The quantum computing, quantum cryptography and quantum communication protocols are pillars on the quantumentanglement with GreenbergerHorneZeilinger (GHZ) states. The fact of multi-qubit entangled states is difficult tointuitively interpret although it is important theoretically even in the noise and decoherence case. In this paper, it isproposed to present the quantum simulator that aims to create and simulate and visualize various qubit GHZ states inthree popular quantum noise models including the depolarizing, amplitude and phase damping. The system is codedin Flask and the Qiskit and Qiskit Aer on the circuit building and circulation and the Matplotlib on the heatmap of thedensity matrices, bar plots in three dimensions, and the Bloch sphere. One of them is that it can be parameterized withan amplitude coefficient 8 that can be used to research unequal entanglement amplitude parameter of interest inquantum secret sharing applications. It is based on containers and can be obtained using Docker, as well as can beviewed using any current browser and the localization of quantum frameworks is not necessary. The dynamics of thesimulation demonstrates that the system is a good model of the theoretical behavior of the noise: depolarizing noisetakes states to the maximum mixture, amplitude damping takes the populations to ground states and phase dampingselectively decays the coherences. It is applied by teachers and learners, and researchers who were interested inobtaining an interactive and graphical interface that allows offering an interface between the abstract quantumformalism and the real quantum dynamics of information.
The quantum computing, quantum cryptography and quantum communication protocols are pillars on the quantumentanglement with GreenbergerHorneZeilinger (GHZ) states. The fact of multi-qubit entangled states is difficult tointuitively interpret although it is important theoretically even in the noise and decoherence case. In this paper, it isproposed to present the quantum simulator that aims to create and simulate and visualize various qubit GHZ states inthree popular quantum noise models including the depolarizing, amplitude and phase damping. The system is codedin Flask and the Qiskit and Qiskit Aer on the circuit building and circulation and the Matplotlib on the heatmap of thedensity matrices, bar plots in three dimensions, and the Bloch sphere. One of them is that it can be parameterized withan amplitude coefficient 8 that can be used to research unequal entanglement amplitude parameter of interest inquantum secret sharing applications. It is based on containers and can be obtained using Docker, as well as can beviewed using any current browser and the localization of quantum frameworks is not necessary. The dynamics of thesimulation demonstrates that the system is a good model of the theoretical behavior of the noise: depolarizing noisetakes states to the maximum mixture, amplitude damping takes the populations to ground states and phase dampingselectively decays the coherences. It is applied by teachers and learners, and researchers who were interested inobtaining an interactive and graphical interface that allows offering an interface between the abstract quantumformalism and the real quantum dynamics of information.
Quantum state visualisation remains a significant challenge in quantum computing education and research due to the abstract mathematical properties of quantum mechanics. This paper presents a new Quantum State Visualiser, an interactive web app that tries to bridge the gap between theoretical quantum mechanics and real-world understanding. The proposed solution operates with multi-qubit quantum circuits, employing partial trace operations to derive single-qubit reduced density matrices, which are then depicted as dynamic 3D Bloch sphere representations. The tool helps you understand abstract ideas like superposition, entanglement, and quantum interference by turning hard math into easy-to-understand pictures. This is useful for students, teachers, researchers, and people who work on quantum computers.The prototype uses Qiskit for quantum Traditional quantum co simulation, Python for computational backends, and modern web technologies for interactive visualisation. The system can accurately show quantum states in real time, which means that circuit changes get instant visual feedback. The new thing is that it combines quantum simulation in real time with 3D visualisation that you can interact with. This creates a fun place to learn that helps people understand quantum phenomena faster. This tool fills a big gap in education and could be used in schools, to fix problems with quantum algorithms, and to make quantum circuits work better. In the future, it will be possible to work with bigger qubit systems, connect it to quantum hardware platforms, and add features for augmented reality visualisation
We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.
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.
The advent of noisy intermediate-scale quantum (NISQ) devices has not only opened up new possibilities to studying quantum computational benefits, but it has also presented new challenges associated with noise and short coherence times. Entanglement is one of the inherent resources that can be used to perform quantum computation and implement the performance and reliability of quantum algorithms. This paper looks at entanglement dynamics in NISQ machines subjected to natural noises. The study focuses on the problem of examining the role of various noise channels in the creation, dynamics, and decay of the entanglement during quantum operations, such as depolarizing, amplitude damping, and phase damping. The study is based on theoretical modeling and numerical simulations of multi-qubit quantum circuits to determine the stability of entangled states with respect to circuit depth and intensity of noise. Concurrence and von Neumann entropy are examples of entanglement measures that are used to characterize correlations between qubits as well as to trace the dynamics of these correlations across computational interactions. The results show that noise has major impacts on entanglement distribution, which tends to cause rapid decays in highly entangled states with increase in circuit complexity. The findings, however, also show that there are some circuit architectures and error-mitigation schemes that can somewhat sustain entanglement with moderate levels of noise. The paper also emphasizes the relevance of minimalizing sequence of gates, and reduced circuit depth in an effort to preserve useful entanglement in present-day quantum hardware. These observations help in understanding the behaviour of quantum correlations better in real world quantum devices and provide a way of developing more resilient quantum algorithms that would work on NISQ systems. In general, the article offers a systematic view on entanglement behavior in disordered quantum systems and highlights its value in the development of quantum computing applications in the near term.
This work investigates the transformation and behavior of quantum states using Bloch sphere visualizations to provide an intuitive understanding of quantum phenomena, incorporating concepts from both quantum computing and nano physics.By applying quantum gates such as Hadamard, Pau-li-X, Pauli-Y, and Pauli-Z, the evolution of qubits is demonstrated.The study leverages principles of quantum superposition, entanglement, and coherence, which are pivotal in nanoscale systems, to analyze qubit dynamics.Additionally, phase noise, a critical factor in nanoscale quantum devices, is introduced to simulate real-world quantum errors, and fidelity is calculated to measure the robustness of quantum states under such noise.The approach addresses noise resilience in nanoscale quantum devices by combining phase noise analysis, fidelity measurement, and quantum entanglement.The novelty of the approach is emphasized through comparisons with the existing studies on quantum state tomography and machine learning-based quantum optimization.Results will have direct applications in quantum key distribution (QKD), quantum error correction, and secure quantum communication.
Abstract The visualization of qubit states plays a fundamental role in understanding quantum information processing. This study explores the use of the Bloch sphere as a geometrical tool for representing and interpreting single-qubit and two-qubit states. Using the Qiskit framework, we simulate quantum circuits to demonstrate the action of quantum gates and the generation of entangled states, such as Bell states. The effects of various gate operations on qubit orientation are analyzed in the Bloch sphere representation. Furthermore, we examine the matrix formalism of quantum states and provide a statistical analysis of measurement outcomes. This work bridges the gap between theoretical quantum mechanics and experimental simulation, offering insights for both educational and research purposes in quantum computing.