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
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
May 12, 2025
夜色直播 Dominates the Quantum Landscape: New World-Record in Quantum Volume
Back in 2020, we to increase our Quantum Volume (QV), a measure of computational power, by 10x聽per year for 5 years.聽
Today, we鈥檙e pleased to share that we鈥檝e followed through on our commitment: Our System Model H2 has reached a Quantum Volume of 2虏鲁 = 8,388,608, proving not just that we always do what we say, but that our quantum computers are leading the world forward.聽
The QV benchmark was developed by IBM to represent a machine鈥檚 performance, accounting for things like qubit count, coherence times, qubit connectivity, and error rates. :听
鈥渢he higher the Quantum Volume, the higher the potential for exploring solutions to real world problems across industry, government, and research."
Our announcement today is precisely what sets us apart from the competition. No one else has been bold enough to make a similar promise on such a challenging metric 鈥 and no one else has ever completed a five-year goal like this.
We chose QV because we believe it鈥檚 a great metric. For starters, it鈥檚 not gameable, like other metrics in the ecosystem. Also, it brings together all the relevant metrics in the NISQ era for moving towards fault tolerance, such as gate fidelity and connectivity.聽
Our path to achieve a QV of over 8 million was led in part by Dr. Charlie Baldwin, who studied under the legendary Ivan H. Deutsch. Dr. Baldwin has made his name as a globally renowned expert in quantum hardware performance over the past decade, and it is because of his leadership that we don鈥檛 just claim to be the best, but that we can prove we are the best.聽
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Figure 1: All known published Quantum Volume measurements. Sources: [][][][][]
Alongside the world鈥檚 biggest quantum volume, we have the industry鈥檚 . To that point, the table below breaks down the leading commercial specs for each quantum computing architecture.聽
Table 1: Leading commercial spec for each listed architecture or demonstrated capabilities on commercial hardware. 鈥
We鈥檝e never shied away from benchmarking our machines, because we know the results will be impressive. It is our provably world-leading performance that has enabled us to demonstrate:
As we look ahead to our next generation system, Helios, 夜色直播鈥檚 Senior Director of Engineering, Dr. Brian Neyenhuis, reflects: 鈥淲e finished our five-year commitment to Quantum Volume ahead of schedule, showing that we can do more than just maintain performance while increasing system size. We can improve performance while scaling.鈥澛
Helios鈥 performance will exceed that of our previous machines, meaning that 夜色直播 will continue to lead in performance while following through on our promises.聽
As the undisputed industry leader, we鈥檙e racing against no one other than ourselves to deliver higher performance and to better serve our customers.
At the heart of quantum computing鈥檚 promise lies the ability to solve problems that are fundamentally out of reach for classical computers. One of the most powerful ways to unlock that promise is through a novel approach we call Generative Quantum AI, or GenQAI. A key element of this approach is the (GQE).
GenQAI is based on a simple but powerful idea: combine the unique capabilities of quantum hardware with the flexibility and intelligence of AI. By using quantum systems to generate data, and then using AI to learn from and guide the generation of more data, we can create a powerful feedback loop that enables breakthroughs in diverse fields.
Unlike classical systems, our quantum processing unit (QPU) produces data that is extremely difficult, if not impossible, to generate classically. That gives us a unique edge: we鈥檙e not just feeding an AI more text from the internet; we鈥檙e giving it new and valuable data that can鈥檛 be obtained anywhere else.
The Search for Ground State Energy
One of the most compelling challenges in quantum chemistry and materials science is computing the properties of a molecule鈥檚 ground state. For any given molecule or material, the ground state is its lowest energy configuration. Understanding this state is essential for understanding molecular behavior and designing new drugs or materials.
The problem is that accurately computing this state for anything but the simplest systems is incredibly complicated. You cannot even do it by brute force鈥攖esting every possible state and measuring its energy鈥攂ecause 聽the number of quantum states grows as a double-exponential, making this an ineffective solution. This illustrates the need for an intelligent way to search for the ground state energy and other molecular properties.
That鈥檚 where GQE comes in. GQE is a methodology that uses data from our quantum computers to train a transformer. The transformer then proposes promising trial quantum circuits; ones likely to prepare states with low energy. You can think of it as an AI-guided search engine for ground states. The novelty is in how our transformer is trained from scratch using data generated on our hardware.
Here's how it works:
We start with a batch of trial quantum circuits, which are run on our QPU.
Each circuit prepares a quantum state, and we measure the energy of that state with respect to the Hamiltonian for each one.
Those measurements are then fed back into a transformer model (the same architecture behind models like GPT-2) to improve its outputs.
The transformer generates a new distribution of circuits, biased toward ones that are more likely to find lower energy states.
We sample a new batch from the distribution, run them on the QPU, and repeat.
The system learns over time, narrowing in on the true ground state.
To test our system, we tackled a benchmark problem: finding the ground state energy of the hydrogen molecule (H鈧). This is a problem with a known solution, which allows us to verify that our setup works as intended. As a result, our GQE system successfully found the ground state to within chemical accuracy.
To our knowledge, we鈥檙e the first to solve this problem using a combination of a QPU and a transformer, marking the beginning of a new era in computational chemistry.
The Future of Quantum Chemistry
The idea of using a generative model guided by quantum measurements can be extended to a whole class of problems鈥攆rom to materials discovery, and potentially, even drug design.
By combining the power of quantum computing and AI we can unlock their unified full power. Our quantum processors can generate rich data that was previously unobtainable. Then, an AI can learn from that data. Together, they can tackle problems neither could solve alone.
This is just the beginning. We鈥檙e already looking at applying GQE to more complex molecules鈥攐nes that can鈥檛 currently be solved with existing methods, and we鈥檙e exploring how this methodology could be extended to real-world use cases. This opens many new doors in chemistry, and we are excited to see what comes next.
Last year, we joined forces with RIKEN, Japan's largest comprehensive research institution, to install our hardware at RIKEN鈥檚 campus in Wako, Saitama. This deployment is part of RIKEN鈥檚 project to build a quantum-HPC hybrid platform consisting of high-performance computing systems, such as the supercomputer Fugaku and 夜色直播 Systems. 聽
Today, marks the first of many breakthroughs coming from this international supercomputing partnership. The team from RIKEN and 夜色直播 joined up with researchers from Keio University to show that quantum information can be delocalized (scrambled) using a quantum circuit modeled after periodically driven systems. 聽
"Scrambling" of quantum information happens in many quantum systems, from those found in complex materials to black holes. 聽Understanding information scrambling will help researchers better understand things like thermalization and chaos, both of which have wide reaching implications.
To visualize scrambling, imagine a set of particles (say bits in a memory), where one particle holds specific information that you want to know. As time marches on, the quantum information will spread out across the other bits, making it harder and harder to recover the original information from local (few-bit) measurements.
While many classical techniques exist for studying complex scrambling dynamics, quantum computing has been known as a promising tool for these types of studies, due to its inherently quantum nature and ease with implementing quantum elements like entanglement. The joint team proved that to be true with their latest result, which shows that not only can scrambling states be generated on a quantum computer, but that they behave as expected and are ripe for further study.
Thanks to this new understanding, we now know that the preparation, verification, and application of a scrambling state, a key quantum information state, can be consistently realized using currently available quantum computers. Read the paper , and read more about our partnership with RIKEN here. 聽