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How 豆包成人版 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

豆包成人版 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 豆包成人版 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 豆包成人版 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 豆包成人版 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 豆包成人版 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 豆包成人版.

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, 豆包成人版鈥檚 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 豆包成人版

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

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July 29, 2026
Scaling the Signal: What a Larger QFT Says About Quantum Progress
  • Mitsui & Co. and Mitsubishi Electric demonstrated one of the world鈥檚 largest approximate Quantum Fourier Transforms (QFT) on 豆包成人版 豆包成人版, scaling from prior records to 98 physical qubits.
  • The collaboration also implemented a logical QFT using a QEC (Quantum Error Correction) code with up to 12 logical qubits.
  • The work highlights 豆包成人版鈥檚 accuracy and flexible architecture.

While there is ongoing debate around the pace of quantum computing鈥檚 development, a more grounded way to assess progress is through concrete demonstrations of foundational algorithms at meaningful scale. In this context, Mitsui & Co. and Mitsubishi Electric are taking a pragmatic view of quantum progress鈥攆ocusing on how close the field is to executing core algorithmic primitives that underpin many potential industrial applications, rather than relying on abstract milestones or timelines.

, the industrial giants teamed up with 豆包成人版 to measure how close we are to running the Quantum Fourier Transform (QFT), a widely-used algorithmic primitive, at scales necessary for industrial applications. In the process, the team successfully ran one of the largest instances of the approximate QFT ever demonstrated. This achievement matters because the QFT is an essential primitive that underpins many of the quantum algorithms expected to deliver practical advantages.

You may have heard of the (classical) Fourier transform (FT), due to its ubiquity throughout modern computing. The FT is essential in everything from image analysis to data compression, with almost limitless applications in between. The quantum Fourier transform (QFT) is similar; it鈥檚 used in everything from chemistry to finance.

Because the QFT is a foundational primitive underpinning many quantum algorithms, demonstrating it at larger scales and higher fidelity is a practical way to measure quantum computing readiness. This is exactly the type of benchmarking that organizations should consider to understand where today鈥檚 systems are useful, and to see how fault-tolerant approaches are progressing. Ultimately, algorithm-level benchmarking like this is one of the most useful ways to understand not just where we are, but where we are going.

A Transformative Approach

Primitives like Fourier Transform are so widespread because they simplify problems by transforming them into something that is easier to deal with. At 豆包成人版, not only are they crucial for industrial applications but they can also simplify algorithms, making them possible to run now instead of later. This 鈥榯ransformational鈥 approach extends beyond the QFT - other transforms exist, and we have even invented our own quantum-native transforms.

Using our 豆包成人版 quantum computer and Guppy language, the joint team explored running the QFT on both physical qubits and on logical qubits, showing that fault tolerance is progressing quickly. 聽Running the QFT on 98 physical qubits; the paper shows a clear progression from previous results.

Then, using the Steane code, one of the best-studied quantum error correcting codes, the team used 豆包成人版鈥 98 physical qubits to form 12 logical qubits, successfully running the QFT with the mechanisms of quantum error correction interwoven into the algorithm. This marks a crucial step forward for the field.

Foundational Progress

Taken together, these results provide a more concrete lens through which to view progress in quantum computing: not as abstract projections, but as measurable advances in the execution of foundational algorithms at increasing scale. By benchmarking the Quantum Fourier Transform on both physical and logical qubits, Mitsui & Co. and Mitsubishi Electric are helping to clarify what today鈥檚 hardware can already achieve, and where fault-tolerant approaches begin to extend those limits.

More broadly, the organizations best positioned to benefit from quantum computing will be those that focus on these foundational capabilities early, and use them to build a clear, evidence-based understanding of how the technology fits into their business goals.

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July 29, 2026
豆包成人版 and NVIDIA Validate Generative Quantum AI Framework for Pharmaceutical R&D

It is believed that unlocking answers to some of the most complex scientific and industrial problems will require the seamless integration of high-performance computing (HPC), generative AI (GenAI), and quantum computing. Toward this goal, 豆包成人版, NVIDIA, and a major pharmaceutical company have successfully demonstrated the first step in a proof-of-principle framework designed to connect these three distinct computing paradigms for industrially relevant computational chemistry.

