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!

We're announcing the world’s first scalable, error-corrected, end-to-end computational chemistry workflow. With this, we are entering the future of computational chemistry.

Quantum computers are uniquely equipped to perform the complex computations that describe chemical reactions – computations that are so complex they are impossible even with the world’s most powerful supercomputers.

However, realizing this potential is a herculean task: one must first build a large-scale, universal, fully fault-tolerant quantum computer – something nobody in our industry has done yet. We are the farthest along that path, as our roadmap, and our robust body of research, proves. At the moment, we have the world’s most powerful quantum processors, and are moving quickly towards universal fault tolerance. Our commitment to building the best quantum computers is proven again and again in our world-leading results.

While we do the work to build the world’s best quantum computers, we aren’t waiting to develop their applications. We have teams working right now on making sure that we hit the ground running with each new hardware generation. In fact, our team has just taken a huge leap forward for computational chemistry using our System Model H2.

In our latest paper, we have announced the first-ever demonstration of a scalable, end-to-end workflow for simulating chemical systems with quantum error correction (QEC). This milestone shows that quantum computing will play an essential role, in tandem with HPC and AI, in unlocking new frontiers in scientific discovery.

In the paper, we showcase the first practical combination of quantum phase estimation (QPE) with logical qubits for molecular energy calculations – an essential step toward fault-tolerant quantum simulations. It builds on our previous work implementing quantum error detection with QPE and marks a critical step toward achieving quantum advantage in chemistry.  

By demonstrating this end-to-end workflow on our H2 quantum computer using our state-of-the-art chemistry platform InQuanto™, we are proving that quantum error-corrected chemistry simulations are not only feasible, but also scalable and —crucially—implementable in our quantum computing stack.

This work sets key benchmarks on the path to fully fault-tolerant quantum simulations. Building such capabilities into an industrial workflow will be a milestone for quantum computing, and the demonstration reported here represents a new high-water mark as we continue to lead the global industry in pushing towards universal fault-tolerant computers capable of widespread scientific and commercial advantage.  

As we look ahead, this workflow will serve as the foundation for future quantum-HPC integration, enabling chemistry simulations that are impossible today.

Showcasing Quantinuum’s Full-Stack Advantage

Today’s achievement wouldn’t be possible without the Quantinuum’s full stack approach. Our vertical integration - from hardware to software to applications - ensures that each layer works together seamlessly.  

Our H2 quantum computer, based on the scalable QCCD architecture with its unique combination of high-fidelity operations, all-to-all connectivity, mid-circuit measurements and conditional logic, enabled us to run more complex quantum computing simulations than previously possible. The work also leverages Quantinuum’s real-time QEC decoding capability and benefitted from the quantum error correction advantages also provided by QCCD.

We will make this workflow available to customers via InQuanto, our quantum chemistry platform, allowing users to easily replicate and build upon this work. The integration of high-quality quantum computing hardware with sophisticated software creates a robust environment for iterating and accelerating breakthroughs in fields like chemistry and materials science.

A Collaborative Future: The Role of AI and Supercomputing

Achieving quantum advantage in chemistry will require more than just quantum hardware; it will require a synergistic approach that combines such quantum computing workflows demonstrated here with classical supercomputing and AI. Our strategic partnerships with leading supercomputing providers – with Quantinuum being selected as a founding collaborator for NVIDIA’s Accelerated Quantum Research Center – as well as our commitment to exploring generative quantum AI, place us in a unique position to maximize the benefit of quantum computing, and supercharge quantum advantage with the integration of classical supercomputing and AI.

Conclusion

Quantum computing holds immense potential for transforming industries across the globe. Our work today experimentally demonstrates the first complete and scalable quantum chemistry simulation, showing that the long-awaited quantum advantage in simulating chemical systems is not only possible, but within reach. With the development of new error correction techniques and the continued advancement of our quantum hardware and software we are paving the way for a future where quantum simulations can address challenges that are impossible today. Quantinuum’s ongoing collaborations with HPC providers and its exploration of AI-driven quantum techniques position our company to capitalize on this trifecta of computing power and achieve meaningful breakthroughs in quantum chemistry and beyond.

We encourage you to explore this breakthrough further by reading our latest research on arXiv and try out the Python code for yourself.

I continue to be inspired by our team's pioneering efforts to redefine what’s possible through quantum computing. With more than 550 dedicated employees, we’re constantly pushing the boundaries to uncover meaningful applications for this transformative technology.

This week marked one of my proudest moments: the announcement of a joint venture with Al Rabban Capital to accelerate the commercial adoption of quantum technology in Qatar and the Gulf region. This partnership lays the groundwork for up to USD $1 billion in investment from Qatar over the next decade in Quantinuum’s state-of-the-art quantum technologies, co-development of quantum computing applications tailored to regional needs, and workforce development. This collaboration is a major step forward in our strategy to expand our commercial reach through long-term, strategic alliances that foster economic growth in both the U.S. and Qatar.

