How a little known but essential operation in Quantum Computing helped achieve a major scientific breakthrough
Quantinuum's feed-forward functionality is worth getting to know
Quantinuum’s recent announcement about its breakthrough on topological qubits garnered headlines across both the specialist scientific media as well as those more broadly interested in the advances that will make quantum computing useful more quickly than anticipated. However, hidden in the details was a reference to a technology that is as rare as it is valuable. The fact is that the topological qubit that was generated could only have been done via Quantinuum’s H-Series quantum processors due to their various qualities and functions of which measurement and ‘feed-forward’ is critical.
As we know, great advances are often built on the back of little-known utilities - functions and tools that rarely get mentioned. These are sometimes technological constructs that might seem simple on the surface, but which are difficult (in the case of feed-forward make that “very difficult” to create), and without which critical advances would remain merely theoretical.
As detailed in two manuscripts that have been uploaded onto the pre-print repository, arXiv, Quantinuum researchers and their collaborators successfully demonstrated, for the first time, a large-scale implementation of a long-standing theory in quantum information science; namely the use of measurement and feed-forward (see below for a detailed explanation of what this means) to efficiently generate long-range entangled states.
The two experiments, conducted with research partners at the California Institute of Technology, Harvard University, the University of Sydney, the Perimeter Institute for Theoretical Physics and the University of California, Davis, used Quantinuum’s trapped ion quantum computers, Powered by Honeywell, to show how feed-forward enables success by dramatically reducing the resources required to produce highly-entangled quantum states and topologically ordered phases, one of the most exciting areas of research in modern physics.
Feed-forward uses selective measurements during the execution of a quantum circuit and adapts future operations depending on those measurement results. To be successful in running an adaptive quantum circuit, several challenging requirements must be met: (1) a select group of qubits must be measured in the middle of a circuit with high fidelity, and without accidentally measuring other qubits, and (2) the measurement results must be sent to a classical computer and quickly processed to create instructions to be fed-forward to the quantum computer on the fly - all of which must be done fast enough to prevent the active qubits from decohering.
Once these requirements are met, the feed-forward capabilities let quantum computers create long-range entangled states which are emerging as central to various branches of modern physics such as quantum error correction codes and the study of spin liquids in condensed matter. It is also the essential component of topological order and could enable the simulation of quantum systems beyond the reach of classical computation.
In the paper “Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer”, Quantinuum, working with colleagues from the California Institute of Technology and Harvard University use feed-forward to explore topologically ordered phases of matter.
Separately, a different team of scientists from Quantinuum, the University of Sydney, the Perimeter Institute for Theoretical Physics and the University of California, Davis, used feed-forward to explore adaptive quantum circuits in “Experimental Demonstration of the Advantage of Adaptive Quantum Circuits”.
Two of Quantinuum’s physicists who worked on both experiments, Henrik Dreyer and Michael Foss-Feig, offered some observations on the work.
“While it has been clear to theorists that feed-forward would be a useful primitive, doing it with low errors has turned out to be very challenging. The H-Series systems have made it possible to use this primitive efficiently,” said Henrik, managing director and scientific lead at Quantinuum’s office in Munich, Germany.
Michael, who is based at Quantinuum’s world-leading quantum computing laboratory outside of Denver, Colorado, also described feed-forward and adaptive quantum circuits as a jump toward meaningful simulations.
“This capability speeds up the timeline for new scientific discoveries,” he said.
These successful experiments proved that feed-forward operations reduce the quantum resources required for certain algorithms and are a valuable building block for more advanced research.
"I am really excited by the opportunities opened up by this demonstration: using wave-function collapse is a very powerful tool for preparing very exotic entangled states further down the road, where there are no good scalable alternatives," said Dr. Ruben Verresen, a physicist at Harvard University and a co-author of the topological order paper.
The authors note that “the primary technical challenge in implementing adaptive circuits is the requirement to perform partial measurements of a subset of qubits in the middle of a quantum circuit with minimal cross-talk on unmeasured qubits, return those results to a classical computer for processing, and then condition future operations on the results of that processing in real time.”
The paper describes how quantum hardware has now reached a state where adaptive quantum circuits are possible and can outperform unitary circuits. The experiment detailed in the paper “firmly establishes that given access to the same amount of quantum computational resources with respect to available gates and circuit depth, adaptive quantum circuits can perform tasks that are impossible for quantum circuits without feedback.”
Henrik and Michael noted that the adaptive circuit research provides concrete evidence not only that feed-forward works, but that it now works well enough to achieve tasks that would not be possible without it.
