How a little known but essential operation in Quantum Computing helped achieve a major scientific breakthrough

ҹɫֱ��'s feed-forward functionality is worth getting to know

June 29, 2023

ҹɫֱ��’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 ҹɫֱ��’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, ҹɫֱ�� 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 (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 ҹɫֱ��’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 “”, ҹɫֱ��, 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 ҹɫֱ��, 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 “”.��

Two of ҹɫֱ��’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 ҹɫֱ��’s office in Munich, Germany.

Michael, who is based at ҹɫֱ��’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.

ҹɫֱ��’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 ҹɫֱ��’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 ҹɫֱ��

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

Blog

June 26, 2025

ҹɫֱ�� Overcomes Last Major Hurdle to Deliver Scalable Universal Fault-Tolerant Quantum Computers by 2029

Quantum computing companies are poised to exceed $1 billion in revenues by the close of 2025, to McKinsey & Company, underscoring how today’s quantum computers are already delivering customer value in their current phase of development.

This figure is projected to reach upwards of $37 billion by 2030, rising in parallel with escalating demand, as well as with the scale of the machines and the complexity of problem sets of which they will be able to address.

Several systems on the market today are fault-tolerant by design, meaning they are capable of suppressing error-causing noise to yield reliable calculations. However, the full potential of quantum computing to tackle problems of true industrial relevance, in areas like medicine, energy, and finance, remains contingent on an architecture that supports a fully fault-tolerant universal gate set with repeatable error correction—a capability that, until now, has eluded the industry.

ҹɫֱ�� is the first—and only—company to achieve this critical technical breakthrough, universally recognized as the essential precursor to scalable, industrial-scale quantum computing. This milestone provides us with the most de-risked development roadmap in the industry and positions us to fulfill our promise to deliver our universal, fully fault-tolerant quantum computer, Apollo, by 2029.

In this regard, ҹɫֱ�� is the first company to step from the so-called “NISQ” (noisy intermediate-scale quantum) era towards utility-scale quantum computers.

Unpacking our achievement: first, a ‘full’ primer

A quantum computer uses operations called gates to process information in ways that even today’s fastest supercomputers cannot. The industry typically refers to two types of gates for quantum computers:

Clifford gates, which can be easily simulated by classical computers, and are relatively easy to implement; and
Non-Clifford gates, which are usually harder to implement, but are required to enable true quantum computation (when combined with their siblings).

A system that can run both gates is classified as and has the machinery to tackle the widest range of problems. Without non-Clifford gates, a quantum computer is non-universal and restricted to smaller, easier sets of tasks - and it can always be simulated by classical computers. This is like painting with a full palette of primary colors, versus only having one or two to work with. Simply put, a quantum computer that cannot implement ‘non-Clifford’ gates is not really a quantum computer.

A fault-tolerant, or error-corrected, quantum computer detects and corrects its own errors (or faults) to produce reliable results. ҹɫֱ�� has the best and brightest scientists dedicated to keeping our systems’ error rates the lowest in the world.

For a quantum computer to be fully fault-tolerant, every operation must be error-resilient, across Clifford gates and non-Clifford gates, and thus, performing “a full gate set” with error correction. While some groups have performed fully fault-tolerant gate sets in academic settings, these demonstrations were done with only a few qubits and —too high for any practical use.

Today, we have published that establishes ҹɫֱ�� as the first company to develop a complete solution for a universal fully fault-tolerant quantum computer with repeatable error correction, and error rates low enough for real-world applications.

This is where the magic happens

The describes how scientists at ҹɫֱ�� used our System Model H1-1 to perfect magic state production, a crucial technique for achieving a fully fault-tolerant universal gate set. In doing so, they set a record magic state infidelity (7x10^-5), 10x better than any .

Our simulations show that our system could reach a magic state infidelity of 10^-10, or about one error per 10 billion operations, on a larger-scale computer with our current physical error rate. We anticipate reaching 10^-14, or about one error per 100 trillion operations, as we continue to advance our hardware. This means that our roadmap is now derisked.

Setting a record magic state infidelity was just the beginning. The paper also presents the first break-even two-qubit non-Clifford gate, demonstrating a logical error rate below the physical one. In doing so, the team set another record for two-qubit non-Clifford gate infidelity (2x10^-4, almost 10x better than our physical error rate). Putting everything together, the team ran the first circuit that used a fully fault-tolerant universal gate set, a critical moment for our industry.

Flipping the switch

In the , co-authored with researchers at the University of California at Davis, we demonstrated an important technique for universal fault-tolerance called “code switching”.

Code switching describes switching between different error correcting codes. The team then used the technique to demonstrate the key ingredients for universal computation, this time using a code where we’ve previously demonstrated full error correction and the other ingredients for universality.

In the process, the team set a new record for magic states in a distance-3 error correcting code, over 10x better than with error correction. Notably, this process only cost 28 qubits . This completes, for the first time, the ingredient list for a universal gate setin a system that also has real-time and repeatable QEC.

To perform "code switching", one can implement a logical gate between a 2D code and a 3D code, as pictured above. This type of advanced error correcting process requires ҹɫֱ��'s reconfigurable connectivity.

Fully equipped for fault-tolerance

Innovations like those described in these two papers can reduce estimates for qubit requirements by an order of magnitude, or more, bringing powerful quantum applications within reach far sooner.

