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Quantum Blackhole Learning-Optimized Hadamard Neural Network Model for Dynamic Resource Reservation in Industry Clouds

Deepika Saxena, Hari Mohan Gaur, Ashutosh Kumar Singh, Anand Mohan

arXiv:2608.25754v1cs.DC

TL;DR

Industry-cloud workload prediction must handle high-dimensional, heterogeneous, volatile demand because conventional models have limited generalization and adaptability. The paper proposes QB-HNN, which combines qubit-based Hadamard neural processing with QB-BiO weight optimization. Across six benchmark datasets spanning three workload categories, QB-HNN reduces prediction error relative to five comparison methods, including LSTM and EQNN.

  • Problem

    Conventional machine-learning models struggle with high-dimensional, dynamic, heterogeneous workloads, distribution shifts, nonlinear dependencies, and frequent retraining demands.

  • Method

    QB-HNN transforms workload information into qubits, uses Hadamard-gated neural processing for superposition, and trains qubit weights with the QB-BiO optimization algorithm.

  • Results

    22.83% and 36.36% average prediction-error reductions are reported over EQNN and LSTM, respectively, across three categories of dynamic cloud workloads.

  • Takeaways & Limitations

    QB-HNN predicts sudden workload peaks and falls more closely to actual values and supports both single-resource and simultaneous multi-resource forecasting.

  • Takeaways & Limitations

    Real-world deployment may require interoperability layers for conventional cloud-management tools, while qubit encodings can impose computational and memory overhead on classical systems.

Abstract

from arXiv · show

Accurate workload prediction and proactive resource reservation are crucial for industry clouds. However, the conventional machine learning (CML) models with limited learning capabilities often fail to predict diverse, high-dimensional workloads with sudden changes in resource demand, leading to excessive power consumption and resource management issues. In this context, this article proposes a novel Hadamard neural network with quantum blackhole (QB-HNN) optimization. This model combines the computational efficiency of quantum mechanics with the persuasive learning capability of neural networks (NNs). The workload information is transformed into qubits and propagated via a deep network of qubit neurons comprising a Hadamard-gated activation function to fetch superposition within the QB-HNN model for intuitive pattern learning. Furthermore, a novel quantum blackhole biphase optimization (QB-BiO) algorithm is introduced to train and optimize qubit neural weights. The performance of the proposed model is comprehensively evaluated and compared with five state-of-the-art approaches using six benchmark datasets of three heterogeneous varieties of cloud workloads. The prediction accuracy achieved for an extensive range of workloads confirms its influential performance by minimizing the prediction error up to 36.36% and 22.83% over existing LSTM- and EQNN-based prediction approaches, respectively.

I. INTRODUCTION

Industry-cloud workloads vary sharply across heterogeneous resources, making accurate prediction important for proactive reservation and rational provisioning. QB-HNN addresses these challenges with Hadamard-based qubit learning and QB-BiO optimization, supporting single- and multi-resource forecasting.

  • Motivation: Dynamic workload and resource-demand changes can degrade quality of service, cause outages and inefficient utilization, and increase energy consumption.Accurate prediction supports proactive resource reservation and adaptive provisioning.
  • Research gap: Conventional machine-learning models struggle with high-dimensional, heterogeneous workloads, distribution shifts, nonlinear dependencies, and frequent retraining requirements.These limitations constrain generalization, real-time adaptability, and scalability.
  • Proposed model: QB-HNN combines qubit-based neural weights, Hadamard-gate superposition, and quantum blackhole learning to improve exploration, convergence, and adaptation for dynamic workloads.The architecture uses QB-BiO to optimize qubit weights and supports interaction between quantum and classical modules.
  • Optimization: QB-BiO optimizes qubit weights through qubit clustering, heuristic optimization, and position updates across a population of candidate solutions.The algorithm evaluates candidate fitness using prediction error and designates the best candidate as the quantum black hole.
  • Evaluation: QB-HNN provides distinct variants for single-resource and multiple-resource demand forecasting, evaluated across cluster, HPC, and web-application workload traces.The study compares the model with five state-of-the-art approaches using real cloud workloads.

