Abstract The characterization of quantum noise is fundamental to quantum information processing, quantum control and reliable operation of near-term quantum devices. Conventional descriptions of quantum noise are based on completely positive trace-preserving (CPTP) maps acting on density operators. These models describe effective quantum dynamics after the underlying physical interactions have been represented as a quantum channel. However, in practical cases, imperfections such as calibration errors, control-field fluctuations, finite-resolution waveform generation, and analog hardware noise can act upon the probability amplitudes of a quantum state earlier. The effect of such perturbation in quantum state after normalization has largely been unexplored. In this work, we develop a rigorous mathematical analysis of the normalized additive amplitude noise in a finite-dimensional quantum system. Assuming a zero-mean complex perturbation, we derive a second-order closed form expression for the ensemble-averaged density operator. The analysis leads to state-dependent evolution of the quantum state which cannot be represented by a CPTP map. We further prove that in case of isotropic noise, the ensemble-averaged density operator becomes an effective depolarizing channel. For anisotropic perturbations, we derive the orientation-dependent Bloch-vector contraction which is determined by the covariance geometry of the additive noise. Closed-form expressions are further obtained for measurement probabilities, state fidelity, and ensemble purity, showing that fidelity degradation depends only on the component of the perturbation covariance orthogonal to the input state. Monte Carlo simulations closely match the theoretical analysis, especially for small noise regime. The proposed model establishes a connection between classical additive-noise models and effective quantum dynamics generated by normalized state-space perturbations.
Abstract The characterization of quantum noise is fundamental to quantum information processing, quantum control and reliable operation of near-term quantum devices. Conventional descriptions of quantum noise are based on completely positive trace-preserving (CPTP) maps acting on density operators. These models describe effective quantum dynamics after the underlying physical interactions have been represented as a quantum channel. However, in practical cases, imperfections such as calibration errors, control-field fluctuations, finite-resolution waveform generation, and analog hardware noise can act upon the probability amplitudes of a quantum state earlier. The effect of such perturbation in quantum state after normalization has largely been unexplored. In this work, we develop a rigorous mathematical analysis of the normalized additive amplitude noise in a finite-dimensional quantum system. Assuming a zero-mean complex perturbation, we derive a second-order closed form expression for the ensemble-averaged density operator. The analysis leads to state-dependent evolution of the quantum state which cannot be represented by a CPTP map. We further prove that in case of isotropic noise, the ensemble-averaged density operator becomes an effective depolarizing channel. For anisotropic perturbations, we derive the orientation-dependent Bloch-vector contraction which is determined by the covariance geometry of the additive noise. Closed-form expressions are further obtained for measurement probabilities, state fidelity, and ensemble purity, showing that fidelity degradation depends only on the component of the perturbation covariance orthogonal to the input state. Monte Carlo simulations closely match the theoretical analysis, especially for small noise regime. The proposed model establishes a connection between classical additive-noise models and effective quantum dynamics generated by normalized state-space perturbations.
Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity associated with several standard quantum noise models, including the random Pauli-X, dephasing, depolarizing, Werner-Holevo, generalized Pauli (Weyl), and amplitude-damping channels. For each model, we express the entanglement fidelity in terms of a general input density operator ρ, using Schumacher's Kraus-operator approach, which provides a channel-agnostic recipe applicable to any completely positive trace-preserving (CPTP) map with a finite Kraus representation. We then specialize to a communication scenario in which the source emits a two-letter parametric alphabet, thereby making explicit the dependence of entanglement preservation on both channel and source parameters. The resulting expressions enable direct comparisons of channel performance and rankings for representative families of input states, including common qubit states.
Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity of several standard quantum noise models, including the random Pauli-X, dephasing, depolarizing, Werner-Holevo, generalized Pauli (Weyl), and amplitude-damping channels. For each model, we express the entanglement fidelity in terms of a general input density operatorρ, using Schumacher's Kraus-operator approach, which provides a channel-agnostic recipe for any completely positive trace-preserving map with a finite Kraus representation. We then specialize to a communication scenario in which the source emits a two-letter parametric alphabet, thereby making explicit the dependence of entanglement preservation on both channel and source parameters. The resulting expressions enable direct comparisons of channel performance and rankings for representative families of input states.
