Quantum computing is a young, dynamic field – so young that the community is still exploring multiple different “architectures” for quantum computers. The computer “architecture” can roughly be described as what the computer is made out of – in other words, is it made out of superconductors or semiconductors? Are the qubits made from ions, superconducting “squids”, atoms, or even particles of light? We call these different physical realizations the “architecture” or “modality”.

Exploring the pros and cons of all the different modalities is an important part of current quantum computing research. Because Quantinuum is committed to the community, and even though our hardware is trapped-ion based, we often work in partnership with researchers exploring alternate options. This work allows us to both develop quantum technologies outside our own architecture while better developing our hardware-agnostic software.

Recently, our Oxford team has made big strides in our understanding of “photonic”, or light-based, quantum computing. First, they developed a string-diagram formalism for describing linear and nonlinear optics. Then, they applied their formalism to solve outstanding problems in the field. 

The graphical approach made solving some problems in particular much easier than they would have been using more standard linear algebra techniques, in part because the circuits they are describing have a two-dimensional structure, just like the string diagrams themselves. By creating a diagrammatic representation of the circuits themselves, the researchers are more easily able to compute things such as the change in the circuit when a parameter is adjusted. 

In their most recent paper, the team figured out how to take the derivative of (or “differentiate) linear optical circuits, which means they can now figure out how the circuit will change when certain parameters are adjusted. Differentiation is central to a whole class of algorithms (including optimization algorithms and any algorithm making use of “gradient descent”, which is a key component of many machine learning and AI techniques), making the teams’ results incredibly useful. This work will form the basis for an upcoming software platform for photonic quantum computing. 

In addition, this graphical approach to describing optical circuits is particularly advantageous for reasoning about multiple particles and composite quantum systems, like one must to understand fault-tolerance in quantum computing. While graphical languages are fairly new in the photonics sphere, they already seem to offer an insightful new perspective. Their current results open the door to “variational” approaches, which are used to solve things like combinatorial graph problems or problems in quantum chemistry.

Detecting and correcting errors has become a critical area of development in quantum computing, a key that will unlock results which put quantum computers in a different league from their classical counterparts. 

Researchers are working on ways to handle errors so that the hardware we will have in the coming months will be capable of performing useful tasks that are intractable for any classical computer — in other words, to achieve “quantum advantage”. 

The full monty, known as “large-scale fault-tolerant quantum error correction” remains an open challenge in the quantum computing landscape, placing incredibly demanding constraints on the hardware. A promising start is to implement error detection instead of full error correction. In this approach, the system regularly checks for errors, and if one is detected, throws out the computation and restarts. 

The team at Quantinuum realized that just such a code, nicknamed the “iceberg code”, if optimized to take advantage of the industry-leading components in Quantinuum’s trapped-ion quantum computers, could offer real potential for early fault-tolerance. Quantinuum’s H-Series hardware boasts mobile qubits, mid circuit measurement and the ability to program circuits with arbitrary-angle gates – making it ripe for new algorithm implementation and development. The team’s results, published today in Nature Physics Protecting expressive circuits with a quantum error detection code, detail a code that’s so efficient it was able to protect much deeper and more expressive circuits than had previously been realized with quantum error correction, and it did so making extremely efficient use of the very high-fidelity qubits and gates available in Quantinuum’s quantum charge-coupled device (QCCD) architecture. 

“Our work sets the bar for what more advanced fully fault-tolerant codes need to beat on hardware,” said David Amaro, an author on the paper.

A key advantage of the iceberg code is how efficiently it squeezes out the maximum number of logical qubits from the given set of physical qubits – it can make k logical qubits out of only k+2 physical qubits. Every logical gate is implemented by a unique two-qubit physical gate, making it a very fast, clean, and expressive implementation. In addition to this, it needs only 2 more ancilla qubits for syndrome measurement, making for a very small overhead of only 4 physical qubits. Using the original 12-qubit configuration of Quantinuum’s H1-2 computer (since increased to 20), this meant the team could realize 8 logical qubits.

With these 8 logical qubits, the team implemented much deeper and more expressive circuits than had previously been demonstrated with quantum error correction codes. 

The team’s work is the first experimental demonstration that sophisticated quantum error detection techniques are useful to successfully protect very expressive circuits on a real quantum computer. In contrast, previous demonstrations of fully fault-tolerant codes on hardware showed protection only of basic logical gates or “primitives” (the building blocks of full algorithms). 

