IEEE Quantum Week 2024

• Helix is Quantinuum’s QEC architecture designed for scalability, leveraging reconfigurable connectivity to reduce the physical-qubit and time overhead required for fault-tolerant computation.
• The architecture has been experimentally validated on Helios, demonstrating logical memory, logical computation, and logical entanglement across different QEC codes—all outperforming corresponding physical-level results without post-selection.
• Helix provides a foundation for Apollo, combining efficient logical gates, multiple QEC encodings, and a path to universal fault-tolerant computation. The results on commercial hardware validate Quantinuum’s roadmap toward scalable, fault-tolerant quantum computing.

The NISQ¹ era is coming to an end. At Quantinuum, we’ve already demonstrated numerous QEC codes, all the primitives needed for logical computation, steadily declining logical error rates, and full computations at the logical level.

But there’s still a way to go. One of the defining challenges over the coming years will be putting it all together into a usable – and scalable – fault tolerant architecture. Today, we are excited to announce that we have experimentally validated one of our own leading candidates for such an architecture, the Helix code.

With this demonstration, we have put all the pieces together: logical memory, logical computation, a heterogenous code architecture that optimizes for magic vs gates, all with super efficient operations and record-breaking² fidelity.

The Challenge of Fault Tolerance

The delicate nature of qubits gives them their strength – they can be entangled, placed into superpositions, and even teleported. However, this comes at a cost: on the hardware level, quantum bits (qubits) will always be noisier than classical bits.

Enter quantum error correction (QEC). QEC moves us past prohibitive physical noise to fidelities that really matter; where industrial workflows and scientific discovery live. Our field has been hard at work to realize - and optimize - QEC, and we are finally starting to reap the fruits of that labor.

However, for the most part, this work has taken shape only a few pieces at a time: a demonstration of fault tolerant gates here or memory there, sometimes even a full fault-tolerant algorithm, but rarely do we see demonstrations at the architectural scale needed to build our next generation of machines.

The difficulty is that encoding and performing fault-tolerant computation costs considerable space (qubit number) and time (circuit complexity), which QEC researchers summarize with a “spacetime volume”.

‍Introducing Helix: A QEC Architecture for Apollo

The Helix code was custom-designed to usher in the next generation of fault tolerance.

Using our reconfigurable qubits, we designed Helix to minimize its spacetime volume by employing more exotic entanglement schemes compared to traditional codes (imagine cat’s cradle compared to a simple, 2D net). This entanglement complexity is impossible with processors that don’t have reconfigurable connectivity.

Ultimately, this translates to a code that requires fewer physical qubits per logical qubit, while also giving you fast and simple computing.  

In general, gates between logical qubits can be quite difficult because logical qubits are composed of physical qubits that are entangled together in some specific way. Sometimes, a single physical qubit may even be shared between multiple logical qubits, as is the case with codes that offer lots of logical qubits per physical qubit. Performing gates across these complex structures can be tricky, and can take a lot of individual operations on physical qubit pairs to accomplish.

There are two major exceptions. The first, called a transversal gate, is where the logical operation maps directly onto the physical one: you just perform a regular 2-qubit gate between each physical qubit in each logical qubit.

The second is simpler still: gates can be accomplished by simple software-level qubit relabeling (eg simply renaming qubit A to qubit B), combined with easy, single qubit gates. This type of automorphism, or permutation-based gate, is particularly elegant.

The Helix code makes heavy use of transversal and automorphism gates, making it considerably faster and easier to compute with than a lot of other options. Ultimately, this translates to a significant reduction in both space (qubit) and time (circuit complexity) overheads: less space is needed for block encoding and ancilla; and time is drastically reduced when simple software relabeling or transversal gates are performed in the place of expensive protocols like lattice surgery.

Demonstrating the Building Blocks of a Fault-Tolerant System

Experiment 1: Logical Memory

The team started by showing that the Helix code can successfully preserve encoded quantum information for extended periods of time.

To show this, the team started with their logical qubits in a given state. Then, they performed 20 rounds of syndrome extraction, paying special attention to leakage (a dominant source of error on Helios). To remove leakage, the team leveraged Helios’ new leakage repump capacity, as well as circuit-level leakage reduction units.

Result: per qubit, per round, they achieved an error rate of 4.6 x 10^-5, with no post selection.

This amounts to a block logical error per round of 9.3 x 10^-5, with no post selection. With a small amount of post selection (0.5%), the block logical error per round was reduced to 1.9 x 10^-5.

Why This Matters

Quantum memory is one of the most fundamental building blocks of a fault-tolerant quantum computer. A useful quantum processor must be able to preserve quantum information long enough to perform the computation, error correction, and communication required by larger algorithms.

These results prove that encoded quantum information can be preserved with a lower error rate than the underlying physical operations – all without needing post selection.

Experiment 2: Logical Computation

A central feature of the Helix logical architecture is that encoding multiple logical qubits does not require correspondingly expensive logical computation. By construction, this code has a variety of logical gates all implementable with only physical single-qubit gates and qubit relabeling. These ‘SWAP-transversal’, or ‘automorphism’, gates provide the ability to do some logical circuits essentially for free, as permutations are realized by simple ion-transport and software level relabeling.

