By Dr. Noah Berthusen

The earliest works on quantum error correction showed that by combining many noisy physical qubits into a complex entangled state called a "logical qubit," this state could survive for arbitrarily long times. QEC researchers devote much effort to hunt for codes that function well as "quantum memories," as they are called. Many promising code families have been found, but this is only half of the story.

Being able to keep a qubit around for a long time is one thing, but to realize the theoretical advantages of quantum computing we need to run quantum circuits. And to make sure noise doesn't ruin our computation, these circuits need to be run on the logical qubits of our code. This is often much more challenging than performing gates on the physical qubits of our device, as these "logical gates" often require many physical operations in their implementation. What's more, it often is not immediately obvious which logical gates a code has, and so converting a physical circuit into a logical circuit can be rather difficult.

Some codes, like the famous surface code, are good quantum memories and also have easy logical gates. The drawback is that the ratio of physical qubits to logical qubits (the "encoding rate") is low, and so many physical qubits are required to implement large logical algorithms. High-rate codes that are good quantum memories have also been found, but computing on them is much more difficult. The holy grail of QEC, so to speak, would be a high-rate code that is a good quantum memory and also has easy logical gates. Here, we make progress on that front by developing a new code with those properties.

Building on prior error correcting codes

A recent work from Quantinuum QEC researchers introduced genon codes. The underlying construction method for these codes, called the "symplectic double cover," also provided a way to obtain logical gates that are well suited for Quantinuum's QCCD architecture. Namely, these "SWAP-transversal" gates are performed by applying single qubit operations and relabeling the physical qubits of the device. Thanks to the all-to-all connectivity facilitated through qubit movement on the QCCD architecture, this relabeling can be done in software essentially for free. Combined with extremely high fidelity (~1.2 x10^-5) single-qubit operations, the resulting logical gates are similarly high fidelity.

Given the promise of these codes, we take them a step further in our new paper. We combine the symplectic double codes with the [[4,2,2]] Iceberg code using a procedure called "code concatenation". A concatenated code is a bit like nesting dolls, with an outer code containing codes within it---with these too potentially containing codes. More technically, in a concatenated code the logical qubits of one code act as the physical qubits of another code.

The new codes, which we call "concatenated symplectic double codes", were designed in such a way that they have many of these easily-implementable SWAP-transversal gates. Central to its construction, we show how the concatenation method allows us to "upgrade" logical gates in terms of their ease of implementation; this procedure may provide insights for constructing other codes with convenient logical gates. Notably, the SWAP-transversal gate set on this code is so powerful that only two additional operations (logical T and S) are necessary for universal computation. Furthermore, these codes have many logical qubits, and we also present numerical evidence to suggest that they are good quantum memories.

Concatenated symplectic double codes have one of the easiest logical computation schemes, and we didn’t have to sacrifice rate to achieve it. Looking forward in our roadmap, we are targeting hundreds of logical qubits at ~ 1x 10^-8 logical error rate by 2029. These codes put us in a prime position to leverage the best characteristics of our hardware and create a device that can achieve real commercial advantage.

Every year, the International Conference for High Performance Computing, Networking, Storage, and Analysis (SC) brings together the global supercomputing community to explore the technologies driving the future of computing.

At this year’s conference, from November 16^th – 21^st in St. Louis, Missouri, Quantinuum showcased how our quantum hardware, software, and partnerships are helping define the next era of high-performance and quantum computing.

Quantinuum in the Expo Hall

The Quantinuum team was on-site at booth #4432 to showcase how we’re building the bridge between HPC and quantum. Folks stopped by our booth to see: 

• Live demo unit of our quantum hardware
• Our new Helios replica, providing an up-close look at the design behind our next-generation system
• The Helios chip, highlighting the innovation driving the world’s most advanced trapped-ion quantum computers

Our quantum computing experts hosted daily tutorials at our booth on Helios, our next-generation hardware platform, Nexus, our all-in-one quantum computing platform, and Hybrid Workflows, featuring the integration of NVIDIA CUDA-Q with Quantinuum Systems.

