The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in qutip-qip , QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad density-matrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce experimental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.
The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in qutip-qip , QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad density-matrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce experimental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.
We introduce SpinPulse, an open-source python package for simulating spin qubit-based quantum computers at the pulse-level. SpinPulse models the specific physics of spin qubits, particularly through the inclusion of classical non-Markovian noise. This enables realistic simulations of native gates and quantum circuits, in order to support hardware development. In SpinPulse, a quantum circuit is first transpiled into the native gate set of our model and then converted to a pulse sequence. This pulse sequence is subsequently integrated numerically in the presence of a simulated noisy experimental environment. We showcase workflows including transpilation, pulse-level compilation, hardware benchmarking, quantum error mitigation, and large-scale simulations via integration with the tensor-network library quimb. We expect SpinPulse to be a valuable open-source tool for the quantum computing community, fostering efforts to devise high-fidelity quantum circuits and improved strategies for quantum error mitigation and correction.
This work develops and tests a simulation framework based on Python and the Quantum Toolbox in Python (QuTiP), a library used to build quantum states, operators, and open-system time evolutions. The objective is to simulate noisy quantum circuits with Lindblad dynamics, a master-equation description in which coherent gate evolution and dissipative noise from the environment are treated to- gether. Grover’s search algorithm is used as a reference circuit. It is not used here to optimize the search algorithm itself, but to study how far a realistic numerical description can be pushed when finite-duration gates, local noise models, auxiliary work qubits called ancillas, encoded states, and recovery procedures are included. The first part of the work constructs a realistic unencoded noisy Grover model. In this model, the oracle, which marks the desired solutions, and the diffuser, which amplifies their probability, are decomposed into elementary gates, and noise acts during the execution of each gate. Three noise mechanisms are compared: dephasing, which destroys phase coherence; amplitude damping, which models relaxation from |1〉 to |0〉, and depolarizing noise, which represents a more symmetric loss of quantum information. Quantum Error Correction (QEC) is then studied as a way to protect logical information by encoding one logical qubit into several physical qubits. The QEC models are analyzed through a hierarchy of benchmarks designed to add realism progressively while keeping the simulations computationally feasible. These bench- marks include ideal recovery, recovery with an explicit time cost, semi-realistic oracle or diffuser dynamics, and the combined semi-realistic case. The results show that QEC can improve the marked-state probability in specific intermediate noise regimes, but that this benefit is strongly limited by recovery time, encoding cost, and the semi-realistic treatment of the Grover blocks. The phase-flip code gives the clearest improvement for dephasing noise, while amplitude-damping codes show more constrained gains, especially when success probability or larger encoded spaces are taken into account. Finally, the QuTiP solvers mesolve and mcsolve are compared. The first directly evolves the density matrix, while the sec- ond uses Monte Carlo wave-function trajectories. The trajectory approach reduces memory pressure but introduces statistical convergence costs. Overall, the project identifies both the physical regimes where QEC is informative and the numerical limits of realistic Python/QuTiP simulations.
Abstract This practical guide presents methods for constructing noise models using the Qiskit Aer noise module within the IBM Q ecosystem. The objective is to simulate quantum circuits under realistic error conditions, enabling accurate emulation of noisy quantum processors. The guide demonstrates how to: Use the Qiskit Aer noise module to define custom noise models. Incorporate gate errors, readout errors, and decoherence effects into simulations. Apply noise channels (e.g., depolarizing, amplitude damping, phase damping). Attach noise models to quantum circuit simulations. Analyze how noise affects algorithm performance and output distributions. Building noise models is essential for studying the behavior of quantum algorithms in the NISQ (Noisy Intermediate-Scale Quantum) era. It allows researchers to evaluate algorithm robustness, optimize circuit depth, and test error mitigation strategies before execution on real IBM Quantum hardware. This approach provides a bridge between ideal theoretical circuits and physically realistic quantum devices, enhancing the reliability and applicability of quantum computing experiments.