The team experimentally tested the code’s computational abilities by benchmarking the complete logical Clifford group (i.e., all gates except for T gates) while interleaving up to 27 rounds of active adaptive syndrome extraction.

Result:  2.8 x 10^-4 logical error rate per Clifford gate, a significant improvement (4.28x) over Helios’ physical 2-qubit Clifford error rate, again achieved without post selection.

This impressive result is partially enabled by the team’s clever adaptive syndrome extraction (ASE) technique. Their ASE technique reduces the number of physical gates required per logical gate by about 33%. This pruning also shortens the physical run time, reducing the ‘wall clock duration’ by about 23%. Both gates and idling contribute significantly to errors, so these reductions translate to a lower logical error rate.

Why This Matters

This experiment proves the Helix code’s ability to compute, all while showing significant improvement over the physical level with no post selection. In addition, this marks the first demonstration of randomized benchmarking on a code encoding more than one logical qubit, an important milestone for our community.

Experiment 3: Universality via Logical Entanglement Across Different Codes

Clifford gates alone are insufficient for universal fault-tolerant computation; our QEC architecture must also provide access to non-Clifford resource states (often called “magic”). While the Helix code has many desirable features in terms of Clifford gates, it’s sub-optimal for preparing magic states. Rather than forcing the Helix code to work in this regime, we developed our architecture to employ two codes; one for Clifford gates and memory, and one for magic state preparation. Using different codes each optimized for their own tasks, called a heterogenous architecture, makes the entire assembly considerably more efficient and cost effective.

The trick that makes it all possible is something called chain-mapping, that allows the QPU to smoothly switch between underlying encoding schemes. To test this, the team used a rotated surface code for magic state generation, which would then be injected into the computational (Helix) code to generate non-Clifford gates (enabling fault tolerant universal computation).

Rather than performing magic state injection directly, the team wanted to benchmark the interface (the chain-map). To do this, they used their chain-mapped gates to prepare a three logical qubit GHZ state that spans the two different codes. The resulting GHZ state contained 1 logical qubit from the surface code and two from the Helix code, making for a truly heterogeneous structure.

Result: The logical GHZ state had a fidelity lower bound of 99.925%, and an upper bound of 99.975%. The lower bound exceeded the physical baseline, making all three experiments better than their physical counterparts.

Why This Matters

This experiment demonstrates one of our key architectural advantages: using our reconfigurable connectivity to employ multiple QEC encodings in a single fault tolerant architecture, improving our efficiency and reducing qubit costs.

Accelerating the Path to Apollo

The quantum computing industry has proposed many approaches to error correction. This paper marks one of the first experimentally validated plans for a QEC architecture. With the low logical error rates (all improving on the physical baseline), the practical logical operations (which drastically reduce qubit costs and compute time), and real commercial hardware performance, this result helps to prove that we will deliver on our roadmap.

A crucial element of this demonstration is that these results were obtained on our commercial hardware. This is not a result from a testbed, or a result from hardware that has limited functionality. This is a result from the same computer as our customers use for their own research.

Furthermore, simulations indicate that the improvements in physical fidelity we expect from moving from Helios to Apollo will bring logical error rates in line with our roadmap targets. Because logical error rates depend strongly on physical error rates, Apollo’s expected improvements at the physical level should translate directly into lower logical error rates. Importantly, we expect to achieve these gains without increasing the code distance or using additional physical qubits per logical qubit.

Building a fault-tolerant quantum computer requires solving multiple engineering challenges. In this result we have proven our path to a scalable QEC architecture, showing not just one-off results on test stand hardware, but a harmonious whole consisting of:

✓ A candidate architectural code

✓ Logical memory

✓ Logical computation

✓ A path to magic

✓ Multiple encodings in one architecture

✓ Commercial hardware compatibility

By validating our fault-tolerant architecture on real commercial hardware, Quantinuum has taken a significant step toward Apollo - and toward quantum computers capable of solving meaningful problems at scale.

¹ Noisy Intermediate-Scale Quantum

² Based on a study of existing literature

Progressing your organization along the five levels of quantum maturity

Quantum computing has moved from a bet on the future to a race already underway. Early adopters are locking in strategic partnerships, building proprietary IP, and positioning themselves years ahead of competitors who are still watching from the sidelines. For executives, the question isn't whether to engage with quantum computing. It's how far along that journey your organization actually is, and what it takes to move forward.

That's a harder question to answer than it sounds. Quantum maturity isn't a single milestone you either hit or miss. It's a progression, built across talent, technology access, workflow integration, partnerships, and value realization, and most organizations aren't entirely sure where they currently stand and what to do next.

Our new paper, A Roadmap for Quantum Maturity, is built to answer exactly that.

A Framework for Where You Stand, and Where to Go Next

Drawing on extensive client experience, the paper lays out five distinct levels of quantum maturity, from early awareness through full transformation, along with the leadership actions that move an organization from one level to the next.