Speaking Sessions at SC25

Join our team as they share insights on the opportunities and challenges of quantum integration within the HPC ecosystem:

Panel Session: The Quantum Era of HPC: Roadmaps, Challenges and Opportunities in Navigating the Integration Frontier
November 19^th | 10:30 – 12:00pm CST

During this panel session, Kentaro Yamamoto from Quantinuum, will join experts from Lawrence Berkeley National Laboratory, IBM, QuEra, RIKEN, and Pawsey Supercomputing Research Centre to explore how quantum and classical systems are being brought together to accelerate scientific discovery and industrial innovation.

BoF Session: Bridging the Gap: Making Quantum-Classical Hybridization Work in HPC
November 19^th | 5:15 – 6:45pm CST

Quantum-classical hybrid computing is moving from theory to reality, yet no clear roadmap exists for how best to integrate quantum processing units (QPUs) into established HPC environments. In this Birds of a Feather discussion, co-led by Quantinuum’s Grahame Vittorini and representatives from BCS, DOE, EPCC, Inria, ORNL NVIDIA, and RIKEN we hope to bring together a global community of HPC practitioners, system architects, quantum computing specialists and workflow researchers, including participants in the Workflow Community Initiative, to assess the state of hybrid integration and identify practical steps toward scalable, impactful deployment.

Quantinuum’s real world experiment, on the world’s most powerful quantum computer, is the largest of its kind— so large that no amount of classical computing could match it

In 1911, a student working under famed physicist Heike Kamerlingh Onnes made a discovery that would rewire our understanding of electricity. The student was studying the electrical resistance of wires, a seemingly simple question that held secrets destined to surprise the world. 

Kamerlingh Onnes had recently succeeded in liquefying helium, a feat so impressive it earned him the Nobel Prize in Physics two years later. With this breakthrough, scientists could now immerse other materials in a cold bath of liquid Helium, cooling things to unprecedented temperatures and observing their behavior.

Many theories existed about what would happen to a wire at such low temperatures. Lord Kelvin predicted that electrons would freeze in place, making the resistance infinite and stopping the conduction of electricity. Others expected resistance to decrease linearly with temperature—a hypothesis that led to thermometer designs still in use today.

When the student cooled a mercury wire to 3.6 degrees above absolute zero, he found something remarkable: the electrical resistivity suddenly vanished.

Onnes quickly devised an ingenious experiment: as a diligent researcher, he knew that he needed to validate these surprising findings. He took a closed loop of wire, set a current running through it, and watched as it flowed endlessly without fading—a type of perpetual motion that seemed to defy everything we know about physics. And so, superconductivity was born. 

More than a century later, all known superconductors still require extreme conditions like brutal cold or high pressure. If we could instead design a material that superconducts at room temperature, and under normal conditions, our world would be profoundly reshaped.  “Room temperature superconductivity”, as it is generally called, would enable a raft of technological breakthroughs from affordable MRI machines to nearly lossless power grids.

Designing such a material means answering many open questions, and scientists are pursuing diverse strategies to find answers. One promising approach is light-induced superconductivity. In one astonishing study, researchers at the Max Planck Institute in Hamburg used light to entice a material that normally superconducts at roughly -180 °C to superconduct at room temperature - but only for a few picoseconds. This effect raised new questions: how does light achieve something that scientists have been grappling with for decades? What is the microscopic mechanism behind this phenomenon? Could understanding it unlock practical room-temperature superconductors?

Nature’s language is mathematics and mathematics is the language of the world’s most powerful quantum computer, Helios

Physics is a surprisingly profound field when you stop to think about it. At its core lies the idea that nature speaks the language of mathematics—and that by discovering the right equations, we can reveal her secrets. As bold as that sounds, history has proven it true time and again. Whenever we peek behind the veil; mathematics is there.

To understand a phenomena like superconductivity, physicists first need a mathematical model, or a set of equations that describe how it works. With the right model, they can predict and even design new superconductors that operate under more practical conditions. This is a key frontier in the search for room temperature superconductors, one of science’s holy grails.

