λambeq Gen II: A Quantum-Enhanced Interpretable and Scalable Text-based NLP Software Package
By Bob Coecke and Dimitri Kartsaklis
Introduction
Today we announce the next generation of λambeq , Quantinuum’s quantum natural language processing (QNLP) package.
Incorporating recent developments in both quantum NLP and quantum hardware, λambeq Gen II allows users not only to model the semantics of natural language (in terms of vectors and tensors), but to convert linguistic structures and meaning directly into quantum circuits for real quantum hardware.
Five years ago, our team reported the first realization of Quantum Natural Language Processing (QNLP). In their work, the team realized that there is a direct correspondence between the meanings of words and quantum states, and between grammatical structures and quantum entanglement. As that article put it: “Language is effectively quantum native”.
Our team realized an NLP task on quantum hardware and provided the data and code via a GitHub repository, attracting the interest of a then-nascent quantum NLP community, which has since grown around successive releases of λambeq. We released it 18 months later, supported by a research paper on the arXiv.
Λambeq: an open-source python library that turns sentences into quantum circuits, and then feeds these to quantum computers subject to VQC methodologies. Initial release in October 2021 arXiv:2110.04236
From that moment onwards, anyone could play around with QNLP on the then freely available quantum hardware. Our λambeq software has been downloaded over 50,000 times, and the user community is supported by an active Discord page, where practitioners can interact with each other and with our development team.
The QNLP Back-Story
In order to demonstrate that QNLP was possible, even on the hardware available in 2021, we focused exclusively on small noisy quantum computers. Our motivation was to produce some exploratory findings, looking for a potential quantum advantage for natural language processing using quantum hardware. We published our original scientific work in 2016, detailing a quadratic speedup over classical computers (in certain circumstances). We are strongly convinced that there is a lot more potential than indicated in that paper.
That first realization of QNLP marked a shift away from brute-force machine learning, which has now taken the world by storm in the shape of large language models (LLMs) running on algorithms called “transformers”.
Instead of the transformer approach, we decoded linguistic structure using a compositional theory of meaning. With deep roots in computational linguistics, our approach was inspired by research into compositional linguistic algorithms, and their resemblance to other quantum primitives such as quantum teleportation. As we continued our work, it became clear that our approach reduced training requirements by relying on a natural relationship between linguistic structure and quantum structure, offering near-term QNLP in practice.
Embedding recent progress in λambeq Gen II
We haven’t sat still, and neither have the teams working in the field of quantum hardware. Quantinuum’s stack now performs at a level we only dreamed of in 2020. While we look forward to continued progress on the hardware front, we are getting ahead of these future developments by shifting the focus in our algorithms and software packages, to ensure we and λambeq’s users are ready to chase far more ambitious goals!
We moved away from the compositional theory of meaning that was the focus of our early experiments, called DisCoCat, to a new mathematical foundation called DisCoCirc. This enabled us to explore the relationship between text generation and text circuits, concluding that “text circuits are generative for text”.
Formally speaking, DisCoCirc embraces substantially more compositional structure present in language than DisCoCat does, and that pays off in many ways:
- Firstly, the new theoretical backbone enables one to compose the structure of sentences into text structure, so we can now deal with large texts.
- Secondly, the compositional structure of language is represented in a compressed manner, that, in fact, makes the formalism language-neutral, as reported in this blog post.
- Thirdly, the augmented compositional linguistic structure, together with the requirement of learnability, makes a quantum model now canonical, and we now have solid theoretical evidence for genuine enhanced performance on quantum hardware, as shown in this arXiv paper.
- Fourthly, the problems associated with trainability of quantum machine learning models vanish, thanks to compositional generalization, which was the subject of this paper.
- Lastly, and surely not least, we reported on the achievement of compositional interpretability and explored the myriad ways that it supports explainable AI (XAI), which we also discussed extensively in this blog post.
Today, our users can benefit from these recent developments with the release λambeq Gen II. Our open-source tools have always benefited from the attention and feedback we receive from our users. Please give it a try, and we look forward to hearing your feedback on λambeq Gen II.
Enjoy!
About Quantinuum
Quantinuum, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. Quantinuum’s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, Quantinuum leads the quantum computing revolution across continents.
- University of Southern Denmark (SDU) to use Quantinuum Helios, supported by the Danish e-Infrastructure Consortium (DeiC)
- Access to Helios enables SDU to test and refine fault-tolerant algorithms and error-correction codes under realistic hardware conditions
- The collaboration supports at a scale of 48 logical qubits, positioning Denmark at the forefront of scalable, practical quantum computing
- Researchers exploring the scientific foundations for future development of applications in fields including pharmaceuticals, finance, and defense
Progress in quantum computing is measured by hardware advances plus the algorithms and quantum error-correction codes that turn quantum systems into useful computational tools.
