This document introduces a bi-directional, hybrid algorithmic paradigm that integrates Quantum-Selected Configuration Interaction (QSCI) with Early Fault-Tolerant (EFTQC) and fully Fault-Tolerant Quantum Computing (FTQC) regimes. It addresses the limitations of current NISQ-era algorithms by demonstrating how EFTQC hardware can generate highly correlated input states (e.g., via Adiabatic State Preparation and QPE-CASCI) to improve QSCI subspace quality. Conversely, it establishes QSCI as a deterministic classical pre-processor for FTQC, providing sparse, multi-determinant wavefunctions that solve the orthogonality catastrophe and precondition Hamiltonian simulations, thereby ensuring high-fidelity results for advanced algorithms like Quantum Phase Estimation and HHL. KSCCN Mamun, SM (2026)......................................1 The Convergence of Quantum-Selected Configuration Interaction and Fault-Tolerant Quantum Computing: A Bi-Directional Algorithmic Paradigm Also available on Academia.edu: https://www.academia.edu/attachments/133495435/download_file?s=portfolio
This document introduces a bi-directional, hybrid algorithmic paradigm that integrates Quantum-Selected Configuration Interaction (QSCI) with Early Fault-Tolerant (EFTQC) and fully Fault-Tolerant Quantum Computing (FTQC) regimes. It addresses the limitations of current NISQ-era algorithms by demonstrating how EFTQC hardware can generate highly correlated input states (e.g., via Adiabatic State Preparation and QPE-CASCI) to improve QSCI subspace quality. Conversely, it establishes QSCI as a deterministic classical pre-processor for FTQC, providing sparse, multi-determinant wavefunctions that solve the orthogonality catastrophe and precondition Hamiltonian simulations, thereby ensuring high-fidelity results for advanced algorithms like Quantum Phase Estimation and HHL. KSCCN Mamun, SM (2026)......................................1 The Convergence of Quantum-Selected Configuration Interaction and Fault-Tolerant Quantum Computing: A Bi-Directional Algorithmic Paradigm Also available on Academia.edu: https://www.academia.edu/attachments/133495435/download_file?s=portfolio
This document explores the role of Quantum-Selected Configuration Interaction (QSCI) as an automated paradigm for scalable electronic structure theory. It addresses the computational bottleneck of active-space selection, which remains a primary barrier to high-throughput multireference chemistry. By delegating configurational sampling to quantum hardware and retaining energy evaluation for classical supercomputing, QSCI mitigates NISQ-era challenges such as statistical shot noise, barren plateaus, and physical decoherence. The review analyzes evolutionary variants including Time-Evolved (TE-QSCI), Hamiltonian Simulation-Based (HSB-QSCI), and Doubly Occupied (DOCI-QSCI) methods, and examines their integration with embedding frameworks like DMET-SQD and WF-in-DFT. Ultimately, the report positions QSCI as an architectural bridge between near-term heuristic algorithms and the rigorous precision required for fault-tolerant quantum computing (FTQC). KSCCN Mamun, SM (2026)..................................1 Quantum-Informed Active-Space and Embedding Discovery: QSCI Sampling as an Automated Paradigm for Scalable Electronic Structure Theory Also available on Academia.edu: https://www.academia.edu/attachments/133495143/download_file?s=portfolio
The pursuit of exact solutions to the many-body electronic Schrödinger equation is constrained by the exponential scaling of the Hilbert space. While Quantum-Selected Configuration Interaction (QSCI) provides a robust, hybrid quantum-classical alternative to standard Variational Quantum Eigensolvers, it is hampered by significant sampling inefficiencies and finite-shot bottlenecks in strongly correlated regimes. This report analyzes the integration of generative machine-learning models—including autoregressive transformers, Neural-Network Quantum States (NQS), and discrete diffusion models—as a transformative approach to the QSCI paradigm. By treating classical diagonalization outputs as high-quality training data, these generative architectures internalize complex electron correlation patterns, enabling active configuration discovery, dramatic wavefunction compression, and optimized quantum circuit design. This synthesis provides a scalable blueprint for achieving chemical accuracy in KSCCN Mamun, SM (2026) ………………………………..1 Integration of Generative Machine-Learning Models with Quantum-Selected Configuration Interaction: An Academic Extension K S C electronic structure simulations while maintaining the strict variational upper-bound guarantee of classical diagonalization. KSCCN Mamun, SM (2026) ………………………………..2 Integration of Generative Machine-Learning Models with Quantum-Selected Configuration Interaction: An Academic Extension Also available on Academia.edu: https://www.academia.edu/attachments/133495242/download_file?s=portfolio