Since the discovery of superconductivity, a lot of work has gone into finding this right model – one that can act as a sort of ‘Rosetta stone’ for harnessing this phenomenon. One of the best bets for describing high temperature superconductors like the one in the Hamburg study is called the “non-equilibrium Fermi-Hubbard” model, which describes how electrons interact and move in a crystal. 

A surprising element of models that describe superconductivity is the prediction that electrons ‘pair up’ when the material becomes superconducting, dancing around in a waltz, two at a time. These pairs are referred to as “cooper pairs” after the famous physicist Leon Cooper. Now, scientists studying superconductors look for “pairing correlations”, a key signature of superconductivity.

Even armed with the Fermi-Hubbard model, light-induced superconductivity has been very difficult to study. The world’s most powerful supercomputers can only handle very small versions, limiting their utility. Even quantum platforms, like analog simulators, limit researchers to observing ‘average’ quantities and obscuring the microscopic details that are crucial for unravelling this mystery.

Light-induced superconductivity has proved challenging to study with quantum computers as well, as doing so requires low error rates, many qubits, and extreme flexibility to measure the fickle symptoms of superconductivity.

That was, until now: Quantinuum’s Helios is one of the first machines in the world able to handle the complexity of the non-equilibrium Fermi-Hibbard model at scales previously out of reach. 

Hopping across the lattice and connecting the dots

Before Helios, we were limited to small explorations of this model, stalling research on this critical frontier. Now, with Helios, we have a quantum computer uniquely suited for this problem. With a novel fermionic encoding and using up to 90 qubits (72 system qubits plus 18 ancilla), Helios can simulate the dynamics of a 6×6 lattice — a system so large that its full quantum state spans over 2^72 dimensions.

Using Helios to study a system like this offers researchers a sort of “qubit-based laboratory.” Capable of handling complex quantum mechanical effects better than classical computers, Helios allows researchers to thoroughly explore phenomena like this without wasting expensive laboratory time and materials, or spending lots of money and energy running it on a supercomputer. 

Our qubit-based laboratory is a dream come true for several reasons. First, it allows arbitrary state preparation – preparing states far from equilibrium, a challenging task for classical computers. Second, it allows for meaningfully long ‘dynamical simulation’ – seeing how the state evolves in time as entanglement spreads and complexity increases. This is notoriously difficult for classical computers, in part due to their difficulty with handling distinctly quantum phenomena like entanglement. Finally, it allows for flexible measurements and experimental parameters – you can measure any observable, including critical “off-diagonal” observables that carry the signature of superconductivity, and simulate any system, such as those with laser pulses or electric fields. 

This last point is the most significant. While analog quantum simulators, like cold atom systems, can take snapshots of atom positions or measure densities, they struggle with off-diagonal observables—the very ones that signal the formation of Cooper pairs in superconductors.

Breaking new ground: a light-induced pairing

In our work, we've simulated three different regimes of the Fermi-Hubbard model and successfully measured non-zero superconducting pairing correlations — a first for any quantum computing platform.

We began by preparing a low-energy state of the model at half-filling — a standard benchmark for testing quantum simulations. Then, using simulated laser pulses or electric fields, we perturbed the system and observed how it responded.

After these perturbations, we measured a notable increase in the so-called “eta” pairing correlations, a mathematical signature of superconducting behavior. These results prove that our computers can help us understand light-induced superconductivity, such as the results from the Max Planck researchers. However, unlike those physical experiments, Helios offers a new level of control and insight. By tuning every aspect of the simulation — from pulse shape, to field strength, to lattice geometry — researchers can explore scenarios that are completely inaccessible to real materials or analog simulators.

Looking to a future where superconductors permeate our lives

Why does any of this matter? If we could predict which materials will become superconducting — and at what temperature, field, or current — it would transform how we search for new superconductors. Instead of trial-and-error in the lab, scientists could design and test new materials digitally first, saving huge amounts of time and money.

In the long run, Helios and its successors will become essential tools for materials science — not just confirming theories but generating new ones. And perhaps, one day, they’ll help us crack the code behind room-temperature superconductors.