A. QB-HNN-SAP: Single Attribute Prediction Model

QB-HNN-SAP predicts one cloud resource attribute by encoding normalized workload samples as qubits and processing them through Hadamard-based hidden and output layers. Its qubit-weighted propagation, superposition, nonlinear activation, and MSE-driven learning produce bounded predictions for a single resource.

  • Architecture: QB-HNN-SAP predicts a single resource attribute, such as CPU utilization, using input, hidden, and output qubit-neuron layers.The architecture includes one input layer, multiple hidden layers, and one output layer.
  • Input encoding: Normalized real-valued samples are encoded into a qubit input vector before training.The input samples are normalized to [0, 1].
  • Forward propagation: Qubit weights determine the strength of synaptic connections and the input vectors’ influence on neuron outputs during forward propagation.Weighted connections span input, hidden, and output qubit neurons, with bias qubit vectors included in the linear function.
  • Quantum activation: Each hidden and output neuron applies qubit summation, Hadamard-induced superposition, and activation to create nonlinear transformations.The sequence is described as three consecutive steps: summation, superposition, and activation.
  • Output and training: A sigmoid activation constrains predictions to [0, 1], while MSE serves as the QB-BiO fitness function for minimizing prediction error.The bounded output supports direct comparison with normalized workload traces during supervised training.

B. QB-HNN-MAP: Multi-Attribute Prediction Model

QB-HNN-MAP extends the architecture from single-attribute forecasting to simultaneous multi-attribute cloud-resource prediction. It uses qubit-neuron sets and shared weights to support joint prediction and classification for resource provisioning.

  • Multi-attribute architecture: QB-HNN-MAP predicts multiple resource attributes, such as CPU, memory, and bandwidth, simultaneously.The number of qubits in each neuron set equals the number of attributes being predicted.
  • Network structure: Input, hidden, and output layers contain sets of qubit neurons denoted Q∗I, Q∗H, and Q∗O, respectively.The model computes its network size from the connections among these qubit-neuron sets.
  • Nonlinear processing: QB-HNN-MAP uses the same nonlinear hidden- and output-layer transformation principles as the preceding architecture.The model applies the operations described in Eqs. (7)–(14).
  • Shared learning: QB-HNN-MAP reuses shared qubit neural weights across attributes to support joint prediction and classification.The stated application is efficient resource-provisioning decisions in multi-resource cloud environments.
  • Training and deployment: Both QB-HNN-SAP and QB-HNN-MAP are trained with QB-BiO, using offline prior workload data while prediction occurs concurrently in real time.QB-BiO searches qubit-network populations to minimize prediction error and select weights and biases.

III. QUBIT WEIGHTS LEARNING BY QB-BIO

QB-BiO trains QB-HNN models through population-based quantum blackhole optimization. It iteratively searches qubit-network candidates using clustering, heuristic optimization, and position updates to reduce prediction error.

  • Optimization objective: QB-BiO updates qubit synaptic weights and bias parameters toward solutions that minimize the EvalMSE fitness function.The method is inspired by classical Black Hole Optimization and treats the best candidate as a quantum black hole.
  • Population model: Each candidate solution is treated as a Qubit star, and the candidate with the best fitness is designated the Quantum Black-hole.The population searches multiple directions in the solution space.
  • Optimization stages: QB-BiO proceeds through three consecutive stages: Qubit cluster optimization, Heuristic optimization, and Position Update.The paper presents these stages as the sequential structure of the optimization process.

A. Qubit cluster optimization

Qubit cluster optimization initializes a population of qubit networks, groups them by qubit-weight amplitude similarity, and identifies the best candidate in each cluster. Subsequent heuristic crossover creates offspring to improve population diversity and fitness.

  • Qubit cluster optimization: QB-BiO generates a random population of qubit-star network vectors and organizes them into K clusters using K-Means.The initial population contains Z qubit stars, while clustering distinguishes networks by similarities in qubit-weight amplitudes.
  • Qubit representation: The clustering stage uses probability amplitudes α and β to represent the |0⟩ and |1⟩ states of each qubit.The qubit state is described within Hilbert vector space, with α and β as the corresponding amplitudes.
  • Cluster selection: Fitness is evaluated for cluster members, and the best solution in each cluster becomes that cluster’s blackhole, QCbest.Cluster assignments use similarity of qubit-weight amplitudes, and the best candidate is selected by the fitness function.
  • Heuristic optimization: Heuristic crossover combines two parent chromosomes to produce offspring closer to the parent with better fitness.A randomly generated crossover rate COi is used for each gene, and one offspring is produced from each cluster member.
  • Heuristic optimization: The resulting offspring are compared with parent candidates to enhance population diversity and introduce candidates with improved fitness values.This process supports broader search-space exploration through new qubit-network candidates.

