Skinny Logic: Quantum Codes Go on a Diet

March 4, 2026

In our latest paper, we’ve taken a big step toward large scale fault-tolerant quantum computing, squeezing up to 94 error-detected qubits (and 48 error-corrected qubits) out of just 98 physical qubits, a low-fat encoding that cuts overhead to the bone. With 64 of our logical qubits, we were able to simulate quantum magnetism at a scale that can be exceedingly difficult for classical computers.

The "holy grail" of quantum computing is universal fault-tolerance: the ability to correct errors faster than they occur during any computation. To realize this, we aim to create “logical qubits,” which are groups of entangled physical qubits that share quantum information in a way that protects it. Better protection leads to lower “logical” error rate and greater ability to solve complex problems.

However, it’s never that easy. An unofficial law of physics is “there’s no such thing as a free lunch”. Creating high quality, low error-rate logical qubits often costs many physical qubits, thus reducing the size of calculations you can run, despite your new, lower-than-ever error rates.

With our , we are thrilled to announce that we have hit a key milestone on the 91�� roadmap: an ultra-efficient method for creating logical qubits, extracting a whopping 48 error-corrected and 64 error-detected logical qubits out of just 98 physical qubits. Our logical qubits boasted better than “break-even” fidelity, beating their physical counterparts with lower error rates on several different fronts. And still that isn’t the end of the story: we used our 64 error-detected logical qubits in a large-scale quantum magnetism simulation, laying the groundwork for future studies of exotic interactions in materials.

Stacking Wins

To get this world-leading result, we employed a neat trick: ‘nesting’ super efficient quantum error-detecting codes together to make a new, ultra-efficient error-correcting code. Dr. DeCross, a primary author on the paper, said this nesting is like “braiding together ropes made out of ropes made out of ropes”. Physicists call this ‘code concatenation’, and you can think of it as adding layers of protection on top of each other.

To begin, we took the now-famous ‘iceberg code’, a quantum error detection code that gives an almost 1:1 ratio of physical qubits to logical qubits. The iceberg code only detects errors, however, which means that instead of actually correcting errors it lets you throw out bits where errors were detected. To make a code that could both detect and correct errors, we concatenated two iceberg codes together, giving a code that can correct small errors while still boasting a world-record 2:1 physical:logical ratio (physicists call this a “high encoding rate”).

The team then benchmarked the logical qubits, checking large system-scale operations and comparing them to their physical counterparts. This introduces a crucial hurdle to clear: oftentimes, researchers end up with logical qubits that perform *worse* than their physical counterparts. It’s critical that logical qubits actually beat physical ones, after all – that is the whole point!

Thanks to some clever circuit design and our natively high fidelities, the new logical qubits outperformed their physical counterparts in every test we performed, sometimes by a factor of 10 to 100.

Computing Logically

Of course, the whole point is to use our logical qubits for something useful, the ultimate measure of functionality. With 64 error-detected qubits, we performed a simulation of quantum magnetism; a crucial milestone that validates our roadmap.

The team took extra care to perform their simulation in 3 dimensions to best reflect the real-world (often, studies like this will only be in 1D or 2D to make them easier). Problems like this are both incredibly important for expanding our understanding of materials, but are also incredibly hard, as their complexity scales quickly. To make qubits interact as if they are in a 3D material when they are trapped in 2D inside the computer, we used our all-to-all connectivity, a feature that results from our movable qubits.

Maximizing Entanglement

Breaking the encoding rate record and performing a world-leading logical simulation wasn’t enough for the team. For their final feat, the team generated 94 error-detected logical qubits, and entangled them all in a special state called a “GHZ” state (also known as a ‘cat’ state, alluding to Schrödinger’s cat). GHZ states are often used by experts as a simple benchmark for showcasing quantum computing’s unique capacity to use entanglement across many qubits. Our best 94-logical qubit GHZ state boasted a fidelity of 94.9%, crushing its un-encoded counterpart.

Logical Qubits Are the New Normal

Taken together, these results show that we can suppress errors more effectively than ever before, proving that Helios is capable of delivering complex, high-fidelity operations that were previously thought to be years away. While the magnetism simulation was only error-detected, it showcases our ability to protect universal computations with partially fault-tolerant methods. On top of that, the team also demonstrated key error-corrected primitives on Helios at scale.

All of this has real-world implications for the quantum ecosystem: we are working to package these iceberg codes into QCorrect, an upcoming tool that will help developers automatically improve the performance of their own applications.

This is just the beginning: we are officially entering the era of large-scale logical computing. The path to fault-tolerance is no longer just theoretical—it is being built, gate by gate, on Helios.