I had the unique opportunity to attend a business roundtable in Doha with President Trump, U.S. and Qatari policymakers, and other industry leaders. The conversation centered on the importance of U.S.-Qatari relations and the role of shared commercial interests in strengthening that bond.

A recurring theme was innovation in Artificial Intelligence (AI), reinforcing the role that hybrid quantum-classical systems will play in enhancing AI capabilities across sectors. By integrating quantum computing, AI, and high-performance computing, we can unlock powerful new use cases critical to economic growth and national security. 

We also addressed the growing energy demands of AI-powered data centers. Quantum computing offers a potential path forward here, as well. Our H2-1 system has demonstrated an estimated 30,000x reduction in power consumption compared to classical supercomputers, making it a highly efficient tool for solving complex computational challenges.

What struck me most about the conversations in Qatar was the emphasis on cooperation over competition. While quantum is often framed as a race, our partnership with Al Rabban Capital underscores the value of cross-border collaboration. As I noted in a recent Time Magazine article co-authored with Honeywell CEO Vimal Kapur, quantum computing isn’t just a technology—it’s a national capability. Countries that lead will shape how it is regulated, protected, and deployed. Our joint venture and this week’s dialogue reaffirm that both the U.S. and Qatar are taking the necessary first steps to lead in this space. Yet much work remains.

I believe we’re witnessing the emergence of a new kind of global alliance—one rooted not just in trade, but in shared technological advancement. Quantum computing holds the promise to unlock innovative solutions that will tackle challenges that have long been beyond reach. Realizing that promise will require visionary leadership, global collaboration, and a bold commitment to shaping the future together.

I was honored to attend today’s roundtable during the President’s State Visit to Qatar and to see our announcement featured as part of that engagement. This milestone reflects a shared commitment by the U.S. and Qatar to strengthen strategic ties, spur bilateral investment in future-defining industries, and foster technological leadership and shared prosperity. 

Quantinuum’s expansion into the Gulf region, starting with Qatar, follows our successful growth in the U.S., U.K., Europe and Indo-Pacific. We will continue working across borders and sectors to accelerate the commercial adoption of quantum computing and realize quantum’s full potential—for the benefit of all!

Details of the JV are available in this link, along with the official White House communication.

Onward and Upward,
Rajeeb Hazra

Back in 2020, we made a promise to increase our Quantum Volume (QV), a measure of computational power, by 10x per year for 5 years. 

Today, we’re pleased to share that we’ve followed through on our commitment: Our System Model H2 has reached a Quantum Volume of 2²³ = 8,388,608, proving not just that we always do what we say, but that our quantum computers are leading the world forward. 

The QV benchmark was developed by IBM to represent a machine’s performance, accounting for things like qubit count, coherence times, qubit connectivity, and error rates. In IBM's words: 

“the higher the Quantum Volume, the higher the potential for exploring solutions to real world problems across industry, government, and research."

Our announcement today is precisely what sets us apart from the competition. No one else has been bold enough to make a similar promise on such a challenging metric – and no one else has ever completed a five-year goal like this.

We chose QV because we believe it’s a great metric. For starters, it’s not gameable, like other metrics in the ecosystem. Also, it brings together all the relevant metrics in the NISQ era for moving towards fault tolerance, such as gate fidelity and connectivity. 

Our path to achieve a QV of over 8 million was led in part by Dr. Charlie Baldwin, who studied under the legendary Ivan H. Deutsch. Dr. Baldwin has made his name as a globally renowned expert in quantum hardware performance over the past decade, and it is because of his leadership that we don’t just claim to be the best, but that we can prove we are the best. 

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Alongside the world’s biggest quantum volume, we have the industry’s most benchmarked quantum computers. To that point, the table below breaks down the leading commercial specs for each quantum computing architecture. 

We’ve never shied away from benchmarking our machines, because we know the results will be impressive. It is our provably world-leading performance that has enabled us to demonstrate:

• Quantum Supremacy via Random Circuit Sampling
• Quantum Magnetism at the Frontier of Classical Simulations
• Encoded Memory that Outperforms All Previous Implementations
• Quantum Supremacy for Certified Randomness
• High Fidelity Teleportation of Logical Qubits

As we look ahead to our next generation system, Helios, Quantinuum’s Senior Director of Engineering, Dr. Brian Neyenhuis, reflects: “We finished our five-year commitment to Quantum Volume ahead of schedule, showing that we can do more than just maintain performance while increasing system size. We can improve performance while scaling.” 

Helios’ performance will exceed that of our previous machines, meaning that Quantinuum will continue to lead in performance while following through on our promises. 