C. Position Update

QB-BiO updates qubit-star positions through attraction toward cluster and global blackholes, event-horizon checks, and diversity-preserving replacement.

  • Position Update: Qubit stars are repositioned using attraction toward the cluster blackhole and heuristic global blackhole, with distances computed from their fitness values.The update uses attraction forces and random factors to control movement toward both blackhole solutions.
  • Position Update: The algorithm evaluates updated qubit stars with prediction-error fitness and relocates the cluster and global blackholes when better solutions are admissible.Prediction error is the fitness function, so updates seek lower prediction error.
  • Position Update: Event-horizon radii are determined from blackhole fitness relative to the fitness of the corresponding subpopulation.Separate radii are computed for cluster and global blackholes using their relative fitness values.
  • Position Update: A qubit star collapses when its fitness enters a cluster or global blackhole event horizon, and replacement candidates preserve population diversity.Collapsed solutions are prevented from returning and are replaced to retain a uniform number of solutions.
  • Position Update: QB-BiO iterates initialization, HQNN fitness evaluation, population updates, and event-horizon operations across optimization intervals.The reported complexity includes O(Z × QI^2 × M) for network training and fitness evaluation, with additional K- and t-dependent iterations.

D. Convergence and Stability Analysis of QB-BiO

The convergence analysis models QB-BiO as a stochastic search process under bounded-fitness and landscape assumptions, establishing convergence and stability properties.

  • Convergence and Stability Analysis of QB-BiO: Under a bounded continuous fitness function and diverse random initialization, QB-BiO is stated to converge with probability 1 to a global or near-global optimum.The theorem requires the initial qubit-star population to be diverse and randomly initialized.
  • Convergence and Stability Analysis of QB-BiO: The analysis assumes uniformly sampled crossover, non-zero attraction forces that gradually decrease, a finite-minima fitness landscape, and relative-fitness event-horizon updates.These assumptions support a transition from exploration toward exploitation and probabilistic replacement of weaker solutions.
  • Convergence and Stability Analysis of QB-BiO: Fitness variance is reported to decrease over time while population diversity is preserved through the event-horizon mechanism.Surviving solutions cluster around the best-fitness region as iterations increase.
  • Convergence and Stability Analysis of QB-BiO: Random sampling, position updates, and reinitialization make the QB-BiO process an ergodic, irreducible, and aperiodic Markov chain over the population space.The mechanism allows every search-space region to be visited with non-zero probability while maintaining diversity.
  • Convergence and Stability Analysis of QB-BiO: Greedy fitness-based selection ensures monotonic improvement or no degradation in the best global fitness, with global convergence under stated isolated-minima conditions.The global-optimum claim depends on the fitness landscape being unimodal or multimodal with isolated minima.

A. Experimental Set-up

The experiments use a two-CPU server with 40 cores, 128 GB RAM, Ubuntu 16.04 LTS, and Python 3.7 to evaluate the QB-HNN configuration.

  • Experimental Set-up: The simulation server uses two Intel Xeon Silver 4114 CPUs, a 40-core 2.20 GHz processor, 128 GB RAM, and 64-bit Ubuntu 16.04 LTS.The proposed model is implemented in Python 3.7.
  • Experimental Set-up: Table I specifies the QB-HNN neural-network architecture, training ratio, and quantum optimization settings.These parameters define the experimental configuration of the proposed model.

B. Datasets

The evaluation spans six datasets across cluster, web-server, and HPC workloads, using single- and multivariate prediction settings with varied prediction windows.