• Awareness — early conversations, but no clear ownership or use cases yet
• Exploration — exploring partnerships and prioritizing use cases with limited budget
• Experimentation — quantum roadmap established and guiding dedicated teams, funding, and partners to execute pilot use case projects
• Integration — quantum computing applications are being embedded into business unit workflows, and the quantum roadmap is integrated with broader digital technology strategy, including AI, HPC, and data
• Transformation — quantum capabilities are embedded in core products and decision-making, with differentiated, proprietary advantage

Most industry leaders today sit at the exploration or experimentation stages, with clear ambitions to reach transformation within the next several years. The paper breaks down what separates organizations that progress from those that stall out at proof-of-concept.

The Advantage Is Built, Not Bought

One of the paper's central takeaways is one many executives underestimate: investing in quantum technology alone isn't enough. Organizations that advance fastest pair that investment with a deliberate strategy, building quantum literacy across leadership and technical teams, honestly assessing capability gaps, focusing on a small number of high-impact use cases tied to real business metrics, and defining a clear roadmap that connects research to business advantage.

How Quantinuum Can Help

Achieving quantum maturity is a journey, not a single step, and most organizations don't need to make that journey alone. Quantinuum's consulting services are built to support every stage of it, from advisory and use-case identification, to capability building, technology access, and the co-development of scalable quantum solutions.

Whether your organization is just starting to build awareness or already scaling toward transformation, our team can help you identify exactly where you stand today, and what it takes to move to the next level.

• SoftBank Corp. and Quantinuum articulated a roadmap connecting quantum algorithms, hardware evolution, and commercial applications, helping organizations understand when quantum computing can address real-world challenges.
• The analysis demonstrates that quantum value will emerge in stages, with early opportunities in data analysis and longer-term breakthroughs in scientific computing as fault-tolerant systems mature.
• The work provides a practical planning framework for enterprises preparing to integrate quantum computing alongside AI and classical high-performance computing infrastructure in quantum-AI data centers.

Quantum computing is increasingly moving from exploratory discussion to structured enterprise planning. As organizations begin to assess where and when quantum technologies may deliver real business impact, a new class of work is emerging: integrated roadmaps that connect algorithmic feasibility, hardware development, and commercial opportunity.

A recent white paper from SoftBank Corp. and Quantinuum represents one of the most comprehensive examples of this approach to date. Rather than treating quantum computing as a distant, abstract capability, the study constructs a detailed, quantitative framework for understanding how real-world use cases evolve as hardware matures—and what this means for enterprise strategy.

A Comprehensive Roadmap

The SoftBank–Quantinuum white paper is broad in scope. It attempts to answer a fundamental question:

Which real-world problems can benefit from quantum computation, at what scale, with what accuracy requirements, and under what hardware conditions?

To address this, the study adopts a structured methodology that connects:

• Algorithmic resource estimates (logical qubits, circuit depth, gate counts)
• Explicit error correction assumptions and overhead models
• Hardware roadmaps across multiple generations
• Timelines for when specific classes of problems may become feasible

Two representative domains anchor the analysis:

• ‍Quantum chemistry, particularly excited-state dynamics and photochemical processes‍
• Topological data analysis (TDA), including graph-based structure and anomaly detection

These domains were selected because they combine industrial relevance with computational structures that scale poorly on classical systems but map naturally onto quantum approaches.

Quantum chemistry is closely tied to materials science, energy systems, and the development of sustainable technologies. TDA, by contrast, offers tools for understanding complex data structures in networks, finance, and large-scale systems—where identifying structure and anomalies is increasingly critical.

Together, they illustrate how quantum computing may create value across both deep scientific domains and high-impact data applications.

An important caveat is that the resulting roadmap assumes a widely-studied but inefficient error correcting code. As more error correcting codes come online, the resources required to run algorithms will shrink. That means that the timelines detailed in this work can be thought of as “worst case” scenarios, which adds to the value by setting out a clear limit.

A distinguishing feature of the work is its emphasis on implementation over abstraction. Rather than relying solely on theoretical models, the study explicitly constructs quantum circuits and executes them on Quantinuum’s Helios and H2 system.

Parallel Paths to Value

A notable insight from the study is that quantum value creation will not follow a single linear path.

Instead, two complementary regimes are expected to emerge:

• In quantum chemistry, the focus is on fault-tolerant, logical-qubit-based computation, where error correction is essential for scaling toward meaningful scientific and industrial outcomes.
• In TDA, value can emerge earlier, where partial quantum advantage may already support useful computational tasks without full error correction.

This dual-track structure is important: it shows that quantum computing is not a single “threshold technology,” but a spectrum of capabilities that unlock value at different stages of maturity.

The Vision for Quantum Industrialization

The framework ultimately supports a broader strategic vision: the evolution of Quantum AI Data Centers—hybrid infrastructures where quantum processors operate alongside AI and classical HPC systems.

For enterprises, the implication is clear: quantum computing readiness is no longer about speculation. It is about structured preparation, disciplined modeling, and early engagement with the full stack of capabilities that will define the next generation of computational infrastructure.