Tag Archives: David Thouless

Exotic magnetism: a quantum simulation from D-Wave Sytems

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Vancouver (Canada) area company, D-Wave Systems is trumpeting itself (with good reason) again. This 2021 ‘milestone’ achievement builds on work from 2018 (see my August 23, 2018 posting for the earlier work). For me, the big excitement was finding the best explanation for quantum annealing and D-Wave’s quantum computers that I’ve seen yet (that explanation and a link to more is at the end of this posting).

A February 18, 2021 news item on phys.org announces the latest achievement,

D-Wave Systems Inc. today [February 18, 2021] published a milestone study in collaboration with scientists at Google, demonstrating a computational performance advantage, increasing with both simulation size and problem hardness, to over 3 million times that of corresponding classical methods. Notably, this work was achieved on a practical application with real-world implications, simulating the topological phenomena behind the 2016 Nobel Prize in Physics. This performance advantage, exhibited in a complex quantum simulation of materials, is a meaningful step in the journey toward applications advantage in quantum computing.

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A February 18, 2021 D-Wave Systems press release (also on EurekAlert), which originated the news item, describes the work in more detail,

The work by scientists at D-Wave and Google also demonstrates that quantum effects can be harnessed to provide a computational advantage in D-Wave processors, at problem scale that requires thousands of qubits. Recent experiments performed on multiple D-Wave processors represent by far the largest quantum simulations carried out by existing quantum computers to date.

The paper, entitled “Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets”, was published in the journal Nature Communications (DOI 10.1038/s41467-021-20901-5, February 18, 2021). D-Wave researchers programmed the D-Wave 2000Q™ system to model a two-dimensional frustrated quantum magnet using artificial spins. The behavior of the magnet was described by the Nobel-prize winning work of theoretical physicists Vadim Berezinskii, J. Michael Kosterlitz and David Thouless. They predicted a new state of matter in the 1970s characterized by nontrivial topological properties. This new research is a continuation of previous breakthrough work published by D-Wave’s team in a 2018 Nature paper entitled “Observation of topological phenomena in a programmable lattice of 1,800 qubits” (Vol. 560, Issue 7719, August 22, 2018). In this latest paper, researchers from D-Wave, alongside contributors from Google, utilize D-Wave’s lower noise processor to achieve superior performance and glean insights into the dynamics of the processor never observed before.

“This work is the clearest evidence yet that quantum effects provide a computational advantage in D-Wave processors,” said Dr. Andrew King, principal investigator for this work at D-Wave. “Tying the magnet up into a topological knot and watching it escape has given us the first detailed look at dynamics that are normally too fast to observe. What we see is a huge benefit in absolute terms, with the scaling advantage in temperature and size that we would hope for. This simulation is a real problem that scientists have already attacked using the algorithms we compared against, marking a significant milestone and an important foundation for future development. This wouldn’t have been possible today without D-Wave’s lower noise processor.”

“The search for quantum advantage in computations is becoming increasingly lively because there are special problems where genuine progress is being made. These problems may appear somewhat contrived even to physicists, but in this paper from a collaboration between D-Wave Systems, Google, and Simon Fraser University [SFU], it appears that there is an advantage for quantum annealing using a special purpose processor over classical simulations for the more ‘practical’ problem of finding the equilibrium state of a particular quantum magnet,” said Prof. Dr. Gabriel Aeppli, professor of physics at ETH Zürich and EPF Lausanne, and head of the Photon Science Division of the Paul Scherrer Institute. “This comes as a surprise given the belief of many that quantum annealing has no intrinsic advantage over path integral Monte Carlo programs implemented on classical processors.”

“Nascent quantum technologies mature into practical tools only when they leave classical counterparts in the dust in solving real-world problems,” said Hidetoshi Nishimori, Professor, Institute of Innovative Research, Tokyo Institute of Technology. “A key step in this direction has been achieved in this paper by providing clear evidence of a scaling advantage of the quantum annealer over an impregnable classical computing competitor in simulating dynamical properties of a complex material. I send sincere applause to the team.”

“Successfully demonstrating such complex phenomena is, on its own, further proof of the programmability and flexibility of D-Wave’s quantum computer,” said D-Wave CEO Alan Baratz. “But perhaps even more important is the fact that this was not demonstrated on a synthetic or ‘trick’ problem. This was achieved on a real problem in physics against an industry-standard tool for simulation–a demonstration of the practical value of the D-Wave processor. We must always be doing two things: furthering the science and increasing the performance of our systems and technologies to help customers develop applications with real-world business value. This kind of scientific breakthrough from our team is in line with that mission and speaks to the emerging value that it’s possible to derive from quantum computing today.”