  • Datasets: Six benchmark datasets cover cluster workloads, web-server workloads, and high-performance-computing workloads.The categories support evaluation across heterogeneous cloud workload types.
  • Datasets: Google Cluster Data provides CPU and memory traces aggregated into 2 million job entries per resource channel, with 5-, 10-, 30-, and 60-minute windows.The traces record fine-grained usage every 5 minutes over 29 days, with analysis using the first 10 days.
  • Datasets: NASA-HTTP and Saskatchewan provide univariate web-traffic series, while AuverGrid and SHARCNet provide univariate HPC job-submission workloads.The web traces span 31 days and 7 months; the HPC traces span 365 and 11 days, respectively.
  • Results: The predicted values track actual workloads across categories, including sudden demand peaks and random falls.The comparison includes GCD-CPU, NASA web traces, and SHARCNet HPC Grid workloads.
  • Results: MSE and MAE are lower for 5-minute than 60-minute windows, while HPC workloads have the highest errors among the evaluated categories.The reported explanation is greater training and retraining data for shorter windows and fewer samples for HPC workloads.
  • Datasets: QB-HNN-SAP evaluates single-resource datasets, whereas QB-HNN-MAP evaluates synchronized CPU and memory attributes from Google Cluster workloads.The MAP setting uses the multivariate GC and GM workloads; the other datasets contain a single attribute.
  • Results: QB-HNN-MAP achieves prediction accuracy equivalent to QB-HNN-SAP with increased average training time and memory consumption.Simultaneous multiple-resource prediction uses almost two times the single-resource AMC, while time and memory decrease as the prediction interval increases.

D. Comparison

QB-HNN is compared with neural, evolutionary, recurrent, and quantum prediction approaches across heterogeneous dynamic cloud workloads. Across the reported MSE, RelMAE, and RMSE evaluations, QB-HNN achieves the strongest prediction performance.

  • Normalised MSE: QB-HNN reduces prediction error by 22.83%, 72.15%, 72.16%, 36.36%, and 75.12% versus EQNN, SaDE, BaDE, LSTM, and NN-BP, respectively.The comparison covers all three categories of dynamic cloud workloads using normalized MSE.
  • Relative MAE: QB-HNN records the lowest MAE, represented by RelMAE = 1, across all reported experiments.RelMAE normalizes each state-of-the-art method's MAE against QB-HNN and is independent of data scaling.
  • Relative MAE: The relative-MAE ranking places QB-HNN ahead of EQNN, LSTM, BaDE, SaDE, and NN-BP across the compared approaches.The passage reports the ordering as NN-BP < SaDE < BaDE > LSTM < EQNN < QB-HNN.
  • RMSE: QB-HNN achieves the lowest RMSE for every tested prediction window on GC traces, including RMSE = 2.42 at 30 minutes versus 11.6 for MCT-AQNN.For GM traces, QB-HNN reaches RMSE = 0.51 at 5 minutes and remains superior at longer horizons.

4) Absolute Error Frequency:

The evaluation examines absolute-error frequencies, optimization convergence, accuracy distributions, training time, parameter sensitivity, complexity, and deployment considerations. These results generally favor QB-HNN while identifying practical integration and classical-system overhead challenges.

  • Absolute Error Frequency: QB-HNN produces the lowest absolute prediction error for most cloud workloads compared with five existing approaches.Absolute errors are compared by frequency across three workload types and averaged over 30 runs.
  • Convergence Analysis of QB-HNN Optimization: QB-BiO converges before 20 epochs with the lowest EvalMSE, whereas SaDE and BaDE converge after more than 45 epochs with slightly higher prediction error.The comparison uses GCD-CPU and GCD-Mem cluster workloads.
  • Training Time: The QB-HNN training time is higher than NN-BP but lower than EQNN in the reported GC comparison.The text attributes EQNN's highest time to generating qubit-based network weights and describes training as periodic and concurrent-capable.
  • Sensitivity Analysis: K = 5 and Z = 25 achieves the lowest testing MSE of 0.00412 in the QB-BiO sensitivity analysis.The analysis varies population size and qubit cluster count to assess generalization and stability.
  • Computational Complexity: QB-HNN has computational complexity equivalent to SaDE and BaDE in the reported comparison.The complexity analysis defines input neurons, population size, epochs, training samples, memory cells, output units, and prediction intervals.
  • Adaptability, Scalability, and Deployment Feasibility: Real-world integration remains challenging because interoperability with cloud-management tools and classical-system overhead from qubit-based encodings are practical concerns.The stated boundary is that promising convergence and learning efficiency were demonstrated under simulated conditions.
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