{"id":37546,"date":"2026-05-27T13:57:52","date_gmt":"2026-05-27T11:57:52","guid":{"rendered":"https:\/\/www.risc-software.at\/fachbeitraege\/more-than-just-0s-and-1s-how-qudits-are-opening-up-new-paths-in-quantum-computing\/"},"modified":"2026-06-24T12:18:48","modified_gmt":"2026-06-24T10:18:48","slug":"more-than-just-0s-and-1s-how-qudits-are-opening-up-new-paths-in-quantum-computing","status":"publish","type":"publication","link":"https:\/\/www.risc-software.at\/en\/technicalarticles\/more-than-just-0s-and-1s-how-qudits-are-opening-up-new-paths-in-quantum-computing\/","title":{"rendered":"More Than Just 0s and 1s: How Qudits Are Opening Up New Paths in Quantum Computing"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-medium-font-size\">By DI Philipp Moser, PhD<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><em>Quantum computing is considered a promising new computing paradigm that is expected to enable new forms of information processing through quantum mechanical effects such as superposition. What is less well known is that many quantum systems go beyond the familiar qubit with its two states and can utilize more than just two states: These so-called qudits open up new possibilities for more compact data encoding, more expressive models, and potentially more efficient quantum algorithms. <\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\"><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-media-text has-media-on-the-right is-stacked-on-mobile is-image-fill-element\"><div class=\"wp-block-media-text__content\">\n<p class=\"wp-block-paragraph\"><strong>Contents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Quantum Computing as a New Computing Paradigm<\/li>\n\n\n\n<li>After 0 and 1 come 2, 3, \u2026<\/li>\n\n\n\n<li>Between Theory and Practice: The Untapped Potential of Qudits<\/li>\n\n\n\n<li>FWF Project QuditML: The Quantum Algorithms of Tomorrow<\/li>\n\n\n\n<li>References<\/li>\n\n\n\n<li>Author<\/li>\n\n\n\n<li>Read more<\/li>\n<\/ul>\n<\/div><figure class=\"wp-block-media-text__media\"><img data-dominant-color=\"d4cdf1\" data-has-transparency=\"false\" decoding=\"async\" width=\"1024\" height=\"512\" src=\"https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/ChatGPT-Image-26.-Mai-2026-08_47_54-1024x512.webp\" alt=\"\" class=\"wp-image-36870 size-full not-transparent\" style=\"--dominant-color: #d4cdf1; object-position:50% 50%\" srcset=\"https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/ChatGPT-Image-26.-Mai-2026-08_47_54-1024x512.webp 1024w, https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/ChatGPT-Image-26.-Mai-2026-08_47_54-300x150.webp 300w, https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/ChatGPT-Image-26.-Mai-2026-08_47_54-768x384.webp 768w, https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/ChatGPT-Image-26.-Mai-2026-08_47_54-1536x768.webp 1536w, https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/ChatGPT-Image-26.-Mai-2026-08_47_54-640x320.webp 640w, https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/ChatGPT-Image-26.-Mai-2026-08_47_54.webp 1774w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<div class=\"wp-block-group-container alignfull \">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\"><strong>Quantum Computing as a New Computing Paradigm<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"wp-block-paragraph\">When people talk about quantum computers, the term \u201cqubit\u201d almost always comes up first. Qubits are the quantum mechanical analog of classical bits in conventional computers and can not only assume the states 0 and 1, but also exist in a superposition of both; see <em>Figure 1<\/em>. It is precisely these quantum mechanical superpositions that form, among other things, a central foundation for the potential of quantum computing, because they enable novel forms of information processing that go beyond classical computing concepts. A key research area in quantum computing is optimization problems, in which the goal is to find good or optimal solutions as efficiently as possible within very large search spaces. Furthermore, quantum computing is also considered promising for quantum machine learning\u2014a fusion of quantum computing and machine learning\u2014as well as for the simulation of quantum systems, for example in materials and drug discovery research.    <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;6a4b8e3e2296e&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"6a4b8e3e2296e\" class=\"wp-block-image size-large wp-lightbox-container\"><img data-dominant-color=\"52312f\" data-has-transparency=\"true\" style=\"--dominant-color: #52312f;\" decoding=\"async\" width=\"1024\" height=\"962\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on--pointerdown=\"actions.preloadImage\" data-wp-on--pointerenter=\"actions.preloadImageWithDelay\" data-wp-on--pointerleave=\"actions.cancelPreload\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" sizes=\"(max-width: 1024px) 100vw, 1024px\" src=\"https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/Qubit-and-Qudits-Energylevels_-1024x962.webp\" alt=\"Qubit and Qudit Energy Levels\" class=\"wp-image-36903 