The scientific achievements presented in Nature Communications further underpin D-Wave’s ongoing work with world-class customers to develop over 250 early quantum computing applications, with a number piloting in production applications, in diverse industries such as manufacturing, logistics, pharmaceutical, life sciences, retail and financial services. In September 2020, D-Wave brought its next-generation Advantage™ quantum system to market via the Leap™ quantum cloud service. The system includes more than 5,000 qubits and 15-way qubit connectivity, as well as an expanded hybrid solver service capable of running business problems with up to one million variables. The combination of Advantage’s computing power and scale with the hybrid solver service gives businesses the ability to run performant, real-world quantum applications for the first time.

That last paragraph seems more sales pitch than research oriented. It’s not unexpected in a company’s press release but I was surprised that the editors at EurekAlert didn’t remove it.

Here’s a link to and a citation for the latest paper,

Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets by Andrew D. King, Jack Raymond, Trevor Lanting, Sergei V. Isakov, Masoud Mohseni, Gabriel Poulin-Lamarre, Sara Ejtemaee, William Bernoudy, Isil Ozfidan, Anatoly Yu. Smirnov, Mauricio Reis, Fabio Altomare, Michael Babcock, Catia Baron, Andrew J. Berkley, Kelly Boothby, Paul I. Bunyk, Holly Christiani, Colin Enderud, Bram Evert, Richard Harris, Emile Hoskinson, Shuiyuan Huang, Kais Jooya, Ali Khodabandelou, Nicolas Ladizinsky, Ryan Li, P. Aaron Lott, Allison J. R. MacDonald, Danica Marsden, Gaelen Marsden, Teresa Medina, Reza Molavi, Richard Neufeld, Mana Norouzpour, Travis Oh, Igor Pavlov, Ilya Perminov, Thomas Prescott, Chris Rich, Yuki Sato, Benjamin Sheldan, George Sterling, Loren J. Swenson, Nicholas Tsai, Mark H. Volkmann, Jed D. Whittaker, Warren Wilkinson, Jason Yao, Hartmut Neven, Jeremy P. Hilton, Eric Ladizinsky, Mark W. Johnson, Mohammad H. Amin. Nature Communications volume 12, Article number: 1113 (2021) DOI: https://doi.org/10.1038/s41467-021-20901-5 Published: 18 February 2021

This paper is open access.

Quantum annealing and more

Dr. Andrew King, one of the D-Wave researchers, has written a February 18, 2021 article on Medium explaining some of the work. I’ve excerpted one of King’s points,

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Insight #1: We observed what actually goes on under the hood in the processor for the first time

Quantum annealing — the approach adopted by D-Wave from the beginning — involves setting up a simple but purely quantum initial state, and gradually reducing the “quantumness” until the system is purely classical. This takes on the order of a microsecond. If you do it right, the classical system represents a hard (NP-complete) computational problem, and the state has evolved to an optimal, or at least near-optimal, solution to that problem.

What happens at the beginning and end of the computation are about as simple as quantum computing gets. But the action in the middle is hard to get a handle on, both theoretically and experimentally. That’s one reason these experiments are so important: they provide high-fidelity measurements of the physical processes at the core of quantum annealing. Our 2018 Nature article introduced the same simulation, but without measuring computation time. To benchmark the experiment this time around, we needed lower-noise hardware (in this case, we used the D-Wave 2000Q lower noise quantum computer), and we needed, strangely, to slow the simulation down. Since the quantum simulation happens so fast, we actually had to make things harder. And we had to find a way to slow down both quantum and classical simulation in an equitable way. The solution? Topological obstruction.

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If you have time and the inclination, I encourage you to read King’s piece.

D-Wave and the first large-scale quantum simulation of a* topological state of matter

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This is all about a local (Burnaby is one of the metro Vancouver municipalities) quantum computing companies, D-Wave Systems. The company has been featured here from time to time. It’s usually about about their quantum technology (they are considered a technology star in local and [I think] other circles) but my March 9, 2018 posting about the SXSW (South by Southwest) festival noted that Bo Ewald, President, D-Wave Systems US, was a member of the ‘Quantum Computing: Science Fiction to Science Fact’ panel.