The Iceberg code is a method that’s useful today for practitioners, and can be used to protect near-term algorithms like the ‘quantum approximate optimization algorithm’, or the ‘variational quantum eigensolver’, algorithms currently put to work in domains including chemical simulation, quantum machine learning and financial optimization. In fact, it was used by a team at Quantinuum to protect the quantum phase estimation algorithm, a critical piece for many other quantum algorithms, and deployed in a state-of-the-art simulation of a real-world hydrogen molecule using logically-encoded qubits — a feat not possible using any other quantum computing hardware yet developed.

Looking forwards, the team plans to push the code as far as possible to determine if it is sufficient to protect quantum circuits capable of a quantum advantage. This will require setting a “minimal” quantum advantage experiment, working on careful engineering and benchmarking of every aspect of the code, and the use of Quantinuum’s best-in-class high fidelity gates. In parallel, they will also be working to understand if and how the Iceberg code can contribute to minimize the resource overhead of some of the most promising fully fault-tolerant codes.

For the first time, Quantinuum researchers have run scalable quantum natural language processing (QNLP) models, able to parse and process real-world data, on a quantum computer. In a recent paper, the researchers define machine learning models for the task of classifying sequences – which can be anything from sentences in natural language, like movie reviews, to bioinformatic strings, like DNA sequences. Classifying sequences of symbols – letters, words, or longer fragments of text – is an obviously useful computational task, and has led to some of the decade’s biggest changes; we now see this technology in use in everything from chatbots to legal cases.  

Current classical models, which are based on neural networks, primarily look at the statistical distributions of where words are put with respect to each other – they don’t really consider the structure of language a priori (they could, but they don’t). In contrast, syntactic information scaffolds Quantinuum’s new quantum models, which are based on tensor networks, making them “syntax-aware”. Considering things like structure and syntax from the beginning allows scientists to create models with far fewer parameters, that require fewer gate operations to run, while allowing for interpretability thanks to the meaningful structure baked in from the start. Interpretability is the most pressing challenge in artificial intelligence (AI) — because if we don’t know why an algorithm has given an answer, we can’t trust it in critical applications, for instance in making medical decisions, or in scenarios where human lives are at stake.

Both neural and tensor networks can capture complex correlations in large data, but the way they do it is fundamentally different. In addition, since quantum theory inherently is described by tensor networks, using them to build quantum natural language processing models allows for the investigation of the potential that quantum processors can bring to natural language processing specifically, and artificial intelligence in general.

Thanks to best-in-class features like mid-circuit measurement and qubit reuse on Quantinuum’s H2-1 quantum processor, they were able to fit much larger circuits than one might naively expect. For example, the researchers were able to run a circuit that would normally take 64 qubits on only 11 qubits. Combined with the reduced number of gates required, these models are entirely feasible on current quantum hardware.

This paper shows us that we can run, train, and deploy QNLP models on present-day quantum computers. When compared to neural-network-based classifiers, the quantum model does just as well on this task in terms of prediction accuracy. What’s more, this work encourages the exploration of quantum language models, as sampling from quantum circuits of the types used in this work could require polynomially fewer resources than simulating them classically. 

Who is responsible for migrating your systems to quantum-safe algorithms? Is it your vendors or your cybersecurity team?  

The customers I speak to are not always clear on this question. But from my perspective, the answer is your cybersecurity team. They have the ultimate responsibility of ensuring your organization is secure in a post-quantum future. However, they will need a lot of help from your technology vendors.

This article outlines what you should expect (or demand) from your vendors, and what remains the responsibility of your cyber team.

What To Expect From General Vendors

A general vendor does not offer specific cryptographic services to you. Instead, they provide a business service that uses cryptography to maintain security and resilience.

Consider the accounting platform SAP. It is no doubt riddled with cryptography, yet its purpose is to manage your finances. Therefore, SAP’s focus will be on migrating their underlying cryptography to post-quantum technologies, while maintaining your business services without interruption.

You should expect a general vendor to share a quantum-safe migration roadmap with you, complete with timelines. They should explain the activities they will complete to address the quantum threat, and how they will impact you as a user.

Although your vendor will not begin migration until the NIST post-quantum algorithms are standardised next year, you should expect them to already have a roadmap in place. If they don’t, this is a cause for concern.

Some vendors may already offer a test version of their product, which uses post-quantum algorithms. This allows your cyber team to experiment with the impact on performance or interoperability.