Thanks to recent hardware advances, researchers are increasingly sharpening their tools to probe the performance of quantum algorithms and understand how they behave in realistic conditions – where stability, system architecture and algorithm design all shape performance.
A new Denmark-based collaboration between the University of Southern Denmark (SDU), Quantinuum, and the Danish e-Infrastructure Consortium (DeiC) will utilize Quantinuum Helios. Researchers at the SDU’s Centre for Quantum Mathematics, led by Jørgen Ellegaard Andersen, will use Helios to pursue research into topological quantum computing.
Their work could help explain how and why successful quantum algorithms perform as they do, informing the development of high-performance algorithms suited to emerging quantum systems. They’re exploring the scientific foundations that support future quantum applications across areas including pharmaceuticals, finance, and defense.
“We are thrilled to gain access to Quantinuum’s high-fidelity Helios system. This collaboration gives us a unique opportunity to test the limits of our algorithms and evaluate system performance, while advancing fundamental research and laying the foundation for future applications.”
— Professor Jørgen Ellegaard Andersen, Director of the Centre for Quantum Mathematics at University of Southern Denmark
Why topological methods matter
Topological quantum computing is an area of research that connects quantum computation with deep mathematical structures. It includes the study of error correcting codes known as surface codes that encode quantum information in the global properties of systems of logical qubits.
The research team will explore how these codes behave, and how they may support the development of fault-tolerant quantum algorithms in practical implementations under realistic conditions.
This distinction between theory and practical implementation matters. In theory, topological approaches offer a rich framework for designing algorithms and error-correcting codes. In practice, researchers need to understand how those ideas perform when implemented on real systems, where questions of noise, stability, overhead, and scaling become central. The collaboration will allow the SDU team to investigate these questions directly.
New ways to benchmark quantum processors
Beyond individual algorithms and codes, the research will also develop tools for benchmarking quantum processors. The goal is to develop new ways to characterize fidelity and stability in regimes that can be difficult to access.
The team will also explore hybrid quantum–classical approaches, including machine-learning techniques assisted by quantum hardware, to study the mathematical structures at the heart of topological quantum computing. This work reflects a broader field of research in which quantum and classical methods are used together, each contributing to parts of a computational problem.
Strengthening Denmark’s quantum ecosystem
The collaboration reflects the growing role of national quantum infrastructure in supporting research and talent development. Denmark has a long tradition of scientific innovation, and this collaboration is intended to support the country’s continued development in quantum technology.
The initiative is supported by DeiC, which played a central role in securing funding and enabling access to Quantinuum’s systems. DeiC has been assigned a particular role in developing and coordinating quantum infrastructure initiatives for the benefit of universities and industry, operating without its own commercial, sectoral, or geographical interests. This includes securing dedicated access to quantum computers, producing advisory services and supporting the development of new talent in the Danish quantum sector.
“DeiC’s special effort to secure funding and access for this research initiative is rooted in our organization’s role in relation to the Danish Government’s strategy for quantum technology.”
— Henrik Navntoft Sønderskov, Head of Quantum at Danish e-Infrastructure Consortium
This collaboration promises to accelerate the development of practical algorithms. It is grounded in fundamental science – but its focus is practical: discovering and testing mathematical approaches to topological quantum computing that can be implemented, evaluated, and improved on real quantum hardware.
That work requires both theoretical insight and access to a system such as Helios capable of supporting meaningful scientific work.
This month, Quantinuum welcomed its global user community to the first-ever Q-Net Connect, an annual forum designed to spark collaboration, share insights, and accelerate innovation across our full-stack quantum computing platforms. Over two days, users came together not only to learn from one another, but to build the relationships and momentum that we believe will help define the next chapter of quantum computing.
Q-Net Connect 2026 drew over 170 attendees from around the world to Denver, Colorado, including representatives from commercial enterprises and startups, academia and research institutions, and the public sector and non-profits - all users of Quantinuum systems.
The program was packed with inspiring keynotes, technical tracks, and customer presentations. Attendees heard from leaders at Quantinuum, as well as our partners at NVIDIA, JPMorganChase and BlueQubit; professors from the University of New Mexico, the University of Nottingham and Harvard University; national labs, including NIST, Oak Ridge National Laboratory, Sandia National Laboratories and Los Alamos National Laboratory; and other distinguished guests from across the global quantum ecosystem.
Congratulations to Q-Net Connect 2026 Award Recipients!
The mission of the Quantinuum Q-Net user community is to create a space for shared learning, collaboration and connection for those who adopt Quantinuum’s hardware, software and middleware platform. At this year’s Q-Net Connect, we awarded four organizations who made notable efforts to champion this effort.
