This study explores the logical aspects of quantum computation through a detailed analysis of key performance parameters, including qubit number, gate depth, entanglement rate, and logical error rate. Using a dataset of 50 quantum circuit observations, we investigate the relationships between these important metrics that determine computational power and system stability. To model gate depth prediction and evaluate quantum system performance, the research uses two machine learning approaches - Gaussian process regression and gradient boosting regression. Statistical analysis reveals significant correlations between the parameters, in particular a strong negative correlation between qubit number and logical error rate (-0.65), and a moderate positive correlation between gate depth and logical error rate (0.62). Both regression models show excellent performance, with Gaussian process regression reaching R² = 0.9776 on the experimental data and gradient boosting regression reaching R² = 0.9436. The findings indicate that while increasing the number of qubits generally reduces logical errors, deep gate circuits introduce additional error sensitivity. The entanglement rates show minimal correlation with other parameters, indicating independent optimization potential. The research contributes to the understanding of quantum computational logic by providing quantitative insights into the parameter relationships essential for fault-tolerant quantum system design. These results have practical implications for quantum algorithm development, circuit optimization, and error correction strategies. The study demonstrates that machine learning approaches can effectively model quantum computational parameters, providing valuable tools to predict system performance and guide quantum hardware development. This work advances the theoretical foundation for scalable quantum computing by elucidating the logical relationships that govern quantum computational processes. Keywords: Quantum Computation, Fault Tolerance, Machine Learning, Quantum Error Correction, Gate Depth Optimization, Qubit Scaling.
This study explores the logical aspects of quantum computation through a detailed analysis of key performance parameters, including qubit number, gate depth, entanglement rate, and logical error rate. Using a dataset of 50 quantum circuit observations, we investigate the relationships between these important metrics that determine computational power and system stability. To model gate depth prediction and evaluate quantum system performance, the research uses two machine learning approaches - Gaussian process regression and gradient boosting regression. Statistical analysis reveals significant correlations between the parameters, in particular a strong negative correlation between qubit number and logical error rate (-0.65), and a moderate positive correlation between gate depth and logical error rate (0.62). Both regression models show excellent performance, with Gaussian process regression reaching R² = 0.9776 on the experimental data and gradient boosting regression reaching R² = 0.9436. The findings indicate that while increasing the number of qubits generally reduces logical errors, deep gate circuits introduce additional error sensitivity. The entanglement rates show minimal correlation with other parameters, indicating independent optimization potential. The research contributes to the understanding of quantum computational logic by providing quantitative insights into the parameter relationships essential for fault-tolerant quantum system design. These results have practical implications for quantum algorithm development, circuit optimization, and error correction strategies. The study demonstrates that machine learning approaches can effectively model quantum computational parameters, providing valuable tools to predict system performance and guide quantum hardware development. This work advances the theoretical foundation for scalable quantum computing by elucidating the logical relationships that govern quantum computational processes. Keywords: Quantum Computation, Fault Tolerance, Machine Learning, Quantum Error Correction, Gate Depth Optimization, Qubit Scaling.
This Study explores the logical aspects of quantum computation through a detailed analysis of key performance parameters, including qubit number, gate depth, entanglement rate, and logical error rate. Using a dataset of 50 quantum circuit observations, we investigate the relationships between these important metrics that determine computational power and system stability. To model gate depth prediction and evaluate quantum system performance, the research uses two machine learning approaches - Gaussian process regression and gradient boosting regression. Statistical analysis reveals significant correlations between the parameters, in particular a strong negative correlation between qubit number and logical error rate (-0.65), and a moderate positive correlation between gate depth and logical error rate (0.62). Both regression models show excellent performance, with Gaussian process regression reaching R² = 0.9776 on the experimental data and gradient boosting regression reaching R² = 0.9436. The findings indicate that while increasing the number of qubits generally reduces logical errors, deep gate circuits introduce additional error sensitivity. The entanglement rates show minimal correlation with other parameters, indicating independent optimization potential. The research contributes to the understanding of quantum computational logic by providing quantitative insights into the parameter relationships essential for faulttolerant quantum system design. These results have practical implications for quantum algorithm development, circuit optimization, and error correction strategies. The study demonstrates that machine learning approaches can effectively model quantum computational parameters, providing valuable tools to predict system performance and guide quantum hardware development. This work advances the theoretical foundation for scalable quantum computing by elucidating the logical relationships that govern quantum computational processes. Keywords: Quantum Computation, Fault Tolerance, Machine Learning, Quantum Error Correction, Gate Depth Optimization, Qubit Scaling.
