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Computational and physical complexity of synthesizing random multi-qudit quantum states and unitary operators

arXiv Quantum Physics
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Ashhab and Basyildiz analyze two distinct approaches to synthesizing random quantum states and unitary operators in multi-qudit systems, comparing computational gate-based methods with physical control-pulse optimization. Computational complexity—measured by the minimum gates needed—scales exponentially with qudit count, revealing fundamental limits for gate-based quantum synthesis in large systems. Physical complexity, defined by minimum time using optimized control pulses, grows more slowly than computational complexity, suggesting hardware-level advantages for certain quantum operations. The study combines analytical arguments and optimal-control-theory simulations, providing numerical evidence that physical implementations may outperform gate-based approaches for random state preparation. Implications extend to pseudorandom states, questioning whether near-term devices can efficiently approximate true randomness without exponential overhead.
Computational and physical complexity of synthesizing random multi-qudit quantum states and unitary operators

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Quantum Physics arXiv:2605.07374 (quant-ph) [Submitted on 8 May 2026] Title:Computational and physical complexity of synthesizing random multi-qudit quantum states and unitary operators Authors:Sahel Ashhab, Bora Basyildiz View a PDF of the paper titled Computational and physical complexity of synthesizing random multi-qudit quantum states and unitary operators, by Sahel Ashhab and Bora Basyildiz View PDF HTML (experimental) Abstract:We analyze the complexity of synthesizing random states and unitary operators in a multi-qudit system in two paradigms. In one case, we consider the situation in which we manipulate the system by applying a sequence of one- and two-qudit quantum gates that constitute the elementary, and universal, gate set. The minimum number of gates required to perform the desired operation represents the computational complexity. In the other case, we consider the situation in which we manipulate the physical system using physical fields with optimized control pulses. The minimum time required to perform the desired operation represents the physical complexity. In both cases, we use analytical arguments in combination with optimal-control-theory numerical calculations to determine the complexity of random operations. We show that the computational complexity of random states or unitary operators scales exponentially with the number of qudits. Our numerical results suggest that the physical complexity of preparing random quantum states and unitary operators scales more slowly than the computational complexity. We discuss various implications of our results, especially concerning the relationship between random and pseudorandom states and unitary operators. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.07374 [quant-ph] (or arXiv:2605.07374v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.07374 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sahel Ashhab [view email] [v1] Fri, 8 May 2026 07:30:21 UTC (21 KB) Full-text links: Access Paper: View a PDF of the paper titled Computational and physical complexity of synthesizing random multi-qudit quantum states and unitary operators, by Sahel Ashhab and Bora BasyildizView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)

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Source: arXiv Quantum Physics