As the undisputed industry leader, we’re racing against no one other than ourselves to deliver higher performance and to better serve our customers.

At the heart of quantum computing’s promise lies the ability to solve problems that are fundamentally out of reach for classical computers. One of the most powerful ways to unlock that promise is through a novel approach we call Generative Quantum AI, or GenQAI. A key element of this approach is the Generative Quantum Eigensolver (GQE).

GenQAI is based on a simple but powerful idea: combine the unique capabilities of quantum hardware with the flexibility and intelligence of AI. By using quantum systems to generate data, and then using AI to learn from and guide the generation of more data, we can create a powerful feedback loop that enables breakthroughs in diverse fields.

Unlike classical systems, our quantum processing unit (QPU) produces data that is extremely difficult, if not impossible, to generate classically. That gives us a unique edge: we’re not just feeding an AI more text from the internet; we’re giving it new and valuable data that can’t be obtained anywhere else.

The Search for Ground State Energy

One of the most compelling challenges in quantum chemistry and materials science is computing the properties of a molecule’s ground state. For any given molecule or material, the ground state is its lowest energy configuration. Understanding this state is essential for understanding molecular behavior and designing new drugs or materials.

The problem is that accurately computing this state for anything but the simplest systems is incredibly complicated. You cannot even do it by brute force—testing every possible state and measuring its energy—because  the number of quantum states grows as a double-exponential, making this an ineffective solution. This illustrates the need for an intelligent way to search for the ground state energy and other molecular properties.

That’s where GQE comes in. GQE is a methodology that uses data from our quantum computers to train a transformer. The transformer then proposes promising trial quantum circuits; ones likely to prepare states with low energy. You can think of it as an AI-guided search engine for ground states. The novelty is in how our transformer is trained from scratch using data generated on our hardware.

Here's how it works:

• We start with a batch of trial quantum circuits, which are run on our QPU.
• Each circuit prepares a quantum state, and we measure the energy of that state with respect to the Hamiltonian for each one.
• Those measurements are then fed back into a transformer model (the same architecture behind models like GPT-2) to improve its outputs.
• The transformer generates a new distribution of circuits, biased toward ones that are more likely to find lower energy states.
• We sample a new batch from the distribution, run them on the QPU, and repeat.
• The system learns over time, narrowing in on the true ground state.

To test our system, we tackled a benchmark problem: finding the ground state energy of the hydrogen molecule (H₂). This is a problem with a known solution, which allows us to verify that our setup works as intended. As a result, our GQE system successfully found the ground state to within chemical accuracy.

To our knowledge, we’re the first to solve this problem using a combination of a QPU and a transformer, marking the beginning of a new era in computational chemistry.

The Future of Quantum Chemistry

The idea of using a generative model guided by quantum measurements can be extended to a whole class of problems—from combinatorial optimization to materials discovery, and potentially, even drug design.

By combining the power of quantum computing and AI we can unlock their unified full power. Our quantum processors can generate rich data that was previously unobtainable. Then, an AI can learn from that data. Together, they can tackle problems neither could solve alone.

This is just the beginning. We’re already looking at applying GQE to more complex molecules—ones that can’t currently be solved with existing methods, and we’re exploring how this methodology could be extended to real-world use cases. This opens many new doors in chemistry, and we are excited to see what comes next.

Last year, we joined forces with RIKEN, Japan's largest comprehensive research institution, to install our hardware at RIKEN’s campus in Wako, Saitama. This deployment is part of RIKEN’s project to build a quantum-HPC hybrid platform consisting of high-performance computing systems, such as the supercomputer Fugaku and Quantinuum Systems.  

Today, a paper published in Physical Review Research marks the first of many breakthroughs coming from this international supercomputing partnership. The team from RIKEN and Quantinuum joined up with researchers from Keio University to show that quantum information can be delocalized (scrambled) using a quantum circuit modeled after periodically driven systems.  

"Scrambling" of quantum information happens in many quantum systems, from those found in complex materials to black holes.  Understanding information scrambling will help researchers better understand things like thermalization and chaos, both of which have wide reaching implications.

To visualize scrambling, imagine a set of particles (say bits in a memory), where one particle holds specific information that you want to know. As time marches on, the quantum information will spread out across the other bits, making it harder and harder to recover the original information from local (few-bit) measurements.

While many classical techniques exist for studying complex scrambling dynamics, quantum computing has been known as a promising tool for these types of studies, due to its inherently quantum nature and ease with implementing quantum elements like entanglement. The joint team proved that to be true with their latest result, which shows that not only can scrambling states be generated on a quantum computer, but that they behave as expected and are ripe for further study.

Thanks to this new understanding, we now know that the preparation, verification, and application of a scrambling state, a key quantum information state, can be consistently realized using currently available quantum computers. Read the paper here, and read more about our partnership with RIKEN here.