Quantum Computers Will Make AI Better
Quantum computers will drive AI to new heights, enabling better accuracy and therefore better performance, and scalable sustainable growth.
Today’s LLMs are often impressive by past standards – but they are far from perfect
Quietly, and determinedly since 2019, we’ve been working on Generative Quantum AI. Our early focus on building natively quantum systems for machine learning has benefitted from and been accelerated by access to the world’s most powerful quantum computers, and quantum computers that cannot be classically simulated.
Our work additionally benefits from being very close to our Helios generation quantum computer, built in Colorado, USA. Helios is 1 trillion times more powerful than our H2 System, which is already significantly more advanced than all other quantum computers available.
While tools like ChatGPT have already made a profound impact on society, a critical limitation to their broader industrial and enterprise use has become clear. Classical large language models (LLMs) are computational behemoths, prohibitively huge and expensive to train, and prone to errors that damage their credibility.
Training models like ChatGPT requires processing vast datasets with billions, even trillions, of parameters. This demands immense computational power, often spread across thousands of GPUs or specialized hardware accelerators. The environmental cost is staggering—simply training GPT-3, for instance, consumed nearly 1,300 megawatt-hours of electricity, equivalent to the annual energy use of 130 average U.S. homes.
This doesn’t account for the ongoing operational costs of running these models, which remain high with every query.
Despite these challenges, the push to develop ever-larger models shows no signs of slowing down.
Enter quantum computing. Quantum technology offers a more sustainable, efficient, and high-performance solution—one that will fundamentally reshape AI, dramatically lowering costs and increasing scalability, while overcoming the limitations of today's classical systems.
Quantum Natural Language Processing: A New Frontier
At Quantinuum we have been maniacally focused on “rebuilding” machine learning (ML) techniques for Natural Language Processing (NLP) using quantum computers.
Our research team has worked on translating key innovations in natural language processing — such as word embeddings, recurrent neural networks, and transformers — into the quantum realm. The ultimate goal is not merely to port existing classical techniques onto quantum computers but to reimagine these methods in ways that take full advantage of the unique features of quantum computers.
We have a deep bench working on this. Our Head of AI, Dr. Steve Clark, previously spent 14 years as a faculty member at Oxford and Cambridge, and over 4 years as a Senior Staff Research Scientist at DeepMind in London. He works closely with Dr. Konstantinos Meichanetzidis, who is our Head of Scientific Product Development and who has been working for years at the intersection of quantum many-body physics, quantum computing, theoretical computer science, and artificial intelligence.
A critical element of the team’s approach to this project is avoiding the temptation to simply “copy-paste”, i.e. taking the math from a classical version and directly implementing that on a quantum computer.
This is motivated by the fact that quantum systems are fundamentally different from classical systems: their ability to leverage quantum phenomena like entanglement and interference ultimately changes the rules of computation. By ensuring these new models are properly mapped onto the quantum architecture, we are best poised to benefit from quantum computing’s unique advantages.
These advantages are not so far in the future as we once imagined – partially driven by our accelerating pace of development in hardware and quantum error correction.
Making computers “talk”- a short history
The ultimate problem of making a computer understand a human language isn’t unlike trying to learn a new language yourself – you must hear/read/speak lots of examples, memorize lots of rules and their exceptions, memorize words and their meanings, and so on. However, it’s more complicated than that when the “brain” is a computer. Computers naturally speak their native languages very well, where everything from machine code to Python has a meaningful structure and set of rules.
In contrast, “natural” (human) language is very different from the strict compliance of computer languages: things like idioms confound any sense of structure, humor and poetry play with semantics in creative ways, and the language itself is always evolving. Still, people have been considering this problem since the 1950’s (Turing’s original “test” of intelligence involves the automated interpretation and generation of natural language).
Up until the 1980s, most natural language processing systems were based on complex sets of hand-written rules. Starting in the late 1980s, however, there was a revolution in natural language processing with the introduction of machine learning algorithms for language processing.
Initial ML approaches were largely “statistical”: by analyzing large amounts of text data, one can identify patterns and probabilities. There were notable successes in translation (like translating French into English), and the birth of the web led to more innovations in learning from and handling big data.