This paper presents a statistical framework for characterizing quantum noise effects in amplitude-encoded images through the analysis of noise-induced amplitude perturbations. Classical grayscale images are encoded as normalized quantum amplitude vectors and subjected to stochastic amplitude damping, phase damping, and depolarizing channels. The resulting perturbations are quantified and modeled using a bounded-domain distribution obtained via a nonlinear transformation of the Ola distribution. A single shape parameter is estimated via maximum-likelihood methods, providing a compact descriptor of perturbation concentration across images, noise channels, and noise levels. Experimental results reveal a consistent decreasing relationship between the estimated parameter and noise level, along with clear channel-dependent statistical signatures. Phase damping, despite producing negligible visual changes in reconstructed images, yields measurable perturbations that are accurately captured by the proposed model. Goodness-of-fit analysis based on Kullback–Leibler divergence, mean absolute error, and likelihood-based criteria demonstrates stable model performance across noise regimes, supported by bootstrap uncertainty analysis. The proposed approach provides a unified and statistically robust representation of quantum noise-induced perturbations in amplitude-encoded images, enabling systematic comparison of noise effects beyond visual inspection. This characterization supports noise-aware quantum image processing by offering a compact, channel-dependent statistical description that can inform algorithm design and evaluation under realistic noise conditions.
This paper investigates the dynamic suppression of quantum noise within the framework of quantum control theory. The core challenge in implementing precise quantum operations lies in the significant influence of environmental noise, which introduces uncertainties and degrades control fidelity. We propose a novel approach utilizing real-time feedback control, leveraging quantum sensors to monitor the noise levels within a quantum system. Based on this continuous assessment, control parameters are dynamically adjusted to mitigate the impact of noise. The effectiveness of this method is demonstrated through theoretical analysis and mathematical modeling. We aim to enhance the accuracy and stability of quantum control processes, ultimately contributing to the reliable execution of complex quantum operations. The system is described by the following Hamiltonian: H=H0+HI, where H0 is the system Hamiltonian and HI represents the interaction Hamiltonian. The time evolution of the system is governed by the equation: dtd∣ψ(t)>=ℏi[H,∣ψ(t)]. Noise is modeled as a stochastic term, adding to the Hamiltonian: H=H0+HI+HN, where HN represents the noise Hamiltonian. The control pulse can be described as: U(t)=∑i=1Nαie−iωit, where αi are the amplitudes and ωi are the carrier frequencies. The fidelity of the quantum operation is evaluated using the overlap between the initial and final states: Fidelity=∣∣2. The control parameters are optimized to maximize the fidelity. The quantum state evolution is described by the equation: ∣ψ(t+δt)>=U(t)∣ψ(t)>, where U(t) is the control pulse. The time-dependent Schrodinger equation is: i/ħ ∂/∂t |ψ(t)> = H|ψ(t)>. The noise introduces uncertainties which can be represented as: σ2=−2, where N is the noise operator.
Quantum computing holds immense promise for revolutionizing computation, yet its practical realization is severely hampered by the pervasive issue of quantum noise. This noise, arising from various sources including environmental interactions and imperfect control, introduces errors into quantum computations, degrading their fidelity. This paper explores novel control algorithms designed to mitigate the detrimental effects of quantum noise. We investigate the underlying mechanisms generating noise and propose a method based on precise qubit control and calibration to minimize its impact. The core claim is that effective noise control is crucial for achieving reliable quantum computation. The proposed algorithms leverage feedback control and adaptive calibration techniques to dynamically compensate for noise fluctuations, aiming to enhance the accuracy and robustness of quantum algorithms. The mathematical framework presented includes noise models, control equations, and performance metrics, demonstrating the feasibility and potential of this approach. Specifically, we introduce a closed-loop control system described by the equation: (Δsn+1 = K(en - sn)) + wn+1, where Δsn+1 represents the change in state, K is the gain, en is the desired state, sn is the actual state, and wn+1 is the noise term. We also examine the effect of decoherence, modeled as: ds = Hdt + Vd, where ds is the time evolution of the quantum state, H is the Hamiltonian describing the system, dt is the time step, and Vd is the damping term due to noise. The research aims to contribute towards the development of more robust and practical quantum computers.
Abstract Quantum image processing methods that rely on amplitude encoding are sensitive to channel-induced noise, yet reusable benchmarks for evaluating these effects under controlled conditions remain limited. We present QN-AEI, a simulation-based benchmark constructed from 200 images in the BSDS500 training subset. Each image is resized to 64 × 64 pixels and normalized to a 4096-dimensional amplitude vector representing a 12-qubit quantum state, then subjected to three noise channels (amplitude damping, Pauli-Z dephasing, and depolarizing noise) at four levels, η ∈ {0.1, 0.3, 0.5, 0.7}, with 200 stochastic trajectory realizations per image–channel–noise condition. This yields 2,400 conditions, 480,000 noisy realizations, and 1,966,080,000 normalized perturbation samples in total. Each record pairs the clean image and amplitude vector with its noisy statevectors, raw and normalized perturbations, and condition-level metadata; the release also includes source-image provenance, a dataset manifest, validation outputs, summary statistics, documentation, and the MATLAB generation and validation code. QN-AEI supports reproducible benchmarking of quantum-noise characterization, denoising, uncertainty and reliability analysis, and bounded-domain perturbation modeling.