“We were trying to find a metric by which somebody can look at our data produced by a shallow adaptive circuit, and convince themselves it could not have been produced with a unitary circuit of the same depth,” Michael said. The metric proposed in the adaptive circuits paper achieved exactly that.
A good match: Trapped ion architecture and feed-forward
Demonstrating this technique required significant performance from the H1-1.
“It's a huge challenge to implement this in a way that works well,” Michael said.
Quantinuum’s H-Series has the capabilities that are crucial to this work: high fidelity gates, low state preparation and measurement (SPAM) error, low memory error, the ability to perform mid-circuit measurement, and all-to-all connectivity.
The feed-forward theory has been well-known for years but challenging to execute in practice, and as the paper states:
“While individual elements of this triad have been demonstrated in the context of error correction and topological order, combining all of these ingredients into one experimental platform has proven elusive since the inception of this idea more than a decade ago. Here, we demonstrate for the first time the deterministic, high-fidelity preparation of long-range entangled quantum states using a protocol with constant depth, using Quantinuum’s H-Series programmable Ytterbium ion trap quantum computer.”
The authors also note that “the all-to-all connectivity of the device was vital for the implementation of the periodic two-dimensional geometry and the conditional dynamics.”
In summary – these papers showcase state-of-the-art demonstrations of what can be done with quantum computers today but are only a preview of what will be done tomorrow.
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.
- Mitsui & Co. and Mitsubishi Electric demonstrated one of the world’s largest approximate Quantum Fourier Transforms (QFT) on Quantinuum Helios, scaling from prior records to 98 physical qubits.
- The collaboration also implemented a logical QFT using a QEC (Quantum Error Correction) code with up to 12 logical qubits.
- The work highlights Quantinuum’s accuracy and flexible architecture.
While there is ongoing debate around the pace of quantum computing’s development, a more grounded way to assess progress is through concrete demonstrations of foundational algorithms at meaningful scale. In this context, Mitsui & Co. and Mitsubishi Electric are taking a pragmatic view of quantum progress—focusing on how close the field is to executing core algorithmic primitives that underpin many potential industrial applications, rather than relying on abstract milestones or timelines.
In a new white paper, the industrial giants teamed up with Quantinuum to measure how close we are to running the Quantum Fourier Transform (QFT), a widely-used algorithmic primitive, at scales necessary for industrial applications. In the process, the team successfully ran one of the largest instances of the approximate QFT ever demonstrated. This achievement matters because the QFT is an essential primitive that underpins many of the quantum algorithms expected to deliver practical advantages.
You may have heard of the (classical) Fourier transform (FT), due to its ubiquity throughout modern computing. The FT is essential in everything from image analysis to data compression, with almost limitless applications in between. The quantum Fourier transform (QFT) is similar; it’s used in everything from chemistry to finance.
Because the QFT is a foundational primitive underpinning many quantum algorithms, demonstrating it at larger scales and higher fidelity is a practical way to measure quantum computing readiness. This is exactly the type of benchmarking that organizations should consider to understand where today’s systems are useful, and to see how fault-tolerant approaches are progressing. Ultimately, algorithm-level benchmarking like this is one of the most useful ways to understand not just where we are, but where we are going.
A Transformative Approach
Primitives like Fourier Transform are so widespread because they simplify problems by transforming them into something that is easier to deal with. At Quantinuum, we are very interested in transforms: not only are they crucial for industrial applications but they can also simplify algorithms, making them possible to run now instead of later. This ‘transformational’ approach extends beyond the QFT - other transforms exist, and we have even invented our own quantum-native transforms.
Using our Helios quantum computer and Guppy language, the joint team explored running the QFT on both physical qubits and on logical qubits, showing that fault tolerance is progressing quickly. Running the QFT on 98 physical qubits; the paper shows a clear progression from previous results.
Then, using the Steane code, one of the best-studied quantum error correcting codes, the team used Helios’ 98 physical qubits to form 12 logical qubits, successfully running the QFT with the mechanisms of quantum error correction interwoven into the algorithm. This marks a crucial step forward for the field.
Foundational Progress
Taken together, these results provide a more concrete lens through which to view progress in quantum computing: not as abstract projections, but as measurable advances in the execution of foundational algorithms at increasing scale. By benchmarking the Quantum Fourier Transform on both physical and logical qubits, Mitsui & Co. and Mitsubishi Electric are helping to clarify what today’s hardware can already achieve, and where fault-tolerant approaches begin to extend those limits.