About 91��

91��, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. 91��’s 91�� drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, 91�� leads the quantum computing revolution across continents.

Blog

technical

June 10, 2026

91��'s Fault-Tolerance Advantage: Turning Quantum Reliability into Commercial Usefulness

91�� continues its progress toward fault-tolerant quantum computing, with a series of peer-reviewed breakthroughs in fault-tolerant operations.‍
Our progress is not only scientific; it is commercial. By improving logical-qubit reliability and encoding efficiency, 91�� is reducing the resource overhead required to scale its quantum computers toward commercially useful workloads.‍
These results were achieved on commercial 91�� hardware, reinforcing that our architecture is not just setting new standards, but building a practical foundation for customers, partners, and researchers preparing for the fault-tolerant era.

Fault-tolerant quantum computing is the threshold the industry must cross before quantum computers can solve the hardest, highest-value problems with confidence. To be commercially useful at scale, the question is not simply who can build more qubits. It is who can build reliable, efficient, scalable systems that reduce technical risk and accelerate the path to commercial usefulness.

91�� is progressing on that path.

Last year, in partnership with Microsoft, we published a breakthrough in logical computing, demonstrating logical qubits that outperformed their physical counterparts by a factor of 800. We are proud to announce that this work is now being published in Nature, one of the most highly regarded scientific journals in the world.

This work highlights our leading fidelities, as shown in Table 1:

Since then, we’ve accelerated our efforts to reach large-scale fault tolerance and advanced what we believe to be the core building blocks of fault-tolerant quantum computing, from logical-qubit teleportation and multiple error-correction breakthroughs to one of the first meaningful computations using logical qubits. Importantly, these results were achieved on commercial 91�� hardware, demonstrating not just scientific progress, but a practical and efficient path toward scalable, customer-ready fault tolerance.

A Recap of Our Recent Technical Progress‍

Since the work with Microsoft, we achieved a milestone years ahead of schedule, demonstrating high-fidelity teleportation of a logical qubit, which was published in one of the world’s most prestigious journals. Later, we beat our own record in this crucial fault tolerance milestone, thanks to continued improvements to our System Model H2’s fidelity.

Then, a series of results demonstrating more error-correcting milestones (and codes):

Better than physical results in a ,
(which significantly reduces resource requirements) in 4 dimensions
with a concatenated code
Observed with concatenated codes
High fidelity magic states and a fully fault tolerant universal gate set in two

Recently, we topped ourselves yet again by performing one of the first meaningful computations with logical qubits – exploring key questions in materials and magnetism, using . This result also includes a leading “encoding rate” squeezing 48 logical qubits out of just 98 physical qubits, emphasizing how our architecture helps to support large scale fault tolerance without enormous resource costs.

It is worth noting that all these results were achieved on our commercial hardware, not on one-off laboratory test-stands – reflecting the performance that we are able to deliver to our customers.

We also did crucial theoretical work, exploring that can reduce resource requirements, time to solution, and shorten the timeline to large scale fault tolerance.

Commercial Implications and the Road Ahead

We believe the commercial implication is clear: 91�� is reducing the uncertainty around the path to fault-tolerant quantum computing. Our architecture, hardware fidelity, full-stack control, and error-correction progress are converging into a practical roadmap for systems that can support valuable scientific and commercial workloads.

For those evaluating when quantum computing will become strategically relevant, we believe the signal is also increasingly clear: the fault-tolerant era is no longer a distant concept. It is becoming an engineering reality, and 91�� is leading the way.

technical

All

Blog

partnership

May 7, 2026

Denmark Strengthens its Quantum Leadership with 91�� Helios

University of Southern Denmark (SDU) to use 91�� 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), 91��, and the Danish e-Infrastructure Consortium (DeiC) will utilize 91�� 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 91��’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 91��.

The initiative is supported by DeiC, which played a central role in securing funding and enabling access to 91��’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 91��.”
‍
— 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.

partnership

All

Blog

corporate

March 25, 2026

Celebrating Our First Annual Q-Net Connect!

This month, 91�� 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 91�� systems.

The program was packed with inspiring keynotes, technical tracks, and customer presentations. Attendees heard from leaders at 91��, 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 91�� Q-Net user community is to create a space for shared learning, collaboration and connection for those who adopt 91��’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 91�� hardware, which they published in a December 2025 .
Qedma, a quantum software startup, received the ‘Startup Partner Engagement’ award for their sustained engagement with 91�� 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 91�� 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.

corporate

All

events

All

Cookie Preferences

Integrity & Compliance

91����