arXiv subjects

Hossein Akhoundi

Publications and source records attributed to Hossein Akhoundi.

5 recordsLinked to original sources

arXiv2026

Gram-Certified Resource Continuation for Structured Quantum Representation Audits

Dense representation of an $n$-qubit pure state requires $2^n$ complex amplitudes, precluding dense classical materialization at large $n$. We develop Gram-certified resource continuation for structured quantum-representation workloads and ask when a solution obtained under a lower-cost resource model remains a justified initialization for a richer one. For coarse and fine state ensembles connected by a declared isometry, fine, coarse, and cross complex amplitude overlaps form a positive-semidefinite block Gram matrix. A signed operator of dimension at most twice the sample count has the nonzero signed spectrum of the fine density minus the lifted coarse density, yielding trace- and operator-norm diagnostics without constructing either density operator. We prove that a coarse weighted spectral flag with objective suboptimality $\delta_c$ has fine-level suboptimality at most $\delta_c+2\varepsilon$, where $\varepsilon$ is the empirical trace distance; the factor two is attainable. We distinguish encoder change from exact feasible-family prolongation, give a gap-dependent subspace-stability test, and show that continuation cannot overcome a final Schmidt-rank ceiling. In deterministic synthetic controls over an 8-to-40-qubit ladder, exact ancilla lifts agree to numerical precision. Transferred initialization reduces final-rung block updates from 30 to 20, but the complete cascade costs $4.80$--$5.43$ times a direct final-rung solve, without material objective improvement. Reordering eight Bell pairs reduces the maximum matrix-product-state bond from 256 to 2. Thus continuation is justified only when cross-rung mismatch, feasible-family inclusion, topology, and total work jointly satisfy prespecified audits. These noise-free classical results neither establish generic 40-qubit simulability nor claim hardware performance or quantum advantage.

quant-ph↗

arXiv2026

Invariance Audits for Quantum Kernels and Variational Rewinding: A Real-to-Hermitian Taxonomy of Projector, Flag, Anchor, and Density Geometry

Machine-learning models often replace vectors by normalized directions, projectors, covariances, subspaces, ordered flags, quantum states, or density operators before any classifier is fitted. This replacement is an invariance decision: it determines which distinctions are kept and which are quotiented out. We develop a self-contained real-to-Hermitian taxonomy for auditing such representations in quantum machine learning. On the real side, we formalize Grassmann and flag projector kernels, prove positive semidefiniteness and block-gauge invariance of a weighted flag kernel, and give a same-span block-swap witness showing when whole-span Grassmann geometry must fail while ordered flags succeed. On the quantum side, we prove that a noiseless fidelity kernel is exactly the Hilbert--Schmidt inner product between the associated rank-one Hermitian projectors, and that a QVR-style return probability is exactly an overlap score between the input projector and a learned anchor operator. Rank-constrained returns correspond to complex Grassmann anchors, while mixed or multimodal class models are naturally represented by density or positive-semidefinite anchors. Controlled vector, subspace, statevector, anomaly, finite-shot, and quotient-witness experiments support the same conclusion: quantum and geometric lifts are useful when their invariances match the task, and fail correctly when discarded information is label-bearing. The paper makes no hardware-speedup or quantum-advantage claim.

quant-ph↗

arXiv2026

A Givens-exchange ansatz for molecular variational eigensolvers

Molecular ground-state energies help determine conformer rankings, reaction energetics, and electronic effects in computational drug discovery, but accurate calculations become difficult when strong correlation or large active spaces are important. Variational quantum eigensolvers estimate these energies by optimizing a parameterized quantum state, making ansatz design central to both accuracy and cost. We study a fixed-topology Givens-exchange ansatz that avoids architecture search. The circuit starts from the computational-basis state with the lowest diagonal Hamiltonian expectation and applies local RY rotations with two ordered all-pair Givens exchange blocks. Parameters are optimized using Hamiltonian expectation values, while exact diagonalization is used only after optimization to compute errors and fidelities. Across six fixed seeds, coefficient-verified LiH-6 and H2O-8 Hamiltonians, together with a BeH2-6 public-specification candidate, are chemically accurate in every run. The corresponding six-seed mean errors are 0.000000124 Hartree, equivalent to 0.000124 milli-Hartree; 0.000128558 Hartree, equivalent to 0.128558 milli-Hartree; and 0.000002152 Hartree, equivalent to 0.002152 milli-Hartree, respectively. On LiH-6 and H2O-8, these mean errors are lower than the published point errors of the compared quantum-architecture-search methods, while the ansatz uses a larger pre-compilation macro budget. The method is therefore an accurate, reproducible, and search-free reference template for molecular variational eigensolvers.

physics.chem-ph↗

arXiv2025

Analyzing Advanced AI Systems Against Definitions of Life and Consciousness

Could artificial intelligence ever become truly conscious in a functional sense; this paper explores that open-ended question through the lens of Life, a concept unifying classical biological criteria (Oxford, NASA, Koshland) with empirical hallmarks such as adaptive self maintenance, emergent complexity, and rudimentary self referential modeling. We propose a number of metrics for examining whether an advanced AI system has gained consciousness, while emphasizing that we do not claim all AI stems can become conscious. Rather, we suggest that sufficiently advanced architectures exhibiting immune like sabotage defenses, mirror self-recognition analogs, or meta-cognitive updates may cross key thresholds akin to life-like or consciousness-like traits. To demonstrate these ideas, we start by assessing adaptive self-maintenance capability, and introduce controlled data corruption sabotage into the training process. The result demonstrates AI capability to detect these inconsistencies and revert or self-correct analogous to regenerative biological processes. We also adapt an animal-inspired mirror self recognition test to neural embeddings, finding that partially trained CNNs can distinguish self from foreign features with complete accuracy. We then extend our analysis by performing a question-based mirror test on five state-of-the-art chatbots (ChatGPT4, Gemini, Perplexity, Claude, and Copilot) and demonstrated their ability to recognize their own answers compared to those of the other chatbots.

cs.AI↗

arXiv2021

Hybrid Classical-Quantum method for Diabetic Foot Ulcer Classification

Diabetes is a raising problem that affects many people globally. Diabetic patients are at risk of developing foot ulcer that usually leads to limb amputation, causing significant morbidity, and psychological distress. In order to develop a self monitoring mobile application, it is necessary to be able to classify such ulcers into either of the following classes: Infection, Ischaemia, None, or Both. In this work, we compare the performance of a classical transfer-learning-based method, with the performance of a hybrid classical-quantum Classifier on diabetic foot ulcer classification task. As such, we merge the pre-trained Xception network with a multi-class variational classifier. Thus, after modifying and re-training the Xception network, we extract the output of a mid-layer and employ it as deep-features presenters of the given images. Finally, we use those deep-features to train multi-class variational classifier, where each classifier is implemented on an individual variational circuit. The method is then evaluated on the blind test set DFUC2021. The results proves that our proposed hybrid classical-quantum Classifier leads to considerable improvement compared to solely relying on transfer learning concept through training the modified version of Xception network.

eess.IV↗