What many consider “modern” NLP was born in the late 2000’s, when expanded compute power and larger datasets enabled practical use of neural networks. Being mathematical models, neural networks are “built” out of the tools of mathematics; specifically linear algebra and calculus.
Building a neural network, then, means finding ways to manipulate language using the tools of linear algebra and calculus. This means representing words and sentences as vectors and matrices, developing tools to manipulate them, and so on. This is precisely the path that researchers in classical NLP have been following for the past 15 years, and the path that our team is now speedrunning in the quantum case.
Quantum Word Embeddings: A Complex Twist
The first major breakthrough in neural NLP came roughly a decade ago, when vector representations of words were developed, using the frameworks known as Word2Vec and GloVe (Global Vectors for Word Representation). In a recent paper, our team, including Carys Harvey and Douglas Brown, demonstrated how to do this in quantum NLP models – with a crucial twist. Instead of embedding words as real-valued vectors (as in the classical case), the team built it to work with complex-valued vectors.
In quantum mechanics, the state of a physical system is represented by a vector residing in a complex vector space, called a Hilbert space. By embedding words as complex vectors, we are able to map language into parameterized quantum circuits, and ultimately the qubits in our processor. This is a major advance that was largely under appreciated by the AI community but which is now rapidly gaining interest.
Using complex-valued word embeddings for QNLP means that from the bottom-up we are working with something fundamentally different. This different “geometry” may provide advantage in any number of areas: natural language has a rich probabilistic and hierarchical structure that may very well benefit from the richer representation of complex numbers.
The Quantum Recurrent Neural Network (RNN)
Another breakthrough comes from the development of quantum recurrent neural networks (RNNs). RNNs are commonly used in classical NLP to handle tasks such as text classification and language modeling.
Our team, including Dr. Wenduan Xu, Douglas Brown, and Dr. Gabriel Matos, implemented a quantum version of the RNN using parameterized quantum circuits (PQCs). PQCs allow for hybrid quantum-classical computation, where quantum circuits process information and classical computers optimize the parameters controlling the quantum system.
In a recent experiment, the team used their quantum RNN to perform a standard NLP task: classifying movie reviews from Rotten Tomatoes as positive or negative. Remarkably, the quantum RNN performed as well as classical RNNs, GRUs, and LSTMs, using only four qubits. This result is notable for two reasons: it shows that quantum models can achieve competitive performance using a much smaller vector space, and it demonstrates the potential for significant energy savings in the future of AI.
In a similar experiment, our team partnered with Amgen to use PQCs for peptide classification, which is a standard task in computational biology. Working on the Quantinuum System Model H1, the joint team performed sequence classification (used in the design of therapeutic proteins), and they found competitive performance with classical baselines of a similar scale. This work was our first proof-of-concept application of near-term quantum computing to a task critical to the design of therapeutic proteins, and helped us to elucidate the route toward larger-scale applications in this and related fields, in line with our hardware development roadmap.
Quantum Transformers - The Next Big Leap
Transformers, the architecture behind models like GPT-3, have revolutionized NLP by enabling massive parallelism and state-of-the-art performance in tasks such as language modeling and translation. However, transformers are designed to take advantage of the parallelism provided by GPUs, something quantum computers do not yet do in the same way.
In response, our team, including Nikhil Khatri and Dr. Gabriel Matos, introduced “Quixer”, a quantum transformer model tailored specifically for quantum architectures.
By using quantum algorithmic primitives, Quixer is optimized for quantum hardware, making it highly qubit efficient. In a recent study, the team applied Quixer to a realistic language modeling task and achieved results competitive with classical transformer models trained on the same data.
This is an incredible milestone achievement in and of itself.
This paper also marks the first quantum machine learning model applied to language on a realistic rather than toy dataset.
This is a truly exciting advance for anyone interested in the union of quantum computing and artificial intelligence, and is in danger of being lost in the increased ‘noise’ from the quantum computing sector where organizations who are trying to raise capital will try to highlight somewhat trivial advances that are often duplicative.
