and density-matrix methods for digital workloads, alongside fixed-step and adaptive Runge–Kutta integrators, Krylov-subspace methods, and direct matrix exponentiation for analog evolution. Monte Carlo trajectories, mid-circuit measurements, and Kraus and Lindbladian noise models support the simulation of noisy quantum systems. Numerical methods and execution settings are selected through structured configuration objects, allowing the same quantum program to run with different simulation strategies without modifying its definition. The poster includes a circuit simulation example and performance comparisons for digital circuit sampling and quantum annealing. The reported benchmarks show competitive CPU performance against Qiskit Aer and Cirq for small to medium circuits, and faster execution than QuTiP and CUDA-Q dynamics for the tested annealing task at a target fidelity of 99%.
QiliSDK is an open-source Python framework for designing and executing digital, analog, and hybrid quantum algorithms. Its modular structure unifies circuit-based and Hamiltonian-based workflows within a single API. It provides high-level abstractions for gates, circuits, Hamiltonians, and optimizers, while remaining fully backend-agnostic: seamlessly switch between CPU, GPU, or QPU execution. The SDK simplifies quantum development through expressive syntax for Pauli algebra, variational programs, and built-in tools for visualization, serialization, and result analysis.
Classical simulation supports the development and validation of quantum algorithms through full-state inspection, controlled noise models and backpropagation, albeit for small quantum systems. Existing frameworks offer gate-level execution, differentiable pulse-level dynamics or optimised hardware execution. Just another quantum simulator (JAQSI) combines gate- and pulse-level simulation in one differentiable circuit model built upon JAX. Circuits are represented as pure functions of numerical inputs which support vectorised batches and JIT compilation. Within a single circuit, matrix-defined operations, gates synthesised from Hamiltonian time evolution and noise channels can be composed freely. For a fast simulation, gate and channel fusion reduces passes over the state, while adjoint differentiation computes expectation-value gradients with a constant number of statevectors. At pulse level, JAQSI reduces evolution under single-term Hamiltonians to a scalar pulse-area integral and reuses cached execution plans and compiled solvers. In a benchmark we compare JAQSI with PennyLane, Qiskit, Qibo, Qulacs, QuTiP and dynamiqs. At gate level, we observe performance either on par or an order of magnitude faster across statevector, density, noise and gradient simulation than the compared simulators up to 12 qubits. Beyond 18 qubits, JAQSI is on par with PennyLane Lightning in both statevector and gradient simulation. In the statevector and noisy density-matrix pulse benchmarks, it is at least 5 times faster than the other simulators, even with its closed-form solve disabled. Disabling the latter increases its runtime by at most a factor of 1.5. We provide JAQSI as open-source software on GitHub and PyPI.
Classical simulation of quantum circuits remains indispensable for algorithm development, hardware validation, and error analysis in the noisy intermediate-scale quantum (NISQ) era. However, state-vector simulation faces exponential memory scaling, with an n-qubit system requiring O(2^n) complex amplitudes, and existing simulators often lack the flexibility to exploit heterogeneous computing resources at runtime. This paper presents a GPU-accelerated quantum circuit simulation framework that introduces three contributions: (1) an empirical backend selection algorithm that benchmarks CuPy, PyTorch-CUDA, and NumPy-CPU backends at runtime and selects the optimal execution path based on measured throughput; (2) a directed acyclic graph (DAG) based gate fusion engine that reduces circuit depth through automated identification of fusible gate sequences, coupled with adaptive precision switching between complex64 and complex128 representations; and (3) a memory-aware fallback mechanism that monitors GPU memory consumption and gracefully degrades to CPU execution when resources are exhausted. The framework integrates with Qiskit, Cirq, PennyLane, and Amazon Braket through a unified adapter layer. Benchmarks on an NVIDIA A100-SXM4 (40 GiB) GPU demonstrate speedups of 64x to 146x over NumPy CPU execution for state-vector simulation of circuits with 20 to 28 qubits, with speedups exceeding 5x from 16 qubits onward. Hardware validation on an IBM quantum processing unit (QPU) confirms Bell state fidelity of 0.939, a five-qubit Greenberger-Horne-Zeilinger (GHZ) state fidelity of 0.853, and circuit depth reduction from 42 to 14 gates through the fusion pipeline. The system is designed for portability across NVIDIA consumer and data-center GPUs, requiring no vendor-specific compilation steps.
This work presents a reproducible workflow for optimizing time-dependent Hamiltonian schedules using QiliSDK, an open-source, backend-agnostic Python framework for analog, digital, and hybrid quantum algorithms. The approach uses variational optimization of parametrized control schedules to improve state preparation beyond standard linear annealing, leveraging non-monotonic and near bang–bang profiles to exploit diabatic effects. The methodology follows a closed optimization loop combining quantum time evolution, expectation-value–based cost evaluation, and classical optimization. Results demonstrate fast convergence and robust improvements in excited-state preparation fidelity compared to naïve interpolation strategies. The contribution also highlights the modular architecture of QiliSDK, showcasing unified abstractions for Hamiltonians, schedules, optimizers, and execution backends, with an emphasis on reproducibility and portability across CPU, GPU, and quantum hardware.
Quantum computing is a promising way to study problems that are difficult for classical methods, but current quantum hardware still faces limits in scale, noise, and fidelity. Running quantum algorithms on physical machines can also be costly. Quantum circuit simulators therefore remain important because they let researchers design and test algorithms on classical computers before using quantum hardware. Most high-performance simulators provide GPU backends, while few offer native support for NPUs. This gap limits the computing platforms available for quantum-algorithm research. We developed Aicir to provide a full-stack quantum circuit simulator with a native Huawei Ascend NPU backend. Aicir connects circuit construction, several state representations, measurement, differentiation, variational algorithms, quantum machine learning, and quantum architecture search through one programming model. It also supports noise simulation, tensor-network and matrix-product-state engines, and distributed state simulation. On the NPU, paired real tensors, fixed-rank gate views, and hardware-specific formulas keep the tested simulation paths on the device. The same representation lets Aicir partition a state across 2p2^{p}2p NPUs while retaining reverse-mode differentiation. We validated native execution with CPU fallback disabled and checked distributed communication and gradients on 2, 4, and 8 NPUs. For the tested fused layered circuits, Aicir's CPU runtime is within 0.970.970.97--1.28×1.28\times1.28× that of Qiskit Aer and 0.760.760.76--1.10×1.10\times1.10× that of Cirq. These results place its CPU execution in the same range as established simulators for this workload, while the NPU tests establish correct native execution rather than CPU-to-NPU speedup.
Quantum circuit simulation remains essential for developing and validating quantum algorithms, especially as current quantum hardware is limited in scale and quality. However, the growing diversity of simulation methods and software tools creates a high barrier to selecting the most suitable backend for a given circuit. We introduce Maestro, a unified interface for quantum circuit simulation that integrates multiple simulation paradigms - state vector, MPS, tensor network, stabilizer, GPU-accelerated, and p-block methods - under a single API. Maestro includes a predictive runtime model that automatically selects the optimal simulator based on circuit structure and available hardware, and applies backend-specific optimizations such as multiprocessing, GPU execution, and improved sampling. Benchmarks across heterogeneous workloads demonstrate that Maestro outperforms individual simulators in both single-circuit and large batched settings, particularly in high-performance computing environments. Maestro provides a scalable, extensible platform for quantum algorithm research, hybrid quantum-classical workflows, and emerging distributed quantum computing architectures.