More broadly, the organizations best positioned to benefit from quantum computing will be those that focus on these foundational capabilities early, and use them to build a clear, evidence-based understanding of how the technology fits into their business goals.
It is believed that unlocking answers to some of the most complex scientific and industrial problems will require the seamless integration of high-performance computing (HPC), generative AI (GenAI), and quantum computing. Toward this goal, Quantinuum, NVIDIA, and a major pharmaceutical company have successfully demonstrated the first step in a proof-of-principle framework designed to connect these three distinct computing paradigms for industrially relevant computational chemistry.
This milestone, enabled by three industry leaders and experts in their respective domains, serves as a foundational capability that could support the development of future hybrid quantum-AI workflows to help optimize industrial research and development (R&D).
The potential value is a path toward more automated, repeatable, and scalable workflows for translating chemistry problems into executable quantum programs—capabilities that could eventually make hybrid computing easier to deploy in industrial R&D.
The GenQAI Framework
The framework, termed Generative Quantum AI (GenQAI), involved a quantum computer simulating a pharmaceutical compound using programming instructions generated by an AI model, which itself was trained on quantum data that was simulated using HPC.
While the vision for GenQAI explores how future industrial simulation workflows might be optimized by training AI models using quantum data derived directly from a quantum computer, the framework currently consists of four main technical steps:
- Simulating quantum data: The process began by simulating quantum data with NVIDIA accelerated computing using NVIDIA CUDA-Q.
- Fine-tuning the AI: This simulated quantum data was used to fine-tune a pre-trained AI model from the open NVIDIA Nemotron family.
- Generating instructions: The AI model then generated quantum circuits, which are the programming instructions required for the quantum simulation.
- Validating accuracy: To validate the results, the circuits were run on Quantinuum’s Helios quantum computer using its InQuanto quantum chemistry platform.
The core novelty of this development lies within the process of the framework itself. In this proof-of-principle experiment, an AI model fine-tuned on simulated quantum data generated circuits that were successfully executed and validated on Quantinuum’s Helios system. Rather than delivering an immediate commercial advantage, this achievement establishes a credible, verifiable baseline for how HPC, AI, and quantum computing can function in tandem.
The Case Study
The validation of the framework represents an early step toward the goal of developing scalable architectures for the pharmaceutical industry.
With a shared view toward eventually scaling the framework for pharmaceutical R&D applications, the researchers simulated a pharmaceutical compound: imipramine. This anti-depressant was chosen because it serves as a model compound for drug degradation and shelf-life studies, which are standard components of the pharmaceutical R&D lifecycle.
Developing hybrid infrastructure that enterprises may adopt requires a deep, coordinated effort among domain experts. As such, this successful test highlights the value of combining the strengths of a quantum computing hardware and software leader (Quantinuum), with a hybrid-quantum classical platform (NVIDIA), and a leading enterprise end-user to build and test future computing capabilities for industrial chemistry.
Scaling the Framework
Although demonstrated on a pharmaceutical compound, the architecture could eventually inform similar molecular-simulation workflows in sectors such as energy, agriculture, advanced materials, and electronics. At this stage, it provides a reference for further testing and development.
Engage Further
Access the paper here to explore the full technical details of this demonstration and contact our team to learn more about joining Quantinuum’s enterprise partner network.
Quantinuum is pleased to announce that applications are now open for the Quantinuum SG Grand Challenge 2026, a global innovation challenge designed to bring together researchers, developers, scientists and innovators to explore practical applications of quantum computing.
Organized by Quantinuum and supported by Singapore's National Quantum Office and Aqora, the three-month program aims to foster collaboration across academia, industry and the quantum developer community while supporting the continued growth of Singapore's quantum ecosystem.
A Platform for Quantum Computing Innovation
Participants will work in teams to develop solutions across a range of challenge areas, including chemistry and molecular simulation, optimization, AI for quantum systems, quantum error correction, condensed matter and materials science, and open innovation. Throughout the program, participants will have access to mentoring, technical enablement and Quantinuum quantum computing resources.
Singapore Grand Finale
Selected finalist teams will be invited to present their work at the Grand Finale hosted in Singapore before representatives from academia, and industry. The event will celebrate innovative applications of quantum computing while providing an opportunity for participants to engage with Singapore's growing quantum community.
Join the Challenge
The Quantinuum SG Grand Challenge welcomes participants from around the world. Whether you are an experienced quantum researcher or beginning your quantum computing journey, the program offers an opportunity to collaborate, learn and contribute to the development of practical quantum applications.
Applications are now open. Spaces are limited and subject to review and approval.