With all of the required pieces now, finally, in place, we are ‘fully’ equipped to become the first company to perform universal fully fault-tolerant computing—just in time for the arrival of Helios, our next generation system launching this year, and what is very likely to remain as the most powerful quantum computer on the market until the launch of its successor, Sol, arriving in 2027.

technical

All

Blog

June 10, 2025

Our Hardware is Now Running Quantum Transformers!

If we are to create ‘next-gen’ AI that takes full advantage of the power of quantum computers, we need to start with quantum native transformers. Today we announce yet again that ҹɫֱ�� continues to lead by demonstrating concrete progress — advancing from theoretical models to real quantum deployment.

The future of AI won't be built on yesterday’s tech. If we're serious about creating next-generation AI that unlocks the full promise of quantum computing, then we must build quantum-native models—designed for quantum, from the ground up.

Around this time last year, we introduced Quixer, a state-of-the-art quantum-native transformer. Today, we’re thrilled to announce a major milestone: one year on, Quixer is now running natively on quantum hardware.

Why this matters: Quantum AI, born native

This marks a turning point for the industry: realizing quantum-native AI opens a world of possibilities.

Classical transformers revolutionized AI. They power everything from ChatGPT to real-time translation, computer vision, drug discovery, and algorithmic trading. Now, Quixer sets the stage for a similar leap — but for quantum-native computation. Because quantum computers differ fundamentally from classical computers, we expect a whole new host of valuable applications to emerge.

Achieving that future requires models that are efficient, scalable, and actually run on today’s quantum hardware.

That’s what we’ve built.

What makes Quixer different?

Until Quixer, quantum transformers were the result of a brute force “copy-paste” approach: taking the math from a classical model and putting it onto a quantum circuit. However, this approach does not account for the considerable differences between quantum and classical architectures, leading to substantial resource requirements.

Quixer is different: it’s not a translation – it's an innovation.

With Quixer, our team introduced an explicitly quantum transformer, built from the ground up using quantum algorithmic primitives. Because Quixer is tailored for quantum circuits, it's more resource efficient than most competing approaches.

As quantum computing advances toward fault tolerance, Quixer is built to scale with it.

What’s next for Quixer?

We’ve already deployed Quixer on real-world data: genomic sequence analysis, a high-impact classification task in biotech. We're happy to report that its performance is already approaching that of classical models, even in this first implementation.

This is just the beginning.

Looking ahead, we’ll explore using Quixer anywhere classical transformers have proven to be useful; such as language modeling, image classification, quantum chemistry, and beyond. More excitingly, we expect use cases to emerge that are quantum-specific, impossible on classical hardware.

This milestone isn’t just about one model. It’s a signal that the quantum AI era has begun, and that ҹɫֱ�� is leading the charge with real results, not empty hype.

Stay tuned. The revolution is only getting started.

technical

All

Blog

June 9, 2025

Join us at ISC25

Our team is participating in (ISC 2025) from June 10-13 in Hamburg, Germany!

As quantum computing accelerates, so does the urgency to integrate its capabilities into today’s high-performance computing (HPC) and AI environments. At ISC 2025, meet the ҹɫֱ�� team to learn how the highest performing quantum systems on the market, combined with advanced software and powerful collaborations, are helping organizations take the next step in their compute strategy.

ҹɫֱ�� is leading the industry across every major vector: performance, hybrid integration, scientific innovation, global collaboration and ease of access.

Our industry-leading quantum computer holds the record for performance with a Quantum Volume of 2²³ = 8,388,608 and the highest fidelity on a commercially available QPU available to our users every time they access our systems.
Our systems have been validated by a #1 ranking against competitors in a recent benchmarking study by Jülich Research Centre.
We’ve laid out a clear roadmap to reach universal, fully fault-tolerant quantum computing by the end of the decade and will launch our next-generation system, Helios, later this year.
We are advancing real-world hybrid compute with partners such as RIKEN, NVIDIA, SoftBank, STFC Hartree Center and are pioneering applications such as our own GenQAI framework.

Exhibit Hall

From June 10–13, in Hamburg, Germany, visit us at Booth B40 in the Exhibition Hall or attend one of our technical talks to explore how our quantum technologies are pushing the boundaries of what’s possible across HPC.

Presentations & Demos

Throughout ISC, our team will present on the most important topics in HPC and quantum computing integration—from near-term hybrid use cases to hardware innovations and future roadmaps.

Multicore World Networking Event

‍Monday, June 9 | 7:00pm – 9:00 PM at Hofbräu Wirtshaus Esplanade
‍In partnership with Multicore World, join us for a ҹɫֱ��-sponsored Happy Hour to explore the present and future of quantum computing with ҹɫֱ�� CCO, Dr. Nash Palaniswamy, and network with our team.

H1 x CUDA-Q Demonstration

‍All Week at Booth B40
‍We’re showcasing a live demonstration of NVIDIA’s CUDA-Q platform running on ҹɫֱ��’s industry-leading quantum hardware. This new integration paves the way for hybrid compute solutions in optimization, AI, and chemistry.
‍Register for a demo

HPC Solutions Forum

‍Wednesday, June 11 | 2:20 – 2:40 PM
‍“Enabling Scientific Discovery with Generative Quantum AI” – Presented by Maud Einhorn, Technical Account Executive at ҹɫֱ��, discover how hybrid quantum-classical workflows are powering novel use cases in scientific discovery.

See You There!

Whether you're exploring hybrid solutions today or planning for large-scale quantum deployment tomorrow, ISC 2025 is the place to begin the conversation.

We look forward to seeing you in Hamburg!

events

All

ҹɫֱ��