This study investigates the application of machine learning techniques for predicting gate depth in quantum computational systems, focusing on the relationship between quantum circuit parameters and computational performance. Using a dataset of 50 observations encompassing qubit count, gate depth, entanglement rate, and logical error rate, we developed and compared Linear Regression (LR) and Random Forest Regression (RFR) models for gate depth prediction. The research addresses critical challenges in quantum fault tolerance and circuit optimization, which are essential for achieving scalable quantum computation. Our analysis revealed strong negative correlation (-0.65) between qubit count and logical error rate, while gate depth showed moderate positive correlation (0.62) with error rates. The Random Forest model demonstrated superior performance with R² values of 0.96068 on training data and 0.87262 on testing data, significantly outperforming Linear Regression (R²: 0.87552 training, 0.60257 testing). Error metrics further confirmed RFR's superiority, achieving RMSE of 2.33 (training) and 2.97 (testing) compared to LR's 4.15 and 5.25 respectively. The study highlights the importance of quantum error correction mechanisms and the inherent trade-offs between circuit complexity and computational reliability. Both models showed expected performance degradation from training to testing, with RFR maintaining better generalization capabilities. These findings contribute to the development of typed models for quantum mechanics in computational applications, offering insights into quantum circuit optimization and fault-tolerant design. The research demonstrates that ensemble methods like Random Forest provide more robust predictions for quantum system parameters, supporting the advancement of practical quantum computing implementations and algorithm development. KeyWords: Quantum Computation, Gate Depth Prediction, Random Forest Regression, Quantum Error Correction, Machine Learning, Fault Tolerance.
Quantum computing holds the potential to address problems that are currently considered intractable for classical processors by leveraging quantum mechanical effects for simulation, optimization, and chemistry. Despite recent technological progress, quantum hardware remains in the noisy intermediate-scale regime, where coherence limits, gate imperfections, and readout errors restrict circuit depth and algorithmic reliability. Although first demonstrations of small-scale Quantum Error Correction exist, logical processors with low logical error rates are still distant. In the near term, even error-corrected qubits are expected to operate with residual error, which means that improving calibration and mitigating errors at the physical and circuit level will remain essential for obtaining meaningful results. Established calibration routines and mitigation methods such as Zero-Noise-Extrapolation (ZNE) are valuable, but need to be further improved and more rigorously validated with respect to their underlying assumptions, stability and quantitative benefits. This thesis addresses error reduction techniques on transmon qubits through calibration, gate analysis, and circuit-level mitigation. First, a systematic comparison of two single-qubit amplitude calibration techniques is carried out (cross-point and ping-pong calibration), followed by an analysis of two implementations of a two-qubit gate, based on the cross-resonance interaction. The results show that cross-point calibration offers faster convergence, higher precision and a more favorable signal to noise ratio than ping-pong calibration. Hamiltonian tomography confirms the validity of a reduced model for the cross-resonance interaction, and algorithmic tests reveal that direct and echoed CNOT gates offer complementary advantages depending on the application. Second, the thesis develops and evaluates the method of Inverted-Circuit Zero-Noise-Extrapolation (IC-ZNE). Its main idea consists of measuring the effective error strength of a circuit through inverted circuits. This quantity is then used for extrapolation towards zero noise rather than relying on simple, approximate noise scaling assumptions as in standard ZNE. This approach constitutes a novel and original method. IC-ZNE consistently produces results closer to ideal reference values than standard ZNE. The method achieves up to 77% error reduction in observable error on the tested circuits compared to standard ZNE and simple post processing filters can yield up to 39% reduction in selected cases compared to standard ZNE. Further refinements introduce noise-adaptive circuit scaling strategies that enhance mitigation outcomes without significant additional cost. The performance of these techniques is examined across several circuits and in the context of variational quantum algorithms. Applications to the Quantum Approximate Optimization Algorithm and the Variational Quantum Eigensolver demonstrate that these techniques extend the useful operating regime of current devices, although their effectiveness decreases for very deep circuits or unfavorable variational ansätze. Taken together, the calibration and mitigation techniques investigated and developed in this thesis demonstrate practical routes toward enhancing the reliability of near-term quantum processors. While they cannot replace full fault-tolerant quantum computation, they offer useful and complementary capabilities that support progress toward scalable quantum technologies.
