Quantum analog-encoding for correlated Gaussian vectors and their exponentiation with application to rough volatility
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Quantum Physics arXiv:2604.22463 (quant-ph) [Submitted on 24 Apr 2026] Title:Quantum analog-encoding for correlated Gaussian vectors and their exponentiation with application to rough volatility Authors:Tassa Thaksakronwong, Koichi Miyamoto View a PDF of the paper titled Quantum analog-encoding for correlated Gaussian vectors and their exponentiation with application to rough volatility, by Tassa Thaksakronwong and Koichi Miyamoto View PDF Abstract:Quantum computing may speed up numerical problems involving large matrices that are demanding for classical computers, and active research on this possibility is ongoing. In this work, we propose quantum algorithms for the exact simulation of a normalised correlated Gaussian random vector $|x\rangle=\vec{x}/\lVert\vec{x}\rVert$, $\vec{x}\sim\mathcal{N}(0,\Sigma)$, and its exponentiation $|e^{\vec{x}} \rangle= e^{\vec{x}}/\lVert e^{\vec{x}}\rVert$. When an $O(\mathrm{polylog} N)$-gate-depth quantum data loader for the covariance matrix $\Sigma\in\mathbb{R}^{N\times N}$ is available, preparing $|x\rangle$ and $|e^{\vec{x}}\rangle$ require $\widetilde{O}\left(\frac{\lVert\Sigma\rVert_F}{\lambda_{\max}}\kappa^{1.5}\right)$ and $\widetilde{O}\left(\lVert\vec{x}\rVert\frac{\lVert\Sigma\rVert_F}{\lambda_{\max}}\kappa^{1.5}\right)$ elementary gate depth respectively, where $\lVert\Sigma\rVert_F$, $\lambda_{\max}$, $\kappa$ denote the Frobenius norm, maximal eigenvalue, and condition number of $\Sigma$. Motivated by financial applications, we provide an end-to-end resource analysis when $\vec{x}$ represents a sample path of a Riemann-Liouville or standard fractional Brownian motion, or of a stationary fractional Ornstein-Uhlenbeck process. As a concrete example, we construct the quantum state encoding the rough Bergomi variance process and analyse the extraction of the integrated variance via quantum amplitude estimation. Under specific conditions, the dependence of $\lVert\Sigma\rVert_F/\lambda_{\max}$ and $\kappa$ on $N$ is small, and subcubic complexity in $N$ is achieved, indicating a quantum advantage over classical Cholesky-based sampling methods. To our knowledge, this constitutes the first quantum algorithmic framework for the amplitude encoding of exponentiated Gaussian processes, providing foundational primitives for quantum-enhanced financial modelling. Comments: Subjects: Quantum Physics (quant-ph); Computational Finance (q-fin.CP) Cite as: arXiv:2604.22463 [quant-ph] (or arXiv:2604.22463v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.22463 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tassa Thaksakronwong [view email] [v1] Fri, 24 Apr 2026 11:29:09 UTC (2,115 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum analog-encoding for correlated Gaussian vectors and their exponentiation with application to rough volatility, by Tassa Thaksakronwong and Koichi MiyamotoView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: q-fin q-fin.CP References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)