Quantum Hidden Variable Extraction (Q-HVE): A Quadratic-Speedup Quantum Algorithm for Epistemic Noise Subtraction, with Direct Solutions to the XPRIZE Quantum Applications Problem Domains in Health, Climate, Energy, and Materials Science
This preprint introduces Quantum Hidden Variable Extraction (Q-HVE), a quantum algorithm that applies Grover-style amplitude amplification to identify which hidden-variable model best explains residual signal in a dataset after classical baselines have been subtracted. The algorithm achieves an unconditional O(√m) quadratic speedup over classical sequential model evaluation for libraries of m candidate models. The work argues that the four XPRIZE Quantum Applications problem domains — human health, climate science, energy systems, and materials engineering — share a common epistemic defect: their classical baseline models systematically exclude documented hidden variables. The Presignal Research Initiative has identified those variables across its published portfolio. Q-HVE provides the quantum acceleration layer that makes rapid model selection over those libraries computationally feasible. The four instantiations are: (1) Immunological Tinnitus Subtype (ITS), supported by peer-reviewed meta-analysis and active clinical trials; (2) heliospheric-ISM climate forcing, supported by published astrophysical modeling and isotopic evidence; (3) Vertical Arcology Hydraulic Spine (VAHS), a conceptual high-head pumped storage architecture; and (4) transport-regime-optimal battery electrode porosity derived from generalized Murray's Law. Epistemic status is explicitly graded for each domain. Resource estimates indicate Q-HVE is practical on a fault-tolerant quantum computer with approximately 85 logical qubits. No new experimental data are presented. This is a theoretical proposal posted for public scientific scrutiny under CC BY 4.0.
This preprint introduces Quantum Hidden Variable Extraction (Q-HVE), a quantum algorithm that applies Grover-style amplitude amplification to identify which hidden-variable model best explains residual signal in a dataset after classical baselines have been subtracted. The algorithm achieves an unconditional O(√m) quadratic speedup over classical sequential model evaluation for libraries of m candidate models. The work argues that the four XPRIZE Quantum Applications problem domains — human health, climate science, energy systems, and materials engineering — share a common epistemic defect: their classical baseline models systematically exclude documented hidden variables. The Presignal Research Initiative has identified those variables across its published portfolio. Q-HVE provides the quantum acceleration layer that makes rapid model selection over those libraries computationally feasible. The four instantiations are: (1) Immunological Tinnitus Subtype (ITS), supported by peer-reviewed meta-analysis and active clinical trials; (2) heliospheric-ISM climate forcing, supported by published astrophysical modeling and isotopic evidence; (3) Vertical Arcology Hydraulic Spine (VAHS), a conceptual high-head pumped storage architecture; and (4) transport-regime-optimal battery electrode porosity derived from generalized Murray's Law. Epistemic status is explicitly graded for each domain. Resource estimates indicate Q-HVE is practical on a fault-tolerant quantum computer with approximately 85 logical qubits. No new experimental data are presented. This is a theoretical proposal posted for public scientific scrutiny under CC BY 4.0.
Abstract This guide is based on the IBM Quantum course Phase Estimation and Factoring and focuses on Grover’s algorithm, a quantum algorithm for unstructured search problems that provides a quadratic speedup over classical approaches. In an unstructured search problem, we are given a function (often represented as an oracle) that marks one or more “correct” solutions among NNN possible candidates. A classical algorithm requires on the order of O(N)O(N)O(N) evaluations in the worst case. In contrast, Grover’s algorithm finds a solution using only O(N)O(\sqrt{N})O(N) oracle queries. This quadratic improvement implies: The quantum algorithm requires roughly the square root of the number of operations needed classically. Any classical algorithm for unstructured search must have cost at least quadratic relative to Grover’s quantum procedure. Core Idea of the Algorithm Grover’s algorithm relies on: Preparation of a uniform superposition (typically using Hadamard gates). An oracle that marks valid solutions via phase inversion. The Grover diffusion operator, which amplifies the probability amplitude of the marked states through interference. By repeatedly applying the Grover operator, the amplitude of the desired solution grows while others diminish, allowing measurement to reveal the correct answer with high probability. Practical Considerations Despite its theoretical elegance and wide applicability, the quadratic speedup of Grover’s algorithm is unlikely to yield near-term practical advantage. Modern classical hardware operates at extremely high clock rates and is vastly more mature than current quantum devices. For problem sizes accessible to today’s quantum computers, classical systems remain dominant. However, history shows that even sub-quadratic classical improvements — such as: Fast Fourier Transform (FFT) Efficient sorting algorithms like quicksort and mergesort have had transformative practical impact. The crucial distinction is that Grover’s algorithm depends on fundamentally different hardware — quantum processors — which are still in early development. Long-Term Perspective As quantum hardware advances in qubit count, coherence time, and error correction, Grover’s quadratic advantage may become practically significant for: Cryptographic key search Optimization heuristics Combinatorial search problems Amplitude amplification subroutines in broader quantum algorithms Through hands-on experimentation on IBM Q, this lesson demonstrates how theoretical amplitude amplification translates into executable quantum circuits, reinforcing the relationship between interference, probability amplitudes, and computational complexity.