Quantum error correction (QEC) represents the cornerstone technology for realizing fault-tolerant quantum computing, addressing the fundamental challenge of quantum state decoherence in noisy intermediate-scale quantum (NISQ) devices. This comprehensive review examines recent advances in QEC implementations from 2020-2024, spanning theoretical foundations to practical hardware demonstrations. We analyze the evolution from pioneering stabilizer codes to modern topological approaches, with particular emphasis on surface codes and low-density parity-check (LDPC) codes that have demonstrated below-threshold error correction in superconducting and trapped-ion systems. The paper provides a comparative analysis of classical and machine learning-based decoder algorithms, evaluating their performance through complexity analysis and threshold comparisons in real-time error correction scenarios. Through examination of breakthrough experiments by Google, IBM, Quantinuum, and emerging platforms, we assess the current state of fault-tolerant quantum computing and identify critical engineering challenges including correlated noise models, cryogenic control systems, and scalable logical gate implementations. Our quantitative analysis reveals that while significant progress has been made toward practical fault-tolerance thresholds, achieving the resource efficiency and reliability required for large-scale quantum computation remains challenging. We provide detailed resource estimates for key applications including Shor's algorithm and optimization problems, along with analysis of industry roadmaps toward thousand-logical-qubit systems. This review serves as a comprehensive guide for researchers and engineers working toward the next generation of fault-tolerant quantum computers, with particular focus on information-theoretic perspectives relevant to quantum information entropy and syndrome processing.
Quantum error correction (QEC) represents the cornerstone technology for realizing fault-tolerant quantum computing, addressing the fundamental challenge of quantum state decoherence in noisy intermediate-scale quantum (NISQ) devices. This comprehensive review examines recent advances in QEC implementations from 2020-2024, spanning theoretical foundations to practical hardware demonstrations. We analyze the evolution from pioneering stabilizer codes to modern topological approaches, with particular emphasis on surface codes and low-density parity-check (LDPC) codes that have demonstrated below-threshold error correction in superconducting and trapped-ion systems. The paper provides a comparative analysis of classical and machine learning-based decoder algorithms, evaluating their performance through complexity analysis and threshold comparisons in real-time error correction scenarios. Through examination of breakthrough experiments by Google, IBM, Quantinuum, and emerging platforms, we assess the current state of fault-tolerant quantum computing and identify critical engineering challenges including correlated noise models, cryogenic control systems, and scalable logical gate implementations. Our quantitative analysis reveals that while significant progress has been made toward practical fault-tolerance thresholds, achieving the resource efficiency and reliability required for large-scale quantum computation remains challenging. We provide detailed resource estimates for key applications including Shor's algorithm and optimization problems, along with analysis of industry roadmaps toward thousand-logical-qubit systems. This review serves as a comprehensive guide for researchers and engineers working toward the next generation of fault-tolerant quantum computers, with particular focus on information-theoretic perspectives relevant to quantum information entropy and syndrome processing.
The performance of quantum neural network models depends strongly on architectural decisions, including circuit depth, placement of parametrized operations, and data-encoding strategies. Selecting an effective architecture is challenging and closely related to the classical difficulty of choosing suitable neural-network topologies, which is computationally hard. This work investigates automated quantum-circuit construction for regression tasks and introduces a genetic-algorithm framework that discovers Reduced Regressor QNN architectures. The approach explores depth, parametrized gate configurations, and flexible data re-uploading patterns, formulating the construction of quantum regressors as an optimization process. The discovered circuits are evaluated against seventeen classical regression models on twenty-two nonlinear benchmark functions and four analytical functions. Although classical methods often achieve comparable results, they typically require far more parameters, whereas the evolved quantum models remain compact while providing competitive performance. We further analyze dataset complexity using twelve structural descriptors and show, across five increasingly challenging meta-learning scenarios, that these measures can reliably predict which quantum architecture will perform best. The results demonstrate perfect or near-perfect predictive accuracy in several scenarios, indicating that complexity metrics offer powerful and compact representations of dataset structure and can effectively guide automated model selection. Overall, this study provides a principled basis for meta-learning-driven quantum architecture design and advances the understanding of how quantum models behave in regression settings--a topic that has received limited exploration in prior work. These findings pave the way for more systematic and theoretically grounded approaches to quantum regression.