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How 夜色直播 researchers used quantum tensor networks to measure the properties of quantum particles at a phase transition

Quantum tensor networks demonstrate potential exponential resource reduction in both time and memory for calculation of critical state properties in digital quantum computers

April 9, 2023

When thinking about changes in phases of matter, the first images that come to mind might be ice melting or water boiling. The critical point in these processes is located at the boundary between the two phases 鈥 the transition from solid to liquid or from liquid to gas.聽

Phase transitions like these get right to the heart of how large material systems behave and are at the frontier of research in condensed matter physics for their ability to provide insights into emergent phenomena like magnetism and topological order. In classical systems, phase transitions are generally driven by thermal fluctuations and occur at finite temperature. On the contrary, quantum systems can exhibit phase transitions even at zero temperatures; the residual fluctuations that control such phase transitions at zero temperature are due to entanglement and are entirely quantum in origin.聽聽

夜色直播 researchers recently used the H1-1 quantum computer to computationally model a group of highly correlated quantum particles at a quantum critical point 鈥 on the border of a transition between a paramagnetic state (a state of magnetism characterized by a weak attraction) to a ferromagnetic one (characterized by a strong attraction).

Simulating such a transition on a classical computer is possible using tensor network methods, though it is difficult. However, generalizations of such physics to more complicated systems can pose serious problems to classical tensor network techniques, even when deployed on the most powerful supercomputers.聽 On a quantum computer, on the other hand, such generalizations will likely only require modest increases in the number and quality of available qubits.

In a technical paper submitted to the arXiv, , the 夜色直播 team demonstrated how the powerful components and high fidelity of the H-Series digital quantum computers could be harnessed to tackle a 128-site condensed matter physics problem, combining a quantum tensor network method with qubit reuse to make highly productive use of the 20-qubit H1-1 quantum computer.

Reza Haghshenas, Senior Advanced Physicist, and the lead author the paper said, 鈥淭his is the kind of problem that appeals to condensed-matter physicists working with quantum computers, who are looking forward to revealing exotic aspects of strongly correlated systems that are still unknown to the classical realm. Digital quantum computers have the potential to become a versatile tool for working scientists, particularly in fields like condensed matter and particle physics, and may open entirely new directions in fundamental research.鈥

The role of quantum tensor networks
A circular structure with many dots and linesDescription automatically generated
Abstract representation of the 128-site MERA used in this work

Tensor networks are mathematical frameworks whose structure enables them to represent and manipulate quantum states in an efficient manner. Originally associated with the mathematics of quantum mechanics, tensor network methods now crop up in many places, from machine learning to natural language processing, or indeed any model with a large number of interacting, high-dimensional mathematical objects.聽

The 夜色直播 team described using a tensor network method--the multi-scale entanglement renormalization ansatz (MERA)--to produce accurate estimates for the decay of ferromagnetic correlations and the ground state energy of the system. MERA is particularly well-suited to studying scale invariant quantum states, such as ground states at continuous quantum phase transitions, where each layer in the mathematical model captures entanglement at different scales of distance.聽

鈥淏y calculating the critical state properties with MERA on a digital quantum computer like the H-Series, we have shown that research teams can program the connectivity and system interactions into the problem,鈥 said Dave Hayes, Lead of the U.S. quantum theory team at 夜色直播 and one of the paper鈥檚 authors. 鈥淪o, it can, in principle, go out and simulate any system that you can dream of.鈥

Simulating a highly entangled quantum spin model

In this experiment, the researchers wanted to accurately calculate the ground state of the quantum system in its critical state. This quantum system is composed of many tiny quantum magnets interacting with one another and pointing in different directions, known as a quantum spin model. In the paramagnetic phase, tiny, individual magnets in the material are randomly oriented, and only correlated with each other over small length-scales. In the ferromagnetic phase, these individual atomic magnetic moments align spontaneously over macroscopic length scales due to strong magnetic interactions.聽

In the computational model, the quantum magnets were initially arranged in one dimension, along a line. To describe the critical point in this quantum magnetism problem, particles in the line needed to be entangled with one another in a complex way, making this as a very challenging problem for a classical computer to solve in high dimensional and non-equilibrium systems.聽

鈥淭hat's as hard as it gets for these systems,鈥 Dave explained. 鈥淪o that's where we want to look for quantum advantage 鈥 because we want the problem to be as hard as possible on the classical computer, and then have a quantum computer solve it.鈥

To improve the results, the team used two error mitigation techniques, symmetry-based error heralding, which is made possible by the MERA structure, and , a method originally developed by researchers at IBM. The first involved enforcing local symmetry in the model so that errors affecting the symmetry of the state could be detected. The second strategy, zero-noise extrapolation, involves adding noise to the qubits to measure the impact it has, and then using those results to extrapolate the results that would be expected under conditions with less noise than was present in the experiment.