has-transparency\" srcset=\"https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/Qubit-and-Qudits-Energylevels_-1024x962.webp 1024w, https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/Qubit-and-Qudits-Energylevels_-300x282.webp 300w, https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/Qubit-and-Qudits-Energylevels_-768x722.webp 768w, https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/Qubit-and-Qudits-Energylevels_.webp 1475w\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\tdata-wp-bind--aria-label=\"state.thisImage.triggerButtonAriaLabel\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.thisImage.buttonRight\"\n\t\t\tdata-wp-style--top=\"state.thisImage.buttonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n<div class=\"wp-block-group-container alignfull \">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\"><strong>After 0 and 1 come 2, 3, \u2026<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">What is less well known is that most quantum computers have more than just these two usable states. Qudits are a generalization of the qubit concept to d states. While the \u201cb\u201d in qubit stands for binary two-state logic, the \u201cd\u201d in qudit refers to d-dimensional\u2014that is, a multi-level quantum system with more than two usable states. A qutrit, for example, has three states. These additional levels are already present in many physical platforms, such as higher energy levels in superconducting or ion-based quantum systems. The central idea is therefore obvious: Why leave these additional states unused if they could potentially be used for more efficient computational algorithms?     <\/p>\n<\/div>\n<\/div>\n\n<div class=\"wp-block-group-container alignfull \">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\"><strong>Between Theory and Practice: The Untapped Potential of Qudits<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A key advantage of qudits is that they allow for a higher information density per quantum system than qubits. This could enable data to be encoded more compactly and more expressive quantum machine learning models to be developed for certain problems. At the same time, the higher number of states opens up the possibility of solving certain tasks even with smaller system sizes. This is of particular interest when considering real-world hardware, because smaller quantum systems are potentially easier to implement than ever-larger qubit-based architectures. The theoretical advantages of such multi-level qudit systems have already been well documented and analyzed in the literature [<a href=\"#ref1\">1<\/a>,<a href=\"#ref2\">2<\/a>]. However, translating this potential into concrete and practically usable quantum algorithms is still in its early stages.     <\/p>\n<\/div>\n<\/div>\n\n<div class=\"wp-block-group-container alignfull \">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\"><strong>FWF Project QuditML: The Quantum Algorithms of Tomorrow<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">These are precisely the questions we are addressing in the FWF-funded research project <strong><a href=\"https:\/\/www.risc-software.at\/en\/referenceprojects\/quditml-multi-level-quantum-computing-for-next-generation-machine-learning\/\">QuditML<\/a><\/strong> [<a href=\"#ref3\">3<\/a>,<a href=\"#ref4\">4<\/a>]. The goal of QuditML is to bridge the gap between the theoretical potential of qudits and practical applications. To this end, we are developing novel qudit-based machine learning algorithms, designing suitable data encodings for tabular, signal-based, and image-based data, and evaluating their practical utility for applications in medicine, high-energy physics, and chemistry. In this way, the QuditML project could serve as a catalyst for more intensive research into multi-level quantum computing, advance quantum technology as a whole, and thus bring us one step closer to a new generation of powerful and practical quantum algorithms.   <\/p>\n<\/div>\n<\/div>\n\n<div class=\"wp-block-group-container alignfull \">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\"><strong>References<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"ref1\">[1] <a href=\"https:\/\/arxiv.org\/abs\/2505.05158\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/2505.05158<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"ref2\">[2] <a href=\"https:\/\/arxiv.org\/abs\/2008.00959\" target=\"_blank\" rel=\"noopener\">https:\/\/arxiv.org\/abs\/2008.00959<\/a> Wang Y, Hu Z, Sanders BC, and Kais S (2020) Qudits and High-Dimensional Quantum Computing. Front. Phys. 8:589504. doi: 10.3389\/fphy.2020.589504<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"ref3\">[3] <a href=\"https:\/\/www.fwf.ac.at\/forschungsradar\/10.55776\/TAI1354725\" target=\"_blank\" rel=\"noopener\">https:\/\/www.fwf.ac.at\/forschungsradar\/10.55776\/TAI1354725<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"ref4\">[4] <a href=\"https:\/\/www.risc-software.at\/en\/referenceprojects\/quditml-multi-level-quantum-computing-for-next-generation-machine-learning\/\">https:\/\/www.risc-software.at\/referenzprojekte\/quditml\/<\/a><\/p>\n<\/div>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">Contact