Until then, the quantum revolution continues, one entangled pair at a time.

We’re pleased to introduce Helios, a technological marvel redefining the possible. 

Building on its predecessor H2, which has already breached quantum advantage, Helios nearly doubles the qubit count and surpasses H2’s industry-leading fidelity, pushing further into the quantum advantage regime than any system before it. With unprecedented capability across its full stack, Helios is the most powerful quantum computer in the world. 

“Helios is a true marvel—a seamless fusion of hardware and software, creating a platform for discovery unlike any other.”- Dr. Rajeeb Hazra, CEO 

Helios’ groundbreaking design and advanced software stack bring quantum programming closer than ever to the ease and flexibility of classical computing—positioning Helios to accelerate commercial adoption. Even before its public debut, Helios had already demonstrated its capabilities as the world’s first enterprise-grade quantum computer. During a two-month early access program, select partners including SoftBank Corp. and JPMorgan Chase conducted commercially relevant research. We also leveraged Helios to perform large-scale simulations in high-temperature superconductivity and quantum magnetism—both with clear pathways to real-world industry applications.

Helios is now available to all customers through our cloud service and on-premise offering, including an option to integrate with NVIDIA GB200 for applications targeting specific end markets.     

A Stellar Quantum Computer 

“You would need to harvest every star in the universe to power a classical machine that could do the same calculations we did with Helios."
- Dr. Anthony Ransford, Helios Lead Architect

As we detailed in a benchmarking paper, Helios sets a new standard for quantum computing performance with the highest fidelity ever released to the market. It features 98 fully connected physical qubits with single-qubit gate fidelity of 99.9975% and two-qubit gate fidelity of 99.921% across all qubit pairs—making it the most accurate commercial quantum computer in the world.  

Our fidelity shines in system-level benchmarks, such as Random Circuit Sampling (RCS), famously used by Google to demonstrate quantum supremacy when it performed an RCS task that would take a classical computer “10 septillion years” to replicate. Now, RCS serves as both a benchmark and the minimum standard for serious competitors in the market. Frequently missed in this conversation, however, is the importance of fidelity, or accuracy. That's why, when benchmarking Helios using RCS, we report the fidelity achieved by Helios on circuits of varying complexity (with complexity quantified by power requirements for classical simulation).

Our results show a classical supercomputer would require more power than the Sun—or, in fact, the combined power of all stars in the visible universe—to complete the same task in the same amount of time. In contrast, Helios achieved it using roughly the power of a single data center rack. 

Like its predecessors, H1 and H2, Helios is designed to improve fidelity and overall system performance over time while sustaining competitive leadership through the launch of its successor.

Qubits at a Crossroads

"When I first saw the rotatable ion storage ring with a junction and gating legs sketched on a napkin, I loved the idea for its simplicity and efficiency. Seeing it finally realized after all of the team’s hard work has been truly incredible." 
- Dr. John Gaebler, Fellow and Chief Scientist, Quantinuum

The Helios ion trap uses tiny currents to generate electromagnetic fields that hold single atomic ions (qubits) hovering above the trap for computation. We introduced a first-of-its-kind “junction”, which acts like a traffic intersection for qubits, enabling efficient routing and improved reliability. This is not only the first commercial implementation of this engineering triumph but it also allows our QCCD (Quantum Charged Coupled Device) architecture to scale, with future systems featuring hundreds of junctions arranged like a city street grid.   

‍

Whereas predecessor systems routed qubits using “physical swaps,” requiring sequential sorting, cooling, and gating that prevented parallel operations, the Helios QPU instead resembles a classical architecture with dedicated memory, cache, and computational zones. Like a spinning hard drive, the Helios QPU rotates qubits through ring storage (memory), passes them through the junction into the cache, moves them to logic zones for gating, and moves them to the leg storage while the next batch is processed. Sorting can now be done in parallel with cooling operations, resulting in a processor that is faster and less error prone.  This parallelism will become a hallmark of Quantinuum’s future generations, enabling faster operating speeds.

Animation: This triumph of engineering demonstrates exquisite control over some of nature’s smallest particles in a way the world has never seen; one colleague likened the ions to a “little marching band.”

