Technical Annex Scalable Industrial Early-Warning System Architecture and Sample-Based Krylov Quantum Diagonalization (SKQD) Integration. and Technical Documentation: Apparent Faster-than-Light (FTL) Signal Transmission Emulator. Purpose and status. This annex consolidates two research-oriented technical notes. Part I proposes a technically realistic, safety-aware architecture for integrating sample-based Krylov quantum diagonalization (SKQD) into an industrial early-warning platform. Part II documents an educational electronics demonstrator that produces an apparent early-arrival timing effect through local prediction and engineered delay, without transmitting information faster than light.
Technical Annex Scalable Industrial Early-Warning System Architecture and Sample-Based Krylov Quantum Diagonalization (SKQD) Integration. and Technical Documentation: Apparent Faster-than-Light (FTL) Signal Transmission Emulator. Purpose and status. This annex consolidates two research-oriented technical notes. Part I proposes a technically realistic, safety-aware architecture for integrating sample-based Krylov quantum diagonalization (SKQD) into an industrial early-warning platform. Part II documents an educational electronics demonstrator that produces an apparent early-arrival timing effect through local prediction and engineered delay, without transmitting information faster than light.
Quantum algorithms based on classical processing of individual samples have recently emerged as a promising route to perform large-scale quantum-chemical calculations on pre-fault-tolerant and early-fault-tolerant quantum devices. In these algorithms, the quantum computer acts as a sampling engine that generates the subspace in which the Hamiltonian is classically diagonalized. The recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) uses quantum Krylov states as circuits from which samples are collected. Convergence guarantees can be derived for SKQD under assumptions similar to those of quantum phase estimation -- namely, a sufficiently large overlap between the reference and the target ground state -- with the additional requirement that the ground-state wave function be well approximated by a polynomial subset of the full Hilbert space. However, implementations of SKQD for complex many-body Hamiltonians, such as quantum chemistry ones, are limited by the depths of time-evolution circuits needed to generate Krylov vectors. In this work, we introduce a method that combines SKQD with a qDRIFT randomized compilation of the Hamiltonian propagator. The resulting algorithm, termed SqDRIFT, enables executing quantum chemistry experiments on present-day quantum processors while retaining provable convergence guarantees, which we extend to account for the error of the randomized compilation and of finite sampling. We demonstrate its viability by applying SqDRIFT to calculate the electronic ground-state energy of several polycyclic aromatic hydrocarbons, up to system sizes beyond the reach of exact diagonalization.
Quantum computing has progressed from early demonstrations across superconducting, trapped ion, photonic, and spin-based platforms to increasingly integrated systems. However, transitioning from the noisy intermediate-scale quantum (NISQ) era to robust, fault tolerant implementations remain a central challenge. This paper presents a systematic review and synthesis of practical quantum computing, encompassing experimental advances, integrated photonics, error correction breakthroughs, software stack evolution, benchmarking practices, algorithmic readiness, and socio-technical dimensions. We critically assess current limitations and highlight emerging directions, including integrated photonic modules with high fidelity interconnects, real time decoders for surface code logical qubits, and hardware aware compiler strategies. Our analysis is grounded in peer-reviewed experimental data and model-based evaluations. Key findings include demonstrated logical error suppression via increased code distance, scalable photonic module prototypes, and refined resource estimates for cryptanalytic and simulation tasks. This paper concludes with a structured research agenda for 2025–2030, proposing four priority thrusts such as hardware QEC co design, reproducible cross platform benchmarking, modular/distributed architectures, and quantum networking with governance frameworks. This evidence based roadmap aims to align researchers and practitioners toward actionable milestones on the path to practical quantum computing.
Quantum Krylov subspace diagonalization (QKSD) is an emerging method used in place of quantum phase estimation in the early fault-tolerant era, where limited quantum circuit depth is available. In contrast to the classical Krylov subspace diagonalization (KSD) or the Lanczos method, QKSD exploits the quantum computer to efficiently estimate the eigenvalues of large-size Hamiltonians through a faster Krylov projection. However, unlike classical KSD, which is solely concerned with machine precision, QKSD is inherently accompanied by errors originating from a finite number of samples. Moreover, due to difficulty establishing an artificial orthogonal basis, ill-conditioning problems are often encountered, rendering the solution vulnerable to noise. In this work, we present a nonasymptotic theoretical framework to assess the relationship between sampling noise and its effects on eigenvalues. We also propose an optimal solution to cope with large condition numbers by eliminating the ill-conditioned bases. Numerical simulations of the one-dimensional Hubbard model demonstrate that the error bound of finite samplings accurately predicts the experimental errors in well-conditioned regions.
Approximating the ground state of many-body systems is a key computational bottleneck underlying important applications in physics and chemistry. The most widely known quantum algorithm for ground state approximation, quantum phase estimation, is out of reach of current quantum processors due to its high circuit-depths. Subspace-based quantum diagonalization methods offer a viable alternative for pre- and early-fault-tolerant quantum computers. Here, we introduce a quantum diagonalization algorithm which combines two key ideas on quantum subspaces: a classical diagonalization based on quantum samples, and subspaces constructed with quantum Krylov states. We prove that our algorithm converges in polynomial time under the working assumptions of Krylov quantum diagonalization and sparseness of the ground state. We then demonstrate the scalability of our approach by performing the largest ground-state quantum simulation of impurity models using a Heron quantum processors and the Frontier supercomputer. We consider both the single-impurity Anderson model with 41 bath sites, and a system with 4 impurities and 7 bath sites per impurity. Our results are in excellent agreement with Density Matrix Renormalization Group calculations.
System-level specification, a runtime assurance and monitoring framework for hybrid quantum–classical computing workloads. The document defines an operational architecture and enforcement logic for maintaining safety under measurement latency, stochastic noise, and partial observability, with emphasis on auditable, deterministic control points rather than post hoc interpretation. Contents include: A layered runtime model (instrumentation, observation/estimation, enforcement, recovery/orchestration) for hybrid quantum–classical pipelines. Decision outputs and enforcement semantics (safety violations vs. acceptable operation) and integration into a verification–safety–recovery loop. Latency management patterns, including asynchronous monitoring and retroactive veto/rollback, and conditions for maintaining safe rollback windows. Monitoring signals and estimation approaches suitable for quantum workloads (e.g., shadow-tomography-style observables) described at specification level. Implementation-specific parameters, operational thresholds, deployment artefacts, source code, environment configurations, and empirical tuning details are intentionally omitted to protect ongoing commercialisation and patent considerations. The manuscript is intended for technical review, research collaboration, and prior-art disclosure without revealing proprietary operational settings.