Abstract Effectively manipulating quantum computing (QC) hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise critically limits the performance and capabilities of today’s so-called noisy intermediate-scale quantum devices, as well as any future QC technologies. Fortunately, quantum control enables efficient execution of quantum logic operations and quantum algorithms with built-in robustness to errors, and without the need for complex logical encoding. In this manuscript we introduce software tools for the application and integration of quantum control in QC research, serving the needs of hardware R&D teams, algorithm developers, and end users. We provide an overview of a set of Python-based classical software tools for creating and deploying optimized quantum control solutions at various layers of the QC software stack. We describe a software architecture leveraging both high-performance distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other software packages and quantum programming languages. Our presentation includes a detailed mathematical overview of key features including a flexible optimization toolkit, engineering-inspired filter functions for analyzing noise susceptibility in high-dimensional Hilbert spaces, and new approaches to noise and hardware characterization. Pseudocode is presented in order to elucidate common programming workflows for these tasks, and performance benchmarking is reported for numerically intensive tasks, highlighting the benefits of the selected cloud-compute architecture. Finally, we present a series of case studies demonstrating the application of quantum control solutions derived from these tools in real experimental settings using both trapped-ion and superconducting quantum computer hardware.
Realistic modeling of qubit systems including noise and constraints imposed by control hardware is required for performance prediction and control optimization of quantum processors. We introduce qopt, a software framework for simulating qubit dynamics and robust quantum optimal control considering common experimental situations. To this end, we model open and closed qubit systems with a focus on the simulation of realistic noise characteristics and experimental constraints. Specifically, the influence of noise can be calculated using Monte Carlo methods, effective master equations or with the efficient filter function formalism, which enables the investigation and mitigation of autocorrelated noise. In addition, limitations of control electronics, including finite bandwidth effects as well as nonlinear transfer functions and drive-dependent noise, can be considered. The calculation of gradients based on analytic results is implemented to facilitate the efficient optimization of control pulses. The software easily interfaces with QuTiP, is published under an open-source license, is well tested, and features a detailed documentation.
Quantum machine learning (QML) integrates quantum computing with classical machine learning. Within this domain, QML-CQ classification tasks, where classical data is processed by quantum circuits, have attracted particular interest for their potential to exploit high-dimensional feature maps, entanglement-enabled correlations, and non-classical priors. Yet, practical realizations remain constrained by the Noisy Intermediate-Scale Quantum (NISQ) era, where limited qubit counts, gate errors, and coherence losses necessitate frugal, noise-aware strategies. The Data Re-Uploading (DRU) algorithm has emerged as a strong NISQ-compatible candidate, offering universal classification capabilities with minimal qubit requirements. While DRU has been experimentally demonstrated on ion-trap, photonic, and superconducting platforms, no implementations exist for spin-based quantum processing units (QPU-SBs), despite their scalability potential via CMOS-compatible fabrication and recent demonstrations of multi-qubit processors. Here, we present a pulse-level, noise-aware DRU framework for spin-based QPUs, designed to bridge the gap between gate-level models and realistic spin-qubit execution. Our approach includes (i) compiling DRU circuits into hardware-proximate, time-domain controls derived from the Loss–DiVincenzo Hamiltonian, (ii) explicitly incorporating coherent and incoherent noise sources through pulse perturbations and Lindblad channels, (iii) enabling systematic noise-sensitivity studies across one-, two-, and four-spin configurations via continuous-time simulation, and (iv) developing a noise-aware training pipeline that benchmarks gate-level baselines against spin-level dynamics using information-theoretic loss functions. Numerical experiments show that our simulations reproduce gate-level dynamics with fidelities near unity while providing a richer error characterization under realistic noise. Moreover, divergence-based losses significantly enhance classification accuracy and robustness compared to fidelity-based metrics. Together, these results establish the proposed framework as a practical route for advancing DRU on spin-based platforms and motivate future work on error-attentive training and spin–quantum-dot noise modeling.