Quantinuum’s QCCD provides full all-to-all connectivity, giving the Helios QPU significant advantages over “fixed qubit” architectures, such as those used in superconducting systems. Its ability to physically move qubits around and entangle any qubit with any other qubit enables algorithms and error-correcting codes that are functionally impossible for fixed qubit architectures. 

We made another “tiny” but significant change: we switched our qubits from ytterbium to barium. Whereas ytterbium largely relied on ultraviolet lasers that are expensive and hard on other components, barium can be manipulated with lasers in the visible part of the spectrum, where mature industrial technology exists, providing a more affordable, reliable and scalable commercial solution.

Barium also naturally allows the quantum computer to detect and remove a certain type of error, known as leakage, at the atomic level. By addressing this error directly, programmers can enhance the performance of their computation.

Delivered on Time – in Real Time

As announced earlier this year, Helios launched with a completely new stack equipped with a new software environment that makes quantum programming feel as intuitive as classical development. 

Our new stack also features a real-time engine that massively improves our capability. With a real-time control system, we are evolving from static, pre-planned circuits to dynamic quantum programs that respond to results on the fly. We can now, for the first time on a quantum computer, interleave GPU-accelerated classical and quantum computations in a single program. 

Our real-time engine also means we have dynamic transport – routing qubits as the moment demands reduces time to solution and diminishes the impact of memory errors.  

‍

‍

Programmers can now use our new quantum programming language, Guppy, to write dynamic circuits that were previously impossible. By combining Guppy with our real-time engine, developers can leverage arbitrary control flow driven by quantum measurements, as well as full classical computation—including loops, higher-order functions, early exits, and dynamic qubit allocation. Far from being mere conveniences, these capabilities are essential stepping stones toward achieving fault-tolerant quantum computing at scale—putting us decisively ahead of the competition.

Fully compatible with industry standards like QIR and tools such as NVIDIA CUDA-Q, Helios bridges classical and quantum computing more seamlessly than ever, making hybrid quantum-classical development simple, natural, and accessible, and establishing Helios as the most programmable, general-purpose quantum computer ever built.  

The Most Logical Path to Fault Tolerance

While everyone else is promising fault-tolerance, we’re delivering it. We are the only company to demonstrate a fully universal fault-tolerant gate set, we’ve demonstrated more codes than anyone else, and our logical fidelities are the best in class.

Now, with 98 physical qubits, we’ve been able to make 94 logical qubits, fully entangled in one of the largest GHZ states ever recorded. We did this with better than break-even fidelity, meaning they outperform physical qubits running the same algorithm. Built on our Iceberg code, published last year in Nature Physics, these logical qubits achieve the industry’s highest encoding efficiency, needing only two ancilla qubits per code block, or roughly a 1:1 physical-to-logical qubit ratio.

With 50 error-detected logical qubits, Helios achieved better than break-even performance, running the largest encoded simulation of quantum magnetism to date—an exceptional example of how users can leverage efficient encodings. This range and flexibility let users tailor the encoding rate to their application: fewer logical qubits deliver higher fidelity for less complex tasks, while larger sets enable more complex simulations.

Helios also produced 48 fully error-corrected logical qubits at a remarkable 2:1 encoding rate, a ratio thought impossible just a few years ago. This super high encoding rate stands in stark contrast to other notable demonstrations from industry peers. For example, the demonstration linked in the previous sentence would need a whopping 4800 qubits to make 48 logical qubits. Our 2:1 encoding rate was achieved through a clever technique called code concatenation, a breakthrough that supports single-shot error correction, transversal logic, and full parallelization—all at 99.99% state preparation and measurement fidelity. 

To extend this performance at scale, all future Quantinuum systems—starting with Helios—will integrate real-time decoding using NVIDIA Grace Hopper GPUs, treating decoding as a dynamic computational process rather than a static lookup. Errors can be corrected as computations run without slowing the logical clock rate. Combined with Guppy, NVIDIA CUDA-Q, and NVQLink, this infrastructure forms the foundation for fault-tolerant, real-time quantum computation, delivering immediate quantum advantage in the near term and a clear path to scalable error-corrected computing. 