What To Expect From Cryptographic Vendors

A cryptographic vendor provides you with services directly related to cryptography, such as network security, data encryption or key management.

The expectations that apply to general vendors also apply to cryptographic vendors. However, you will need more information from your cryptographic vendors to pull off a smooth migration.

Cryptographic vendors must provide you with detailed guidance on how to migrate between their current product suite and the new versions that use post-quantum algorithms. For instance, you might need to understand how to re-process legacy data so that it’s protected by the new algorithms. Similarly, network security vendors will need to provide detailed instructions on migrating traffic flows while maintaining uptime.

I would expect cryptographic vendors to be far more hands-on during your migration. Expect to have discussions of your deployment architecture with their account management teams, and don’t be afraid to ask the hard technical questions.

What Information You Should be Ready to Share

The flow of information will not be one-way. You should be prepared to share information with your vendors to help them help you.

Having your migration plan developed, at least at a high level, will be critical for meaningful conversations with your vendors. This will allow you to contrast their timelines for migration versus your expectations.

Vendors will also benefit from understanding how you use their products in conjunction with products from other vendors. The goal here is to spot edge cases, where you risk business downtime because the vendor wasn’t anticipating how you were using their product.

Finally, make sure you know the configuration of your deployment. The devil is in the details when it comes to planning migration, so be prepared to tell your vendor which features you are using and how you’ve configured product security settings.

What is Out of Scope for Your Vendor?

While your vendors should provide a lot of help and guidance, they are not responsible for everything.

Your cybersecurity team will be responsible for planning your overall migration strategy, including prioritising which systems to migrate first. This will involve understanding the relative importance of business systems, and the requirements for data security.

While vendors should provide some guidance for interoperability, ultimately the IT and cybersecurity teams are responsible for ensuring updates to one service do not impact another service.

Finally, you must ensure your IT and cyber teams are leading the conversation with your end users. You cannot rely on vendors to manage the communication with your customers and internal stakeholders.

What Should You Expect to See Today?

A good vendor will already be talking to you about their plans for quantum-safe migration.

For mass-market products, this might be via blog posts and thought-leadership articles. For products with a deeper client/vendor relationship, the topic of quantum-safe migration should already be appearing in quarterly business reviews.

For cryptographic vendors, you should also be expecting test versions to be available today, to allow for experimentation.

Overall, if any vendor is not able to talk about their plans for quantum-safe migration today, even at a high level, then you should flag this as a cause for concern.

Building a quantum computer that offers advantages over classical computers is the goal of quantum computing groups worldwide. A competitive quantum computer must be “universal”, requiring the ability to perform all operations already possible on a classical computer, as well as new ones specific to quantum computing. Of course, that’s just the beginning – it should also be able to do this in a reasonable amount of time, to deal effectively with noise from the environment, and to perform computations to arbitrary accuracy.

This is a lot to get right, and over the years quantum computer scientists have described ways to solve these often-overlapping challenges. To deal with noise from the environment and achieve arbitrary accuracy, quantum computers need to be able to keep going even as noise accumulates on the quantum bits, or qubits, which hold the quantum information. Such fault-tolerance may be achieved using quantum error correction, where ensembles of physical qubits are encoded into logical qubits and those are used to counteract noise and perform computational operations called gates. Unfortunately, no single quantum error correction code plays well with the goal of universality because all codes lack a complete universal set of fault-tolerant gates (the technical reason for this comes down to the way quantum gates are executed between logical qubits – the native gate set on error-corrected logical qubits are known by experts as transversal gates, and they do not include all the gates needed for universal quantum computing).

The solution to this obstacle to universality is a magic state, a quantum state which provides for the missing gate when error correcting codes are used. High fidelity magic states are achieved by a process of distillation, which purifies them from other noisier magic states. It is widely recognized that magic state distillation is one of the totemic challenges on the path towards universal, fault-tolerant quantum computing. Quantinuum’s scientists, in close collaboration with a team at Microsoft, set out to demonstrate the distillation process in real-time using physical qubits on a quantum computer for the first time.

The results of this work are available in a new paper, Advances in compilation for quantum hardware -- A demonstration of magic state distillation and repeat until success protocols.