us<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<h2 class=\"wp-block-heading\">Author<\/h2>\n\n\n<div class=\"contact-person\">\n      <picture>\n      \n      \n      \n      \n      <img decoding=\"async\" data-aos=\"fade-zoom-in\"\n           data-aos-offset=\"0\" class=\"w-full\" width=\"212\" height=\"293\"\n           src=\"https:\/\/www.risc-software.at\/app\/uploads\/2024\/06\/pmoser1_freigestellt.png\"\n           alt=\"\">\n    <\/picture>\n    \n\n<h5 class=\"wp-block-heading\">DI Philipp Moser, PhD<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">Senior Researcher &amp; Developer<\/p>\n\n  <\/div>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Read more<\/h2>\n\n\n<div class=\"posts-slider-block\" data-aos=\"fade-up\" data-aos-offset=\"0\" data-aos-anchor-placement=\"top-bottom\">\n        <section class=\"splide posts-slider\" aria-label=\"Gallery Slides\">\n            <div class=\"splide__arrows\">\n                <button class=\"splide__arrow splide__arrow--prev\">\n                    <span class=\"sr-only\">Previous<\/span>\n                    <img decoding=\"async\" loading=\"lazy\" width=\"25\" height=\"21\" src=\"https:\/\/www.risc-software.at\/app\/themes\/risc-theme-main\/public\/images\/icon-arrow.35d2ec.svg\"\n                         alt=\"Previous\">\n                <\/button>\n                <button class=\"splide__arrow splide__arrow--next\">\n                    <span class=\"sr-only\">Next<\/span>\n                    <img decoding=\"async\" loading=\"lazy\" width=\"25\" height=\"21\" src=\"https:\/\/www.risc-software.at\/app\/themes\/risc-theme-main\/public\/images\/icon-arrow.35d2ec.svg\"\n                         alt=\"Next\">\n                <\/button>\n            <\/div>\n            <div class=\"inner\">\n                <div class=\"splide__track\">\n                    <div class=\"splide__list\">\n\n                                                    <a href=\"https:\/\/www.risc-software.at\/en\/referenceprojects\/qml4med\/\" class=\"splide__slide blog-post-teaser mb-1 lg:mb-3\">\n                                <div class=\"blog-image\">\n                                                                                                                                <picture>\n                                                                                        <img decoding=\"async\" src=\"https:\/\/www.risc-software.at\/app\/uploads\/2024\/05\/cstaub_A_conceptual_illustration_of_a_qubit_in_quantum_comput_5d5a63bf-5e69-4a54-b3a4-6c91ae0efb86_0-360x214.png\"\n                                                 alt=\"QML4Med: Quantum computing meets machine learning in medicine\">\n                                        <\/picture>\n                                                                    <\/div>\n                                <div class=\"blog-content px-2 py-3 xl:px-4 xl:py-5\">\n                                    <h3>QML4Med: Quantum computing meets machine learning in medicine<\/h3>\n                                    <div class=\"blog-post-excerpt mt-2\">\n                                        The QML4Med research project aims to explore the potential of the promising fusion of quantum computing and machine learning in a medical context.  \n                                    <\/div>\n                                    <span class=\"inline-block mt-2 more\">mehr erfahren <span class=\"ml-1 icon-more\"><\/span><\/span>\n\n                                <\/div>\n                            <\/a>\n                                                    <a href=\"https:\/\/www.risc-software.at\/en\/technicalarticles\/quantum-machine-learning\/\" class=\"splide__slide blog-post-teaser mb-1 lg:mb-3\">\n                                <div class=\"blog-image\">\n                                                                                                                                <picture>\n                                                                                        <img decoding=\"async\" src=\"https:\/\/www.risc-software.at\/app\/uploads\/2025\/05\/Fachbeitrag_QML_Bild-360x214.avif\"\n                                                 alt=\"Quantum Machine Learning\">\n                                        <\/picture>\n                                                                    <\/div>\n                                <div class=\"blog-content px-2 py-3 xl:px-4 xl:py-5\">\n                                    <h3>Quantum Machine Learning<\/h3>\n                                    <div class=\"blog-post-excerpt mt-2\">\n                                        Quantum Machine Learning (QML) combines quantum computing with AI and promises revolutionary advances in data-intensive areas such as medicine, industry and finance. Despite technical hurdles, QML is considered a key technology of the future. \n                                    <\/div>\n                                    <span class=\"inline-block mt-2 more\">mehr erfahren <span class=\"ml-1 icon-more\"><\/span><\/span>\n\n                                <\/div>\n                            <\/a>\n                                                    <a href=\"https:\/\/www.risc-software.at\/en\/fwf-funding-for-quantum-research-project-quditml\/\" class=\"splide__slide blog-post-teaser mb-1 lg:mb-3\">\n                                <div class=\"blog-image\">\n                                                                                                                                <picture>\n                                                                                        <img decoding=\"async\" src=\"https:\/\/www.risc-software.at\/app\/uploads\/2025\/07\/2025-07-16-PA_QuditML-360x214.webp\"\n                                                 alt=\"FWF funding for quantum research project &quot;QuditML&quot;\">\n                                        <\/picture>\n                                                                    <\/div>\n                                <div class=\"blog-content px-2 py-3 xl:px-4 xl:py-5\">\n                                    <h3>FWF funding for quantum research project &#8220;QuditML&#8221;<\/h3>\n                                    <div class=\"blog-post-excerpt mt-2\">\n                                        RISC Software GmbH is launching QuditML, a groundbreaking research project that pushes the boundaries of quantum machine learning &#8211; funded by the Austrian Science Fund (FWF) as part of the &quot;1000 Ideas&quot; call.\n                                    <\/div>\n                                    <span class=\"inline-block mt-2 more\">mehr erfahren <span class=\"ml-1 icon-more\"><\/span><\/span>\n\n                                <\/div>\n                            <\/a>\n                                                    <a href=\"https:\/\/www.risc-software.at\/en\/referenceprojects\/quditml-multi-level-quantum-computing-for-next-generation-machine-learning\/\" class=\"splide__slide blog-post-teaser mb-1 lg:mb-3\">\n                                <div class=\"blog-image\">\n                                                                                                                                <picture>\n                                                                                        <img decoding=\"async\" src=\"https:\/\/www.risc-software.at\/app\/uploads\/2026\/02\/risc_software_A_futuristic_scientific_illustration_of_a_quant_71772071-b795-49b7-bfe2-78e9d4320e8d_2-1-e1770229068523-360x214.webp\"\n                                                 alt=\"QuditML: Multi-level quantum computing for next-generation machine learning\">\n                                        <\/picture>\n                                                                    <\/div>\n                                <div class=\"blog-content px-2 py-3 xl:px-4 xl:py-5\">\n                                    <h3>QuditML: Multi-level quantum computing for next-generation machine learning<\/h3>\n                                    <div class=\"blog-post-excerpt mt-2\">\n                                        The QuditML research project is dedicated to the study of so-called Qudits, i.e. multi-level quantum systems.\n                                    <\/div>\n                                    <span class=\"inline-block mt-2 more\">mehr erfahren <span class=\"ml-1 icon-more\"><\/span><\/span>\n\n                                <\/div>\n                            <\/a>\n                                            <\/div>\n                <\/div>\n            <\/div>\n        <\/section>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p>Quantum computing promises a new computing paradigm through effects such as superposition. But beyond the familiar qubit with its two states, so-called qudits with multiple states open up new possibilities: more compact data encoding, more expressive models, and more efficient quantum algorithms. <\/p>\n","protected":false},"featured_media":37548,"template":"","publication-category":[],"class_list":["post-37546","publication","type-publication","status-publish","has-post-thumbnail","hentry"],"acf":[],"portrait_thumb_url":"https:\/\/www.risc-software.at\/app\/uploads\/2026\/05\/ChatGPT-Image-26.-Mai-2026-08_47_54-360x214.webp","_links":{"self":[{"href":"https:\/\/www.risc-software.at\/en\/wp-json\/wp\/v2\/publication\/37546","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.risc-software.at\/en\/wp-json\/wp\/v2\/publication"}],"about":[{"href":"https:\/\/www.risc-software.at\/en\/wp-json\/wp\/v2\/types\/publication"}],"version-history":[{"count":2,"href":"https:\/\/www.risc-software.at\/en\/wp-json\/wp\/v2\/publication\/37546\/revisions"}],"predecessor-version":[{"id":37700,"href":"https:\/\/www.risc-software.at\/en\/wp-json\/wp\/v2\/publication\/37546\/revisions\/37700"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.risc-software.at\/en\/wp-json\/wp\/v2\/media\/37548"}],"wp:attachment":[{"href":"https:\/\/www.risc-software.at\/en\/wp-json\/wp\/v2\/media?parent=37546"}],"wp:term":[{"taxonomy":"publication-category","embeddable":true,"href":"https:\/\/www.risc-software.at\/en\/wp-json\/wp\/v2\/publication-category?post=37546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}