We remain the only company to perform a fully universal fault-tolerant gate set, with more error-correcting codes and higher logical fidelities than any other company.

Helios is ready to drive practical, commercial quantum applications across industries. Its unprecedented fidelity, scalability, and programmability give users the tools to tackle problems that were previously out of reach. This is just the beginning, and we look forward to seeing what users and companies will achieve with it. 

Read the Helios data sheet

Dive deeper into Helios performance specs

Typically, Quantum Error Detection (QED) is viewed as a short-term solution—a non-scalable, stop-gap until full fault tolerance is achieved at scale.

That’s just changed, thanks to a serendipitous discovery made by our team. Now, QED can be used in a much wider context than previously thought. Our team made this discovery while studying the contact process, which describes things like how diseases spread or how water permeates porous materials. In particular, our team was studying the quantum contact process (QCP), a problem they had tackled before, which helps physicists understand things like phase transitions. In the process (pun intended), they came across what senior advanced physicist, Eli Chertkov, described as “a surprising result.”

While examining the problem, the team realized that they could convert detected errors due to noisy hardware into random resets, a key part of the QCP, thus avoiding the exponentially costly overhead of post-selection normally expected in QED.

To understand this better, the team developed a new protocol in which the encoded, or logical, quantum circuit adapts to the noise generated by the quantum computer. They quickly realized that this method could be used to explore other classes of random circuits similar to the ones they were already studying.

The team put it all together on System Model H2 to run a complex simulation, and were surprised to find that they were able to achieve near break-even results, where the logically encoded circuit performed as well as its physical analog, thanks to their clever application of QED.  Ultimately, this new protocol will allow QED codes to be used in a scalable way, saving considerable computational resources compared to full quantum error correction (QEC).

Researchers at the crossroads of quantum information, quantum simulation, and many-body physics will take interest in this protocol and use it as a springboard for inventing new use cases for QED.

Stay tuned for more, our team always has new tricks up their sleeves.

Learn mode about System Model H2 with this video:

By Konstantinos Meichanetzidis

When will quantum computers outperform classical ones?

This question has hovered over the field for decades, shaping billion-dollar investments and driving scientific debate.

The question has more meaning in context, as the answer depends on the problem at hand. We already have estimates of the quantum computing resources needed for Shor’s algorithm, which has a superpolynomial advantage for integer factoring over the best-known classical methods, threatening cryptographic protocols. Quantum simulation allows one to glean insights into exotic materials and chemical processes that classical machines struggle to capture, especially when strong correlations are present. But even within these examples, estimates change surprisingly often, carving years off expected timelines. And outside these famous cases, the map to quantum advantage is surprisingly hazy.

Researchers at Quantinuum have taken a fresh step toward drawing this map. In a new theoretical framework, Harry Buhrman, Niklas Galke, and Konstantinos Meichanetzidis introduce the concept of “queasy instances” (quantum easy) – problem instances that are comparatively easy for quantum computers but appear difficult for classical ones.

From Problem Classes to Problem Instances

Traditionally, computer scientists classify problems according to their worst-case difficulty. Consider the problem of Boolean satisfiability, or SAT, where one is given a set of variables (each can be assigned a 0 or a 1) and a set of constraints and must decide whether there exists a variable assignment that satisfies all the constraints. SAT is a canonical NP-complete problem, and so in the worst case, both classical and quantum algorithms are expected to perform badly, which means that the runtime scales exponentially with the number of variables. On the other hand, factoring is believed to be easier for quantum computers than for classical ones. But real-world computing doesn’t deal only in worst cases. Some instances of SAT are trivial; others are nightmares. The same is true for optimization problems in finance, chemistry, or logistics. What if quantum computers have an advantage not across all instances, but only for specific “pockets” of hard instances? This could be very valuable, but worst-case analysis is oblivious to this and declares that there is no quantum advantage.