Accurate prediction of lithium-ion battery capacity fade across temperature extremes is critical for energy storage reliability, yet classical machine learning methods face challenges with the small, nonlinear datasets typical of accelerated aging studies. Quantum machine learning offers a potential solution through enhanced feature representation, but demonstrations on real quantum hardware remain limited. Here we benchmark quantum kernel ridge regression (Q-KRR) against classical baselines for battery capacity-fade prediction—a representative small-data problem with nonlinear, physics-driven features. Using six physics-informed descriptors, Q-KRR on a noiseless simulator achieved R 2 = 0.739, an 8.7% relative improvement over classical kernel ridge regression (R 2 = 0.680). On IBM's 127-qubit superconducting processor, systematic circuit optimization and targeted readout mitigation yielded R 2 = 0.770, exceeding both the classical baseline (13% relative gain) and the ideal simulator performance (4% absolute gain). This hardware advantage resulted from reducing circuit depth and qubit count while applying selective error mitigation matched to the dominant noise sources. The results demonstrate that quantum kernels can outperform classical methods on current noisy hardware when algorithms are co-designed with device constraints, offering a practical pathway for quantum-enhanced prediction in materials science and engineering domains characterized by limited training data and structured feature spaces.
This note separates two things often labelled “quantum finance”: the quantum formalism, which applies quantum-mechanical mathematics on classical computers and is judged by empirical fit, and quantum computers, which are judged by whether they complete tasks classical machines cannot. Classifying the evidence into four types (unconditional; beyond-classical under complexity assumptions; empirical claims on specific problems; asymptotic speedups requiring fault tolerance), it finds that, among the public evidence identified and verified here (cut-off 17 October 2026), no economic or financial task has demonstrated broadly accepted practical quantum advantage against strong classical baselines and end-to-end costs. The strongest unconditional results concern information resources rather than computational speed; the formalism has already produced methods usable on classical hardware and testable empirical results; the most mature provable speedup directly relevant to finance is the quadratic speedup of amplitude estimation, which requires fault-tolerant hardware; and because published estimates place the logical-qubit threshold for elliptic-curve discrete logarithms below that for derivative-pricing advantage, cryptographic infrastructure is a channel through which material impact may arrive earlier — a scenario, not a timing prediction, since the two workloads differ in gate counts, runtimes and fault-tolerance assumptions. The note is a structured synthesis of published evidence and reports no new experiments or measurements.
We introduce a variant of Quantum Amplitude Estimation (QAE), called Iterative QAE (IQAE), which does not rely on Quantum Phase Estimation (QPE) but is only based on Grover’s Algorithm, which reduces the required number of qubits and gates. We provide a rigorous analysis of IQAE and prove that it achieves a quadratic speedup up to a double-logarithmic factor compared to classical Monte Carlo simulation with provably small constant overhead. Furthermore, we show with an empirical study that our algorithm outperforms other known QAE variants without QPE, some even by orders of magnitude, i.e., our algorithm requires significantly fewer samples to achieve the same estimation accuracy and confidence level.
Variational Quantum-Classical Algorithm (VQCA) is a potential tool for machine learning (ML) prediction tasks, but its efficacy, adaptability to big datasets, and optimization for noise reduction on quantum hardware are not clear. We aim to accomplish three study goals in this literature review. We begin by reviewing the justifications for ML practitioners' use of VQCA. Second, we compare the accuracy and effectiveness of VQCA in diverse domains to see whether it has a performance advantage over other ML methods. Finally, we evaluate VQCA's immediate and long-term effects on quantum ML and how well it performs compared to ML techniques for prediction tasks across various applications or domains. Our findings show that VQCA can be significantly more accurate and efficient than conventional algorithms. We also compare traditional ML algorithms with VQCA on various datasets and examine their theoretical guarantees. We equally look into how VQCA might be used practically to address problems in a variety of industries, including banking, healthcare, and energy. In various datasets, we assess the performance and efficacy of VQCA for unsupervised learning tasks. Finally, we go through ways to improve VQCA, particularly for big and complicated problems, to lessen the effect of noise and other sources of error in quantum hardware. Overall, we looked at VQCA’s advantages and disadvantages for ML prediction tasks, including possible directions for future study. Our findings show that VQCA has the potential to completely transform the ML industry, particularly in this emerging era of quantum computing.
The choreography of quantum mechanical phenomena has catalysed accelerated advances in the emergence of a quantum computational substrate paradigm that yields the potential to solve some of humanities most complex problems through quantum computing speedup requires exponential computational power that exceeds that of today’s most powerful super computers, to confront the world’s most intractable computational challenges in environment, agriculture, health, energy, climate, materials science, precision medicine, autonomous vehicles in smart cities, renewable energy and problems humanity has not yet even imagined. Current quantum computational substrates are limited by circuit depth, noise processes, qubit count, and fault tolerant quantum computational substrates unlikely to be available in the near term. Hybrid quantum algorithms/Variational Quantum Algorithms (VQAs), operate by using a classical optimizer to orchestrate the parameters of a quantum circuit, have become a prominent approach to address these limitations. However, several challenges manifest that include the training, speedup. accuracy, and impactful practical application of VQAs. This paper reviews novel new frontiers in current VQAs, provides an analysis of VQAs, their strengths and limitations, and outlines potential applications in the quest towards yielding practical quantum advantage. Secondly, this paper also reviews and provides an assessment of quantum software development frameworks.