Magic state distillation

How does magic state distillation work? Imagine a factory, taking in many qubits in imperfect initial states at one end. Broadly speaking, the factory distills the imperfect states into an almost pure state with a smaller error probability, by sending them through a well-defined process over and over. In this case, the process takes in a group of five qubits. It applies a quantum error correcting code that entangles these five qubits, with four used to test whether the fifth, target qubit has been purified. If the process fails, the ensemble is discarded and the process repeats. If it succeeds, the newly distilled target qubit is kept and combined with four other successes to form a new ensemble, which then rejoins the process of continued purification. By undertaking this process many times, the purity of the magic state increases at each step, gradually moving towards the conditions required for universal, fault-tolerant quantum computing.

Despite being the subject of theoretical exploration over decades, real-time magic state distillation had never been realized on a quantum computer. In typical pioneering style, the Quantinuum and Microsoft team decided to take on this challenge. But before they could get started, they recognized that their toolset would have to be significantly sharpened up.

Creating new tools for quantum programming

At the heart of magic state distillation is a highly complex repeating process, which requires state-of-the-art protocols and control flow logic built on a best-in-class programming toolset. The research team turned to Quantum Intermediate Representation (QIR) to simplify and streamline the programming of this complex quantum computing process.

QIR is a is a quantum-specific code representation based on the popular open-sourced classical LLVM intermediate language, with the addition of structures and protocols that support the maturation and modernization of quantum computing. QIR includes elements that are essential in classical computing, but which are yet to be standardized in quantum computing, such as the humble programming loop.

Loops, which often take forms like "for...next" or "do...while," are central to programming, allowing code to repeat instructions in a stepwise manner until a condition is met. In quantum computing, this is a tough challenge because loops require control flow logic and mid-circuit measurement, which are difficult to realize in a quantum computer but have been demonstrated in Quantinuum’s System Model H1-1, Powered by Honeywell. Loops are essential for realizing magic state distillation and it’s well-understood that LLVM is great at optimizing complex control flow, including loops. This made magic state distillation a natural choice for demonstrating a valuable application of QIR and making for a great example of the use of a classical technique in a quantum context.

Result: demonstrating a magic state distillation protocol

The team used Quantinuum’s H1-1 quantum computer – benefiting from industry-leading components such as mid-circuit measurement, qubit reuse and feed-forward – to make possible the quantum looping required for a magic state distillation protocol, and becoming the first quantum computing team ever to run a real-time magic state distillation protocol on quantum hardware.

Four ways to achieve a quantum computer programmable loop

Building on this success, the team designed further experiments to assess the potential of four methods for exploring the use of a quantum protocol called a repeat-until-success (RUS) circuit to achieve a loop process. First, they hard-coded a loop directly into the extended OpenQASM 2.0, a widely used quantum assembly language, but which requires additional overhead to target advanced components on Quantinuum's very versatile H-Series quantum computer. Against this, they compared two alternative methods for coding a loop in a standard high-level programming language: controlled recursion, which was directed through both OpenQASM and through QIR; and a native for loop made possible within QIR.

The results were clear-cut: the hard-coded OpenQASM 2.0 loop performed as well as the theoretical prediction, maintaining high quality results after a number of loops, as did the natively-coded QIR for loop. The two recursive loops saw the quality of their results drop away fast as the loop limit was raised. But in a head-to-head between hard-coded OpenQASM and QIR, which converts high-level source code from many prominent and familiar languages into low-level machine code, QIR won hands-down on the basis of practicality.

Martin Roetteler, Director of Quantum Applications at Microsoft, shared: “This was a very exciting exploration of control flow logic on quantum hardware. In seeking to understand the capabilities of QIR to optimize programming structures on real hardware, we were rewarded with a clear answer, and an important demonstration of the capabilities of QIR.”

H2’s 32 qubits will power the next phase

In follow-up work, the team is now preparing to run a logical magic state protocol on the H2-1 quantum computer with its 32 high-fidelity qubits, and hopes to become the first group to successfully achieve logical magic state distillation. The features and fidelity offered by the H2 make it one of the best quantum computers currently capable of shooting for such a major milestone on the journey towards fault tolerance, while the current work demonstrates that, in QIR, the necessary control flow logic is now available to achieve it.

The paper discussed in this post was authored by Natalie C. Brown, John P. Campora III, Cassandra Granade, Bettina Heim, Stefan Wernli, Ciaran Ryan-Anderson, Dominic Lucchetti, Adam Paetznick, Martin Roetteler, Krysta Svore and Alex Chernoguzov.