To make that idea precise, the researchers turned to a tool from theoretical computer science: Kolmogorov complexity. This is a way of measuring how “regular” a string of bits is, based on the length of the shortest program that generates it. A simple string like 0000000000 can be described by a tiny program (“print ten zeros”), while the description of a program that generates a random string exhibiting no pattern is as long as the string itself. From there, the notion of instance complexity was developed: instead of asking “how hard is it to describe this string?”, we ask “how hard is it to solve this particular problem instance (represented by a string)?” For a given SAT formula, for example, its polynomial-time instance complexity is the size of the smallest program that runs in polynomial time and decides whether the formula is satisfiable. This smallest program must be consistently answering all other instances, and it is also allowed to declare “I don’t know”.

In their new work, the team extends this idea into the quantum realm by defining polynomial-time quantum instance complexity as the size of the shortest quantum program that solves a given instance and runs on polynomial time. This makes it possible to directly compare quantum and classical effort, in terms of program description length, on the very same problem instance. If the quantum description is significantly shorter than the classical one, that problem instance is one the researchers call “queasy”: quantum-easy and classically hard. These queasy instances are the precise places where quantum computers offer a provable advantage – and one that may be overlooked under a worst-case analysis.

Why “Queasy”?

The playful name captures the imbalance between classical and quantum effort. A queasy instance is one that makes classical algorithms struggle, i.e. their shortest descriptions of efficient programs that decide them are long and unwieldy, while a quantum computer can handle the same instance with a much simpler, faster, and shorter program. In other words, these instances make classical computers “queasy,” while quantum ones solve them efficiently and finding them quantum-easy. The key point of these definitions lies in demonstrating that they yield reasonable results for well-known optimisation problems.

By carefully analysing a mapping from the problem of integer factoring to SAT (which is possible because factoring is inside NP and SAT is NP-complete) the researchers prove that there exist infinitely many queasy SAT instances. SAT is one of the most central and well-studied problems in computer science that finds numerous applications in the real-world. The significant realisation that this theoretical framework highlights is that SAT is not expected to yield a blanket quantum advantage, but within it lie islands of queasiness – special cases where quantum algorithms decisively win.

Algorithmic Utility

Finding a queasy instance is exciting in itself, but there is more to this story. Surprisingly, within the new framework it is demonstrated that when a quantum algorithm solves a queasy instance, it does much more than solve that single case. Because the program that solves it is so compact, the same program can provably solve an exponentially large set of other instances, as well. Interestingly, the size of this set depends exponentially on the queasiness of the instance!

Think of it like discovering a special shortcut through a maze. Once you’ve found the trick, it doesn’t just solve that one path, but reveals a pattern that helps you solve many other similarly built mazes, too (even if not optimally). This property is called algorithmic utility, and it means that queasy instances are not isolated curiosities. Each one can open a doorway to a whole corridor with other doors, behind which quantum advantage might lie.

A North Star for the Field

Queasy instances are more than a mathematical curiosity; this is a new framework that provides a language for quantum advantage. Even though the quantities defined in the paper are theoretical, involving Turing machines and viewing programs as abstract bitstrings, they can be approximated in practice by taking an experimental and engineering approach. This work serves as a foundation for pursuing quantum advantage by targeting problem instances and proving that in principle this can be a fruitful endeavour.

The researchers see a parallel with the rise of machine learning. The idea of neural networks existed for decades along with small scale analogue and digital implementations, but only when GPUs enabled large-scale trial and error did they explode into practical use. Quantum computing, they suggest, is on the cusp of its own heuristic era. “Quristics” will be prominent in finding queasy instances, which have the right structure so that classical methods struggle but quantum algorithms can exploit, to eventually arrive at solutions to typical real-world problems. After all, quantum computing is well-suited for small-data big-compute problems, and our framework employs the concepts to quantify that; instance complexity captures both their size and the amount of compute required to solve them.

Most importantly, queasy instances shift the conversation. Instead of asking the broad question of when quantum computers will surpass classical ones, we can now rigorously ask where they do. The queasy framework provides a language and a compass for navigating the rugged and jagged computational landscape, pointing researchers, engineers, and industries toward quantum advantage.