Quantum Tensor Networks. A Scalable Approach
Carys Harvey and Richie Yeung from Quantinuum in the UK worked with a broader team that explored the use of quantum tensor networks for NLP. Tensor networks are mathematical structures that efficiently represent high-dimensional data, and they have found applications in everything from quantum physics to image recognition. In the context of NLP, tensor networks can be used to perform tasks like sequence classification, where the goal is to classify sequences of words or symbols based on their meaning.
The team performed experiments on our System Model H1, finding comparable performance to classical baselines. This marked the first time a scalable NLP model was run on quantum hardware – a remarkable advance.
The tree-like structure of quantum tensor models lends itself incredibly well to specific features inherent to our architecture such as mid-circuit measurement and qubit re-use, allowing us to squeeze big problems onto few qubits.
Since quantum theory is inherently described by tensor networks, this is another example of how fundamentally different quantum machine learning approaches can look – again, there is a sort of “intuitive” mapping of the tensor networks used to describe the NLP problem onto the tensor networks used to describe the operation of our quantum processors.
What we’ve learned so far
While it is still very early days, we have good indications that running AI on quantum hardware will be more energy efficient.
We recently published a result in “random circuit sampling”, a task used to compare quantum to classical computers. We beat the classical supercomputer in time to solution as well as energy use – our quantum computer cost 30,000x less energy to complete the task than Frontier, the classical supercomputer we compared against.
We may see, as our quantum AI models grow in power and size, that there is a similar scaling in energy use: it’s generally more efficient to use ~100 qubits than it is to use ~10^18 classical bits.
Another major insight so far is that quantum models tend to require significantly fewer parameters to train than their classical counterparts. In classical machine learning, particularly in large neural networks, the number of parameters can grow into the billions, leading to massive computational demands.
Quantum models, by contrast, leverage the unique properties of quantum mechanics to achieve comparable performance with a much smaller number of parameters. This could drastically reduce the energy and computational resources required to run these models.
The Path Ahead
As quantum computing hardware continues to improve, quantum AI models may increasingly complement or even replace classical systems. By leveraging quantum superposition, entanglement, and interference, these models offer the potential for significant reductions in both computational cost and energy consumption. With fewer parameters required, quantum models could make AI more sustainable, tackling one of the biggest challenges facing the industry today.
The work being done by Quantinuum reflects the start of the next chapter in AI, and one that is transformative. As quantum computing matures, its integration with AI has the potential to unlock entirely new approaches that are not only more efficient and performant but can also handle the full complexities of natural language. The fact that Quantinuum’s quantum computers are the most advanced in the world, and cannot be simulated classically, gives us a unique glimpse into a future.
The future of AI now looks very much to be quantum and Quantinuum’s Gen QAI system will usher in the era in which our work will have meaningful societal impact.
About Quantinuum
Quantinuum, the world’s largest integrated quantum company, pioneers powerful quantum computers and advanced software solutions. Quantinuum’s technology drives breakthroughs in materials discovery, cybersecurity, and next-gen quantum AI. With over 500 employees, including 370+ scientists and engineers, Quantinuum leads the quantum computing revolution across continents.
Authors:
Quantinuum (alphabetical order): Eric Brunner, Steve Clark, Fabian Finger, Gabriel Greene-Diniz, Pranav Kalidindi, Alexander Koziell-Pipe, David Zsolt Manrique, Konstantinos Meichanetzidis, Frederic Rapp
Hiverge (alphabetical order): Alhussein Fawzi, Hamza Fawzi, Kerry He, Bernardino Romera Paredes, Kante Yin
What if every quantum computing researcher had an army of students to help them write efficient quantum algorithms? Large Language Models are starting to serve as such a resource.
Quantinuum’s processors offer world-leading fidelity, and recent experiments show that they have surpassed the limits of classical simulation for certain computational tasks, such as simulating materials. However, access to quantum processors is limited and can be costly. It is therefore of paramount importance to optimise quantum resources and write efficient quantum software. Designing efficient algorithms is a challenging task, especially for quantum algorithms: dealing with superpositions, entanglement, and interference can be counterintuitive.
