How Quantinuum 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
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 – the transition from solid to liquid or from liquid to gas.
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.
Quantinuum researchers recently used the H1-1 quantum computer to computationally model a group of highly correlated quantum particles at a quantum critical point — 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. 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, Probing critical states of matter on a digital quantum computer, the Quantinuum 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, “This 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.”
The role of quantum tensor networks
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.
The Quantinuum 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.
“By 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,” said Dave Hayes, Lead of the U.S. quantum theory team at Quantinuum and one of the paper’s authors. “So, it can, in principle, go out and simulate any system that you can dream of.”
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.
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.
“That's as hard as it gets for these systems,” Dave explained. “So that's where we want to look for quantum advantage – because we want the problem to be as hard as possible on the classical computer, and then have a quantum computer solve it.”
To improve the results, the team used two error mitigation techniques, symmetry-based error heralding, which is made possible by the MERA structure, and zero-noise extrapolation, 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 Quantinuum team describes this sort of problem as a stepping-stone, which allows the researchers to explore quantum tensor network methods on today’s 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.
“Potentially, our biggest applications over the next couple of years will include studying solid-state systems, physics systems, many-body systems, and modeling them,” said Jenni Strabley, Senior Director of Offering Management at Quantinuum.
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 – quantum states that are much more difficult to calculate classically.
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, Quantinuum’s 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 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.
For a novel technology to be successful, it must prove that it is both useful and works as described.
Checking that our computers “work as described” is called benchmarking and verification by the experts. We are proud to be leaders in this field, with the most benchmarked quantum processors in the world. We also work with National Laboratories in various countries to develop new benchmarking techniques and standards. Additionally, we have our own team of experts leading the field in benchmarking and verification.
Currently, a lot of verification (i.e. checking that you got the right answer) is done by classical computers – most quantum processors can still be simulated by a classical computer. As we move towards quantum processors that are hard (or impossible) to simulate, this introduces a problem: how can we keep checking that our technology is working correctly without simulating it?
We recently partnered with the UK’s Quantum Software Lab to develop a novel and scalable verification and benchmarking protocol that will help us as we make the transition to quantum processors that cannot be simulated.
This new protocol does not require classical simulation, or the transfer of a qubit between two parties. The team’s “on-chip” verification protocol eliminates the need for a physically separated verifier and makes no assumptions about the processor’s noise. To top it all off, this new protocol is qubit-efficient.
The team’s protocol is application-agnostic, benefiting all users. Further, the protocol is optimized to our QCCD hardware, meaning that we have a path towards verified quantum advantage – as we compute more things that cannot be classically simulated, we will be able to check that what we are doing is right.
Running the protocol on Quantinuum System Model H1, the team ended up performing the largest verified Measurement Based Quantum Computing (MBQC) circuit to date. This was enabled by our System Model H1’s low cross-talk gate zones, mid-circuit measurement and reset, and long coherence times. By performing the largest verified MBQC computation to date, and by verifying computations significantly larger than any others to be verified before, we reaffirm the Quantinuum Systems as best-in-class.
Particle accelerators like the LHC take serious computing power. Often on the bleeding-edge of computing technology, accelerator projects sometimes even drive innovations in computing. In fact, while there is some controversy over exactly where the world wide web was created, it is often attributed to Tim Berners-Lee at CERN, who developed it to meet the demand for automated information-sharing between scientists in universities and institutes around the world.
With annual data generated by accelerators in excess of exabytes (a billion gigabytes), tens of millions of lines of code written to support the experiments, and incredibly demanding hardware requirements, it’s no surprise that the High Energy Physics community is interested in quantum computing, which offers real solutions to some of their hardest problems. Furthermore, the HEP community is well-positioned to support the early stages of technological development: with budgets in the 10s of billions per year and tens of thousands of scientists and engineers working on accelerator and computational physics, this is a ripe industry for quantum computing to tap.