- JPMorganChase received the ‘Guppy Adopter Award’ for their exemplary adoption of our quantum programming language, Guppy, in their research workflows.
- Phasecraft, a UK and US-based quantum algorithms startup, received the ‘Rising Star’ award for demonstrating exceptional early impact and advancing science using Quantinuum hardware, which they published in a December 2025 paper.
- Qedma, a quantum software startup, received the ‘Startup Partner Engagement’ award for their sustained engagement with Quantinuum platforms dating back to our first commercially deployed quantum computer, H1.
- Anna Dalmasso from the University of Nottingham received our ‘New Student Award’ for her impressive debut project on Quantinuum hardware and for delivering outstanding results as a new Q-Net student user.
Congratulations, again, and thank you to everyone who contributed to the success of the first Q-Net Connect!
Become a Q-Net Member
Q-Net offers year‑round support through user access, developer tools, documentation, trainings, webinars, and events. Members enjoy many exclusive benefits, including being the first to hear about exclusive content, publications and promotional offers.
By joining the community, you will be invited to exclusive gatherings to hear about the latest breakthroughs and connect with industry experts driving quantum innovation. Members also get access to Q‑Net Connect recordings and stay connected for future community updates.
In a follow-up to our recent work with Hiverge using AI to discover algorithms for quantum chemistry, we’ve teamed up with Hiverge, Amazon Web Services (AWS) and NVIDIA to explore using AI to improve algorithms for combinatorial optimization.
With the rapid rise of Large Language Models (LLMs), people started asking “what if AI agents can serve as on-demand algorithm factories?” We have been working with Hiverge, an algorithm discovery company, AWS, and NVIDIA, to explore how LLMs can accelerate quantum computing research.
Hiverge – named for Hive, an AI that can develop algorithms – aims to make quantum algorithm design more accessible to researchers by translating high-level problem descriptions in mostly natural language into executable quantum circuits. The Hive takes the researcher’s initial sketch of an algorithm, as well as special constraints the researcher enumerates, and evolves it to a new algorithm that better meets the researcher’s needs. The output is expressed in terms of a familiar programming language, like Guppy or NVIDIA CUDA-Q, making it particularly easy to implement.
The AI is called a “Hive” because it is a collective of LLM agents, all of whom are editing the same codebase. In this work, the Hive was made up of LLM powerhouses such as Gemini, ChatGPT, Claude, Llama, as well as NVIDIA Nemotron, which was accessed through AWS’ Amazon Bedrock service. Many models are included because researchers know that diversity is a strength – just like a team of human researchers working in a group, a variety of perspectives often leads to the strongest result.
Once the LLMs are assembled, the Hive calls on them to do the work writing the desired algorithm; no new training is required. The algorithms are then executed and their ‘fitness’ (how well they solve the problem) is measured. Unfit programs do not survive, while the fittest ones evolve to the next generation. This process repeats, much like the evolutionary process of nature itself.
After evolution, the fittest algorithm is selected by the researchers and tested on other instances of the problem. This is a crucial step as the researchers want to understand how well it can generalize.
In this most recent work, the joint team explored how AI can assist in the discovery of heuristic quantum optimization algorithms, a class of algorithms aimed at improving efficiency across critical workstreams. These span challenges like optimal power grid dispatch and storage placement, arranging fuel inside nuclear reactors, and molecular design and reaction pathway optimization in drug, material, and chemical discovery—where solutions could translate into maximizing operational efficiency, dramatic reduction in costs, and rapid acceleration in innovation.
In other AI approaches, such as reinforcement learning, models are trained to solve a problem, but the resulting "algorithm" is effectively ‘hidden’ within a neural network. Here, the algorithm is written in Guppy or CUDA-Q (or Python), making it human-interpretable and easier to deploy on new problem instances.
This work leveraged the NVIDIA CUDA-Q platform, running on powerful NVIDIA GPUs made accessible by AWS. It’s state-of-the art accelerated computing was crucial; the research explored highly complex problems, challenges that lie at the edge of classical computing capacity. Before running anything on Quantinuum’s quantum computer, the researchers first used NVIDIA accelerated computing to simulate the quantum algorithms and assess their fitness. Once a promising algorithm is discovered, it could then be deployed on quantum hardware, creating an exciting new approach for scaling quantum algorithm design.
More broadly, this work points to one of many ways in which classical compute, AI, and quantum computing are most powerful in symbiosis. AI can be used to improve quantum, as demonstrated here, just as quantum can be used to extend AI. Looking ahead, we envision AI evolving programs that express a combination of algorithmic primitives, much like human mathematicians, such as Peter Shor and Lov Grover, have done. After all, both humans and AI can learn from each other.