Future applications

The 夜色直播 team describes this sort of problem as a stepping-stone, which allows the researchers to explore quantum tensor network methods on today鈥檚 devices and compare them either to simulations or analytical results produced using classical computers. It is a chance to learn how to tackle a problem really well before quantum computers scale up in the future and begin to offer solutions that are not possible to achieve on classical computers.聽

鈥淧otentially, our biggest applications over the next couple of years will include studying solid-state systems, physics systems, many-body systems, and modeling them,鈥 said Jenni Strabley, Senior Director of Offering Management at 夜色直播.

The team now looks forward to future work, exploring more complex MERA generalizations to compute the states of 2D and 3D many-body and condensed matter systems on a digital quantum computer 鈥 quantum states that are much more difficult to calculate classically.聽

The H-Series allows researchers to simulate a much broader range of systems than analog devices as well as to incorporate quantum error mitigation strategies, as demonstrated in the experiment. Plus, 夜色直播鈥檚 System Model H2 quantum computer, which was launched earlier this year, should scale this type of simulation beyond what is possible using classical computers.

About 夜色直播

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

Blog
June 26, 2025
夜色直播 Overcomes Last Major Hurdle to Deliver Scalable Universal Fault-Tolerant Quantum Computers by 2029

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

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

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

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

In this regard, 夜色直播 is the first company to step from the so-called 鈥淣ISQ鈥 (noisy intermediate-scale quantum) era towards utility-scale quantum computers.

Unpacking our achievement: first, a 鈥榝ull鈥 primer

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

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

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

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

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

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

This is where the magic happens

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

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

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

Flipping the switch

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

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

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

To perform "code switching", one can implement a logical gate between a 2D code and a 3D code, as pictured above. This type of advanced error correcting process requires 夜色直播's reconfigurable connectivity.
Fully equipped for fault-tolerance

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

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

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Blog
June 10, 2025
Our Hardware is Now Running Quantum Transformers!

If we are to create 鈥榥ext-gen鈥 AI that takes full advantage of the power of quantum computers, we need to start with quantum native transformers. Today we announce yet again that 夜色直播 continues to lead by demonstrating concrete progress 鈥 advancing from theoretical models to real quantum deployment.

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

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

Why this matters: Quantum AI, born native

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

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

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

That鈥檚 what we鈥檝e built.

What makes Quixer different?

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

Quixer is different: it鈥檚 not a translation 鈥 it's an innovation.

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

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

What鈥檚 next for Quixer?

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

This is just the beginning.

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

This milestone isn鈥檛 just about one model. It鈥檚 a signal that the quantum AI era has begun, and that 夜色直播 is leading the charge with real results, not empty hype.

Stay tuned. The revolution is only getting started.

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Blog
June 9, 2025
Join us at ISC25

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

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

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

  • Our industry-leading quantum computer holds the record for performance with a Quantum Volume of 2虏鲁 = 8,388,608 and the highest fidelity on a commercially available QPU available to our users every time they access our systems.
  • Our systems have been validated by a #1 ranking against competitors in a recent benchmarking study by J眉lich Research Centre.
  • We鈥檝e laid out a clear roadmap to reach universal, fully fault-tolerant quantum computing by the end of the decade and will launch our next-generation system, Helios, later this year.
  • We are advancing real-world hybrid compute with partners such as RIKEN, NVIDIA, SoftBank, STFC Hartree Center and are pioneering applications such as our own GenQAI framework.
Exhibit Hall

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

Presentations & Demos

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

Multicore World Networking Event

  • Monday, June 9 | 7:00pm 鈥 9:00 PM at Hofbr盲u Wirtshaus Esplanade
    In partnership with Multicore World, join us for a 夜色直播-sponsored Happy Hour to explore the present and future of quantum computing with 夜色直播 CCO, Dr. Nash Palaniswamy, and network with our team.

H1 x CUDA-Q Demonstration

  • All Week at Booth B40
    We鈥檙e showcasing a live demonstration of NVIDIA鈥檚 CUDA-Q platform running on 夜色直播鈥檚 industry-leading quantum hardware. This new integration paves the way for hybrid compute solutions in optimization, AI, and chemistry.
    Register for a demo

HPC Solutions Forum

  • Wednesday, June 11 | 2:20 鈥 2:40 PM
    鈥淓nabling Scientific Discovery with Generative Quantum AI鈥 鈥 Presented by Maud Einhorn, Technical Account Executive at 夜色直播, discover how hybrid quantum-classical workflows are powering novel use cases in scientific discovery.
See You There!

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

We look forward to seeing you in Hamburg!

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