As the authors of this paper stated: “[Quantum Computing] encompasses several defining characteristics that are of particular interest to experimental HEP: the potential for quantum speed-up in processing time, sensitivity to sources of correlations in data, and increased expressivity of quantum systems... Experiments running on high-luminosity accelerators need faster algorithms; identification and reconstruction algorithms need to capture correlations in signals; simulation and inference tools need to express and calculate functions that are classically intractable”
The authors go on to state: “Within the existing data reconstruction and analysis paradigm, access to algorithms that exhibit quantum speed-ups would revolutionize the simulation of large-scale quantum systems and the processing of data from complex experimental set-ups. This would enable a new generation of precision measurements to probe deeper into the nature of the universe. Existing measurements may contain the signatures of underlying quantum correlations or other sources of new physics that are inaccessible to classical analysis techniques. Quantum algorithms that leverage these properties could potentially extract more information from a given dataset than classical algorithms.”
Our scientists have been working with a team at DESY, one of the world’s leading accelerator centers, to bring the power of quantum computing to particle physics. DESY, short for Deutsches Elektronen-Synchrotron, is a national research center for fundamental science located in Hamburg and Zeuthen, where the Center for Quantum Technologies and Applications (CQTA) is based. DESY operates, develops, and constructs particle accelerators used to investigate the structure, dynamics and function of matter, and conducts a broad spectrum of interdisciplinary scientific research. DESY employs about 3,000 staff members from more than 60 nations, and is part of the worldwide computer network to store and analyze the enormous flood of data that is produced by the LHC in Geneva.
In a recent paper, our scientists collaborated with scientists from DESY, the Leiden Institute of Advanced Computer Science (LIACS), and Northeastern University to explore using a generative quantum machine learning model, called a “quantum Boltzmann machine” to untangle data from CERN’s LHC.
The goal was to learn probability distributions relevant to high energy physics better than the corresponding classical models. The data specifically contains “particle jet events”, which describe how colliders collect data about the subatomic particles generated during the experiments.
In some cases the quantum Boltzmann machine was indeed better, compared to a classical Boltzmann machine. The team is analyzed when and why this happens, understanding better how to apply these new quantum tools in this research setting. The team also studied the effect of the data encoding into a quantum state, noting that it can have a decisive effect on the training performance. Especially enticing is that the quantum Boltzmann machine is efficiently trainable, which our scientists showed in a recent paper published in Nature Communications Physics.
Find the Quantinuum team at this year’s SC24 conference from November 17th – 22nd in Atlanta, Georgia. Meet our team at Booth #4351 to discover how Quantinuum is bridging the gap between quantum computing and high-performance compute with leading industry partners.
The Quantinuum team will be participating various events, panels and poster sessions to showcase our quantum computing technologies. Join us at the below sessions:
Monday, Nov 18, 8:00 - 8:25pm, EST
Panel: KAUST booth 1031
Nash Palaniswamy, Quantinuum’s CCO, will join a panel discussion with quantum vendors and KAUST partners to discuss advancements in quantum technology.
Monday, Nov 18, 9:00 - 11:59pm, EST
Beowulf Bash: World of Coca-Cola
This year, we are proudly sponsoring the Beowulf Bash, a unique event organized to bring the HPC community together for a night of unique entertainment! Join us at the event on Monday, November 18th, 9:00pm at the World of Coca-Cola.
Wednesday, Nov 20, 3:30 – 5:00pm, EST
Panel: Educating for a Hybrid Future: Bridging the Gap between High-Performance and Quantum Computing
Vincent Anandraj, Quantinuum’s Director of Global Ecosystem and Strategic Alliances, will moderate this panel which brings together experts from leading supercomputing centers and the quantum computing industry, including PSC, Leibniz Supercomputing Centre, IQM Quantum Computers, NVIDIA, and National Research Foundation.
Thursday, Nov 21, 11:00 – 11:30am, EST
Presentation: Realizing Quantum Kernel Models at Scale with Matrix Product State Simulation
Pablo Andres-Martinez, Research Scientist at Quantinuum, will present research done in collaboration with HSBC, where the team applied quantum methods to fraud detection.