Now, they’re back making technology announcements like this August 22, 2018 news item on phys.org (Note: Links have been removed),

D-Wave Systems today [August 22, 2018] published a milestone study demonstrating a topological phase transition using its 2048-qubit annealing quantum computer. This complex quantum simulation of materials is a major step toward reducing the need for time-consuming and expensive physical research and development.

The paper, entitled “Observation of topological phenomena in a programmable lattice of 1,800 qubits”, was published in the peer-reviewed journal Nature. This work marks an important advancement in the field and demonstrates again that the fully programmable D-Wave quantum computer can be used as an accurate simulator of quantum systems at a large scale. The methods used in this work could have broad implications in the development of novel materials, realizing Richard Feynman’s original vision of a quantum simulator. This new research comes on the heels of D-Wave’s recent Science paper demonstrating a different type of phase transition in a quantum spin-glass simulation. The two papers together signify the flexibility and versatility of the D-Wave quantum computer in quantum simulation of materials, in addition to other tasks such as optimization and machine learning.

An August 22, 2108 D-Wave Systems news release (also on EurekAlert), which originated the news item, delves further (Note: A link has been removed),

In the early 1970s, theoretical physicists Vadim Berezinskii, J. Michael Kosterlitz and David Thouless predicted a new state of matter characterized by nontrivial topological properties. The work was awarded the Nobel Prize in Physics in 2016. D-Wave researchers demonstrated this phenomenon by programming the D-Wave 2000Q™ system to form a two-dimensional frustrated lattice of artificial spins. The observed topological properties in the simulated system cannot exist without quantum effects and closely agree with theoretical predictions.

“This paper represents a breakthrough in the simulation of physical systems which are otherwise essentially impossible,” said 2016 Nobel laureate Dr. J. Michael Kosterlitz. “The test reproduces most of the expected results, which is a remarkable achievement. This gives hope that future quantum simulators will be able to explore more complex and poorly understood systems so that one can trust the simulation results in quantitative detail as a model of a physical system. I look forward to seeing future applications of this simulation method.”

“The work described in the Nature paper represents a landmark in the field of quantum computation: for the first time, a theoretically predicted state of matter was realized in quantum simulation before being demonstrated in a real magnetic material,” said Dr. Mohammad Amin, chief scientist at D-Wave. “This is a significant step toward reaching the goal of quantum simulation, enabling the study of material properties before making them in the lab, a process that today can be very costly and time consuming.”

“Successfully demonstrating physics of Nobel Prize-winning importance on a D-Wave quantum computer is a significant achievement in and of itself. But in combination with D-Wave’s recent quantum simulation work published in Science, this new research demonstrates the flexibility and programmability of our system to tackle recognized, difficult problems in a variety of areas,” said Vern Brownell, D-Wave CEO.

“D-Wave’s quantum simulation of the Kosterlitz-Thouless transition is an exciting and impactful result. It not only contributes to our understanding of important problems in quantum magnetism, but also demonstrates solving a computationally hard problem with a novel and efficient mapping of the spin system, requiring only a limited number of qubits and opening new possibilities for solving a broader range of applications,” said Dr. John Sarrao, principal associate director for science, technology, and engineering at Los Alamos National Laboratory.

“The ability to demonstrate two very different quantum simulations, as we reported in Science and Nature, using the same quantum processor, illustrates the programmability and flexibility of D-Wave’s quantum computer,” said Dr. Andrew King, principal investigator for this work at D-Wave. “This programmability and flexibility were two key ingredients in Richard Feynman’s original vision of a quantum simulator and open up the possibility of predicting the behavior of more complex engineered quantum systems in the future.”

The achievements presented in Nature and Science join D-Wave’s continued work with world-class customers and partners on real-world prototype applications (“proto-apps”) across a variety of fields. The 70+ proto-apps developed by customers span optimization, machine learning, quantum material science, cybersecurity, and more. Many of the proto-apps’ results show that D-Wave systems are approaching, and sometimes surpassing, conventional computing in terms of performance or solution quality on real problems, at pre-commercial scale. As the power of D-Wave systems and software expands, these proto-apps point to the potential for scaled customer application advantage on quantum computers.