To this end, our joint team used Hiverge’s AI platform for automated algorithm discovery, the Hive, to probe the limits of what can be done in quantum chemistry. The Hive generates optimised algorithms tailored to a given problem, expressed in a familiar programming language, like Python. Thus, the Hive’s outputs allow for increased interpretability, enabling domain experts to potentially learn novel techniques from the AI-discovered solutions. Such AI-assisted workflows lower the barrier of entry for non-domain experts, as an initial sketch of an algorithmic idea suffices to achieve state-of-the-art solutions.
In this initial proof-of-concept study, we demonstrate the advantage of AI-driven algorithmic discovery of efficient quantum heuristics in the context of quantum chemistry, in particular the electronic structure problem. Our early explorations show that the Hive can start from a naïve and simple problem statement and evolve a highly optimised quantum algorithm that solves the problem, reaching chemical precision for a collection of molecules. Our high-level workflow is shown in Figure 1. Specifically, the quantum algorithm generated by the Hive achieves a reduction in the quantum resources required by orders of magnitude compared to current state-of-the-art quantum algorithms. This promising result may enable the implementation of quantum algorithms on near-term hardware that was previously thought impossible due to current resource constraints.
The Electronic Structure Problem in Quantum Chemistry
The electronic structure problem is central to quantum chemistry. The goal is to prepare the ground state (the lowest energy state) of a molecule and compute the corresponding energy of that state to chemical precision or beyond. Classically, this is an exponentially hard problem. In particular, classical treatments tend to fall short when there are strong quantum effects in the molecule, and this is where quantum computers may be advantageous.
The paradigm of variational quantum algorithms is motivated by near-term quantum hardware. One starts with a relatively easy-to-prepare initial state. Then, the main part of the algorithm consists of a sequence of parameterised operators representing chemically meaningful actions, such as manipulating electron occupations in the molecular orbitals. These are implemented in terms of parameterised quantum gates. Finally, the energy of the state is measured via the molecule’s energy operator, the “Hamiltonian”, by executing the circuit on a quantum computer and measuring all the qubits on which the circuit is implemented. Taking many measurements, or “shots”, the energy is estimated to the desired precision. The ground state energy is found by iteratively optimising the parameters of the quantum circuit until the energy converges to a minimum value. The general form of such a variational quantum algorithm is illustrated in Figure 2.
The main challenge in these frameworks is to design an appropriate quantum circuit architecture, i.e. find an efficient sequence of operators, and an efficient optimisation strategy for its parameters. It is important to minimise the number of quantum operations in any given circuit, as each operation is inherently noisy and the algorithm’s output degrades exponentially. Another important quantum resource to be minimised is the total number of circuits that need to be evaluated to compute the energy values during the optimisation of the circuit parameters, which is time-consuming.
To meet these challenges, we task the Hive with designing a variational quantum algorithm to solve the ground state problem, following the workflow shown in Figure 1. The Hive is a distributed evolutionary process that evolves programs. It uses Large Language Models to generate mutations in the form of edits to an entire codebase. This genetic process selects the fittest programs according to how well they solve a given problem. In our case, the role of the quantum computer is to compute the fitness, i.e., the ground state energy. Importantly, the Hive operates at the level of a programming language; it readily imports and uses all known libraries that a human researcher would use, including Quantinuum’s quantum chemistry platform, InQuanto. In addition, the Hive can accept instructions and requests in natural language, increasing its flexibility. For example, we encouraged it to seek parameter optimisation strategies that avoid estimating gradients, as this incurs significant overhead in terms of circuit evaluations. Intuitively, the interaction between a human scientist and the Hive is analogous to a supervisor and a group of eager and capable students: the supervisor provides guidance at a high level, and the students collaborate and flesh out the general idea to produce a working solution that the supervisor can then inspect.