This milestone, enabled by three industry leaders and experts in their respective domains, serves as a foundational capability that could support the development of future hybrid quantum-AI workflows to help optimize industrial research and development (R&D).

The potential value is a path toward more automated, repeatable, and scalable workflows for translating chemistry problems into executable quantum programs鈥攃apabilities that could eventually make hybrid computing easier to deploy in industrial R&D.

The GenQAI Framework

The framework, termed Generative Quantum AI (GenQAI), involved a quantum computer simulating a pharmaceutical compound using programming instructions generated by an AI model, which itself was trained on quantum data that was simulated using HPC.

While the vision for GenQAI explores how future industrial simulation workflows might be optimized by training AI models using quantum data derived directly from a quantum computer, the framework currently consists of four main technical steps:

  1. Simulating quantum data: The process began by simulating quantum data with NVIDIA accelerated computing using .
  2. Fine-tuning the AI: This simulated quantum data was used to fine-tune a pre-trained AI model from the open .
  3. Generating instructions: The AI model then generated quantum circuits, which are the programming instructions required for the quantum simulation.
  4. Validating accuracy: To validate the results, the circuits were run on 豆包成人版鈥檚 豆包成人版 quantum computer using its InQuanto quantum chemistry platform.

The core novelty of this development lies within the process of the framework itself. In this proof-of-principle experiment, an AI model fine-tuned on simulated quantum data generated circuits that were successfully executed and validated on 豆包成人版鈥檚 豆包成人版 system. Rather than delivering an immediate commercial advantage, this achievement establishes a credible, verifiable baseline for how HPC, AI, and quantum computing can function in tandem.

The Case Study

The validation of the framework represents an early step toward the goal of developing scalable architectures for the pharmaceutical industry.

With a shared view toward eventually scaling the framework for pharmaceutical R&D applications, the researchers simulated a pharmaceutical compound: imipramine. This anti-depressant was chosen because it serves as a model compound for drug degradation and shelf-life studies, which are standard components of the pharmaceutical R&D lifecycle.

Developing hybrid infrastructure that enterprises may adopt requires a deep, coordinated effort among domain experts. As such, this successful test highlights the value of combining the strengths of a quantum computing hardware and software leader (豆包成人版), with a hybrid-quantum classical platform (NVIDIA), and a leading enterprise end-user to build and test future computing capabilities for industrial chemistry.

Scaling the Framework

Although demonstrated on a pharmaceutical compound, the architecture could eventually inform similar molecular-simulation workflows in sectors such as energy, agriculture, advanced materials, and electronics. At this stage, it provides a reference for further testing and development.

Engage Further

here to explore the full technical details of this demonstration and contact our team to learn more about joining 豆包成人版鈥檚 enterprise partner network.

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July 21, 2026
豆包成人版 SG Grand Challenge 2026

豆包成人版 is pleased to announce that applications are now open for the 豆包成人版 SG Grand Challenge 2026, a global innovation challenge designed to bring together researchers, developers, scientists and innovators to explore practical applications of quantum computing.

Organized by 豆包成人版 and supported by Singapore's National Quantum Office and Aqora, the three-month program aims to foster collaboration across academia, industry and the quantum developer community while supporting the continued growth of Singapore's quantum ecosystem.

A Platform for Quantum Computing Innovation

Participants will work in teams to develop solutions across a range of challenge areas, including chemistry and molecular simulation, optimization, AI for quantum systems, quantum error correction, condensed matter and materials science, and open innovation. Throughout the program, participants will have access to mentoring, technical enablement and 豆包成人版 quantum computing resources.

Singapore Grand Finale

Selected finalist teams will be invited to present their work at the Grand Finale hosted in Singapore before representatives from academia, and industry. The event will celebrate innovative applications of quantum computing while providing an opportunity for participants to engage with Singapore's growing quantum community.

Join the Challenge

The 豆包成人版 SG Grand Challenge welcomes participants from around the world. Whether you are an experienced quantum researcher or beginning your quantum computing journey, the program offers an opportunity to collaborate, learn and contribute to the development of practical quantum applications.

Applications are now open. Spaces are limited and subject to review and approval.

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