The company has prepared a video describing Richard Feynman’s proposal about quantum computing and celebrating their latest achievement,

Here’s the company’s Youtube video description,

In 1982, Richard Feynman proposed the idea of simulating the quantum physics of complex systems with a programmable quantum computer. In August 2018, his vision was realized when researchers from D-Wave Systems and the Vector Institute demonstrated the simulation of a topological phase transition—the subject of the 2016 Nobel Prize in Physics—in a fully programmable D-Wave 2000Q™ annealing quantum computer. This complex quantum simulation of materials is a major step toward reducing the need for time-consuming and expensive physical research and development.

You may want to check out the comments in response to the video.

Here’s a link to and a citation for the Nature paper,

Observation of topological phenomena in a programmable lattice of 1,800 qubits by Andrew D. King, Juan Carrasquilla, Jack Raymond, Isil Ozfidan, Evgeny Andriyash, Andrew Berkley, Mauricio Reis, Trevor Lanting, Richard Harris, Fabio Altomare, Kelly Boothby, Paul I. Bunyk, Colin Enderud, Alexandre Fréchette, Emile Hoskinson, Nicolas Ladizinsky, Travis Oh, Gabriel Poulin-Lamarre, Christopher Rich, Yuki Sato, Anatoly Yu. Smirnov, Loren J. Swenson, Mark H. Volkmann, Jed Whittaker, Jason Yao, Eric Ladizinsky, Mark W. Johnson, Jeremy Hilton, & Mohammad H. Amin. Nature volume 560, pages456–460 (2018) DOI: https://doi.org/10.1038/s41586-018-0410-x Published 22 August 2018

This paper is behind a paywall but, for those who don’t have access, there is a synopsis here.

For anyone curious about the earlier paper published in July 2018, here’s a link and a citation,

Phase transitions in a programmable quantum spin glass simulator by R. Harris, Y. Sato, A. J. Berkley, M. Reis, F. Altomare, M. H. Amin, K. Boothby, P. Bunyk, C. Deng, C. Enderud, S. Huang, E. Hoskinson, M. W. Johnson, E. Ladizinsky, N. Ladizinsky, T. Lanting, R. Li, T. Medina, R. Molavi, R. Neufeld, T. Oh, I. Pavlov, I. Perminov, G. Poulin-Lamarre, C. Rich, A. Smirnov, L. Swenson, N. Tsai, M. Volkmann, J. Whittaker, J. Yao. Science 13 Jul 2018: Vol. 361, Issue 6398, pp. 162-165 DOI: 10.1126/science.aat2025

This paper too is behind a paywall.

You can find out more about D-Wave here.

*ETA ‘a’ to the post title on February 24, 2021.

The physics of melting in two-dimensional systems

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You might want to skip over the reference to snow as it doesn’t have much relevance to this story about ‘melting’, from a Feb. 1, 2017 news item on Nanowerk (Note: A link has been removed),

Snow falls in winter and melts in spring, but what drives the phase change in between?
Although melting is a familiar phenomenon encountered in everyday life, playing a part in many industrial and commercial processes, much remains to be discovered about this transformation at a fundamental level.

In 2015, a team led by the University of Michigan’s Sharon Glotzer used high-performance computing at the Department of Energy’s (DOE’s) Oak Ridge National Laboratory [ORNL] to study melting in two-dimensional (2-D) systems, a problem that could yield insights into surface interactions in materials important to technologies like solar panels, as well as into the mechanism behind three-dimensional melting. The team explored how particle shape affects the physics of a solid-to-fluid melting transition in two dimensions.

Using the Cray XK7 Titan supercomputer at the Oak Ridge Leadership Computing Facility (OLCF), a DOE Office of Science User Facility, the team’s [latest?] work revealed that the shape and symmetry of particles can dramatically affect the melting process (“Shape and symmetry determine two-dimensional melting transitions of hard regular polygons”). This fundamental finding could help guide researchers in search of nanoparticles with desirable properties for energy applications.

There is a video  of the ‘melting’ process but I have to confess to finding it a bit enigmatic,

A Feb. 1, 2017 ORNL news release (also on EurekAlert), which originated the news item, provides more detail about the research,

o tackle the problem, Glotzer’s team needed a supercomputer capable of simulating systems of up to 1 million hard polygons, simple particles used as stand-ins for atoms, ranging from triangles to 14-sided shapes. Unlike traditional molecular dynamics simulations that attempt to mimic nature, hard polygon simulations give researchers a pared-down environment in which to evaluate shape-influenced physics.