We find that from an extremely basic starting point, consisting of a skeleton for a variational quantum algorithm, the Hive can autonomously assemble a bespoke variational quantum algorithm, which we call Hive-ADAPT. Specifically, the Hive evolves heuristic functions that construct a circuit as a sequence of quantum operators and optimise its parameters. Remarkably, the Hive converged on a structure resembling the current state-of-the-art, ADAPT-VQE. Crucially, however, Hive-ADAPT substantially outperforms this baseline, delivering significant improvements in chemical precision while reducing quantum resource requirements.
A molecule’s ground state energy varies with the distances between its atoms, called the “bond length”. For example, for the molecule H2O, the bond length refers to the length of the O-H bond. The Hive was tasked with developing an algorithm for a small set of bond lengths and reaching chemical precision, defined as within 1.6e-3 Hartree (Ha) of the ground state energy computed with the exact Full Configuration Interaction (FCI) algorithm. As we show in Figure 3, remarkably, Hive-ADAPT achieves chemical precision for more bond lengths than ADAPT-VQE. Furthermore, Hive-ADAPT also reaches chemical precision for other “unseen” bond lengths, showcasing the generalisation ability of the evolved quantum algorithm. Our results were obtained from classical simulations of the quantum algorithms, where we used NVIDIA CUDA-Q to leverage the parallelism enabled by GPUs. Further, relative to ADAPT-VQE, Hive-ADAPT exhibits one to two orders of magnitude reduction in quantum resources, such as the number of circuit evaluations and the number of operators used to construct circuits, which is crucial for practical implementations on actual near-term processors.
For molecules such as BeH2 at large Be-H bond lengths, a complex initial state is required for the algorithm to be able to reach the ground state using the available operators. Even in these cases, by leveraging an efficient state preparation scheme implemented in InQuanto, the Hive evolved a dedicated strategy for the preparation of such a complex initial state, given a set of basic operators to achieve the desired chemical precision.
To validate Hive-ADAPT under realistic conditions, we employed Quantinuum’s H2 Emulator, which provides a faithful classical simulator of the H2 quantum computer, characterised by a 1.05e-3 two-qubit gate error rate. Leveraging the Hive's inherent flexibility, we adapted the optimisation strategy to explicitly penalise the number of two-qubit gates—the dominant noise source on near-term hardware—by redefining the fitness function. This constraint guided the Hive to discover a noise-aware algorithm capable of constructing hardware-efficient circuits. We subsequently executed the specific circuit generated by this algorithm for the LiH molecule at a bond length of 1.5 Å with the Partition Measurement Symmetry Verification (PMSV) error mitigation procedure. The resulting energy of -7.8767 ± 0.0031 Ha, obtained using 10,000 shots per circuit with a discard rate below 10% in the PMSV error mitigation procedure, is close to the target FCI energy of -7.8824 Ha and demonstrates the Hive's ability to successfully tailor algorithms that balance theoretical accuracy with the rigorous constraints of hardware noise and approach chemical precision as much as possible with current quantum technology.
For illustration purposes, we show an example of an elaborate code snippet evolved by the Hive starting from a trivial version:
Quantinuum’s in-house quantum chemistry expert, Dr. David Zsolt Manrique, commented,
“I found it amazing that the Hive converged to a domain-expert level idea. By inspecting the code, we see it has identified the well-known perturbative method, ‘MP2’, as a useful guide; not only for setting the initial circuit parameters, but also for ordering excitations efficiently. Further, it systematically and laboriously fine-tuned those MP2-inspired heuristics over many iterations in a way that would be difficult for a human expert to do by hand. It demonstrated an impressive combination of domain expertise and automated machinery that would be useful in exploring novel quantum chemistry methods.”
Looking to the Future
In this initial proof-of-concept collaborative study between Quantinuum and Hiverge, we demonstrate that AI-driven algorithm discovery can generate efficient quantum heuristics. Specifically, we found a great reduction in quantum resources, which is impactful for quantum algorithmic primitives that are frequently reused. Importantly, this approach is highly flexible; it can accommodate the optimisation of any desired quantum resource, from circuit evaluations to the number of operations in a given circuit. This work opens a path toward fully automated pipelines capable of developing problem-specific quantum algorithms optimised for NISQ as well as future hardware.