The fundamental challenge in electronic structure theory is the factorial scaling of the Full Configuration Interaction (FCI) method. While Quantum-Selected Configuration Interaction (QSCI) has emerged as a promising alternative that utilizes quantum hardware to navigate this Hilbert space, benchmarking studies have identified significant scaling bottlenecks, specifically multinomial sampling inefficiencies and poor wavefunction compactness. This work presents the "hybrid adaptive pipeline" framework, which reconfigures the division of labor between quantum and classical systems. By utilizing quantum processors exclusively as initialization oracles to establish a topological seed of static correlation, and delegating the intensive recovery of dynamic correlation to classical iterative refinement algorithms (such as CIPSI or MCCI), this approach overcomes the limitations of pure sampling-based methods. The hybrid pipeline preserves the essential variational upper-bound guarantee while enabling the efficient, noise-resilient simulation of complex molecular systems on contemporary quantum-centric supercomputing architectures. KSCCN Mamun, SM (2026) …………………………….1 Hybrid Adaptive Pipelines in Quantum Chemistry: Synthesizing Quantum-Selected Configuration Interaction with Classical Iterative Refinement Also available on Academia.edu: https://www.academia.edu/attachments/133434503/download_file?s=portfolio
This document explores the Quantum-Selected Configuration Interaction (QSCI) paradigm, a hybrid architecture designed to overcome the limitations of variational quantum algorithms in electronic structure theory. By delegating configurational basis discovery to quantum processors and reserving energy evaluation for classical hardware, QSCI ensures a strict variational guarantee and resilience to physical noise. The report details "subspace recycling" as a critical methodological extension that enables ab initio molecular dynamics (AIMD) and geometry optimization by reusing compact configurational subspaces across nuclear displacements, thereby bypassing the prohibitive quantum measurement bottleneck. Furthermore, it discusses the implementation of exact analytical nuclear gradients via the Z-vector method and the application of Eigenvector Continuation (EC) to interpolate wavefunctions across chemical parameter spaces, facilitating scalable and efficient simulations in the quantum-centric era. KSCCN Mamun, SM (2026) ………………………………….1 Quantum Subspace Recycling for Ab Initio Molecular Dynamics and Geometry Optimisation: Methodological Advances and Theoretical Frameworks Also available on Academia.edu: https://www.academia.edu/attachments/133434310/download_file?s=portfolio
This document provides a comprehensive analysis of the evolution of Variational Quantum Algorithms (VQAs) from the NISQ era toward Early Fault-Tolerant (EFT) computing. It examines the fundamental trainability crisis through the lens of Dynamical Lie Algebras (DLAs) and the Fubini-Study metric, quantifying the boundary of efficiency collapse. Advanced ansatz engineering, including the State-Efficient Ansatz (SEA) and horizontal quantum gates, is detailed alongside strategies to overcome the "measurement wall" via Overlapped Grouping Measurements (OGM). Finally, the report introduces Partial Quantum Error Correction (pQEC) and magic state injection on rotated surface codes as the pragmatic bridge to high-fidelity variational utility. Mamun, SM (2026) …………………………………….1 Advanced Quantum Aspects of Variational Algorithms A Second Volume on the Evolution Toward Early Fault Tolerance Also available on Academia.edu: https://www.academia.edu/attachments/132458973/download_file?s=portfolio
This review provides a detailed anatomical dissection of Quantum-Selected Configuration Interaction (QSCI), a hybrid quantum-classical algorithm introduced by Kanno et al. (2026) that leverages noisy quantum devices solely for sampling important electron configurations from an input state, followed by exact classical diagonalization of the Hamiltonian in the resulting reduced subspace. We systematically evaluate its methodological innovations, noise resilience, and strict adherence to the variational principle. A comprehensive comparison is drawn with at least twelve competing or complementary paradigms in NISQ-era quantum chemistry and classical selected configuration interaction (SCI), including VQE and its adaptive/excited-state variants, Quantum Subspace Expansion (QSE), ASCI, CIPSI, MCCI, FCIQMC, DMRG, Classically-Boosted VQE, and time-evolved input extensions (TE-QSCI). Pros and cons are articulated with reference to recent critical analyses highlighting sampling inefficiencies and subspace compactness. The review further explores the ontological status of configuration selection via quantum measurement and the epistemological guarantees afforded by classical post-processing. Possible extensions—hybrid adaptive pipelines, subspace recycling for molecular dynamics, and integration with machine-learned wavefunctions—are proposed. Also available on Academia.edu: https://www.academia.edu/attachments/133411942/download_file?s=portfolio