An important question for further investigation regards transferability and generalisation of a discovered quantum solution to other molecules, going beyond the generalisation over bond lengths of the same molecule that we have already observed. Evidently, this approach can be applied to improving any other near-term quantum algorithm for a range of applications from optimisation to quantum simulation.
We have already demonstrated an error-corrected implementation of quantum phase estimation on quantum hardware, and an AI-driven approach promises further hardware-tailored improvements and optimal use of quantum resources. Beyond NISQ, we envision that AI-assisted algorithm discovery will be a fruitful endeavour in the fault-tolerant regime, as well, where high-level quantum algorithmic primitives (quantum fourier transform, amplitude amplification, quantum signal processing, etc.) are to be combined optimally to achieve computational advantage for certain problems.
Notably, we’ve entered an era where quantum algorithms can be written in high-level programming languages, like Quantinuum’s Guppy, and approaches that integrate Large Language Models directly benefit. Automated algorithm discovery is promising for improving routines relevant to the full quantum stack, for example, in low-level quantum control or in quantum error correction.
Quantinuum is focusing on redefining what’s possible in hybrid quantum–classical computing by integrating Quantinuum’s best-in-class systems with high-performance NVIDIA accelerated computing to create powerful new architectures that can solve the world’s most pressing challenges.
The launch of Helios, Powered by Honeywell, the world’s most accurate quantum computer, marks a major milestone in quantum computing. Helios is now available to all customers through the cloud or on-premise deployment, launched with a go-to-market offering that seamlessly pairs Helios with the NVIDIA Grace Blackwell platform, targeting specific end markets such as drug discovery, finance, materials science, and advanced AI research.
We are also working with NVIDIA to adopt NVIDIA NVQLink, an open system architecture, as a standard for advancing hybrid quantum-classical supercomputing. Using this technology with Quantinuum Guppy and the NVIDIA CUDA-Q platform, Quantinuum has implemented NVIDIA accelerated computing across Helios and future systems to perform real-time decoding for quantum error correction.
In an industry-first demonstration, an NVIDIA GPU-based decoder integrated in the Helios control engine improved the logical fidelity of quantum operations by more than 3% — a notable gain given Helios’ already exceptionally low error rate. These results demonstrate how integration with NVIDIA accelerated computing through NVQLink can directly enhance the accuracy and scalability of quantum computation.
This unique collaboration spans the full Quantinuum technology stack. Quantinuum’s next-generation software development environment allows users to interleave quantum and GPU-accelerated classical computations in a single workflow. Developers can build hybrid applications using tools such as NVIDIA CUDA-Q, NVIDIA CUDA-QX, and Quantinuum’s Guppy, to make advanced quantum programming accessible to a broad community of innovators.
The collaboration also reaches into applied research through the NVIDIA Accelerated Quantum Computing Research Center (NVAQC), where an NVIDIA GB200 NVL72 supercomputer can be paired with Quantinuum’s Helios to further drive hybrid quantum-GPU research, including the development of breakthrough quantum-enhanced AI applications.
A recent achievement illustrates this potential: The ADAPT-GQE framework, a transformer-based Generative Quantum AI (GenQAI) approach, uses a Generative AI model to efficiently synthesize circuits to prepare the ground state of a chemical system on a quantum computer. Developed by Quantinuum, NVIDIA, and a pharmaceutical industry leader—and leveraging NVIDIA CUDA-Q with GPU-accelerated methods—ADAPT-GQE achieved a 234x speed-up in generating training data for complex molecules. The team used the framework to explore imipramine, a molecule crucial to pharmaceutical development. The transformer was trained on imipramine conformers to synthesize ground state circuits at orders of magnitude faster than ADAPT-VQE, and the circuit produced by the transformer was run on Helios to prepare the ground state using InQuanto, Quantinuum's computational chemistry platform.
From collaborating on hardware and software integrations to GenQAI applications, the collaboration between Quantinuum and NVIDIA is building the bridge between classical and quantum computing and creating a future where AI becomes more expansive through quantum computing, and quantum computing becomes more powerful through AI.
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.