“Within our simulated 2-D environment, we found that the melting transition follows one of three different scenarios depending on the shape of the systems’ polygons,” University of Michigan research scientist Joshua Anderson said. “Notably, we found that systems made up of hexagons perfectly follow a well-known theory for 2-D melting, something that hasn’t been described until now.”

Shifting Shape Scenarios

In 3-D systems such as a thinning icicle, melting takes the form of a first-order phase transition. This means that collections of molecules within these systems exist in either solid or liquid form with no in-between in the presence of latent heat, the energy that fuels a solid-to-fluid phase change . In 2-D systems, such as thin-film materials used in batteries and other technologies, melting can be more complex, sometimes exhibiting an intermediate phase known as the hexatic phase.

The hexatic phase, a state characterized as a halfway point between an ordered solid and a disordered liquid, was first theorized in the 1970s by researchers John Kosterlitz, David Thouless, Burt Halperin, David Nelson, and Peter Young. The phase is a principle feature of the KTHNY theory, a 2-D melting theory posited by the researchers (and named based on the first letters of their last names). In 2016 Kosterlitz and Thouless were awarded the Nobel Prize in Physics, along with physicist Duncan Haldane, for their contributions to 2-D materials research.

At the molecular level, solid, hexatic, and liquid systems are defined by the arrangement of their atoms. In a crystalline solid, two types of order are present: translational and orientational. Translational order describes the well-defined paths between atoms over distances, like blocks in a carefully constructed Jenga tower. Orientational order describes the relational and clustered order shared between atoms and groups of atoms over distances. Think of that same Jenga tower turned askew after several rounds of play. The general shape of the tower remains, but its order is now fragmented.

The hexatic phase has no translational order but possesses orientational order. (A liquid has neither translational nor orientational order but exhibits short-range order, meaning any atom will have some average number of neighbors nearby but with no predicable order.)

Deducing the presence of a hexatic phase requires a leadership-class computer that can calculate large hard-particle systems. Glotzer’s team gained access to the OLCF’s 27-petaflop Titan through the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program, running its GPU-accelerated HOOMD-blue code to maximize time on the machine.

On Titan, HOOMD-blue used 64 GPUs for each massively parallel Monte Carlo simulation of up to 1 million particles. Researchers explored 11 different shape systems, applying an external pressure to push the particles together. Each system was simulated at 21 different densities, with the lowest densities representing a fluid state and the highest densities a solid state.

The simulations demonstrated multiple melting scenarios hinging on the polygons’ shape. Systems with polygons of seven sides or more closely followed the melting behavior of hard disks, or circles, exhibiting a continuous phase transition from the solid to the hexatic phase and a first-order phase transition from the hexatic to the liquid phase. A continuous phase transition means a constantly changing area in response to a changing external pressure. A first-order phase transition is characterized by a discontinuity in which the volume jumps across the phase transition in response to the changing external pressure. The team found pentagons and fourfold pentilles, irregular pentagons with two different edge lengths, exhibit a first-order solid-to-liquid phase transition.

The most significant finding, however, emerged from hexagon systems, which perfectly followed the phase transition described by the KTHNY theory. In this scenario, the particles’ shift from solid to hexatic and hexatic to fluid in a perfect continuous phase transition pattern.

“It was actually sort of surprising that no one else has found that until now,” Anderson said, “because it seems natural that the hexagon, with its six sides, and the honeycomb-like hexagonal arrangement would be a perfect match for this theory” in which the hexatic phase generally contains sixfold orientational order.

Glotzer’s team, which recently received a 2017 INCITE allocation, is now applying its leadership-class computing prowess to tackle phase transitions in 3-D. The team is focusing on how fluid particles crystallize into complex colloids—mixtures in which particles are suspended throughout another substance. Common examples of colloids include milk, paper, fog, and stained glass.

“We’re planning on using Titan to study how complexity can arise from these simple interactions, and to do that we’re actually going to look at how the crystals grow and study the kinetics of how that happens,” said Anderson.

There is a paper on arXiv,

Shape and symmetry determine two-dimensional melting transitions of hard regular polygons by Joshua A. Anderson, James Antonaglia, Jaime A. Millan, Michael Engel, Sharon C. Glotzer
(Submitted on 2 Jun 2016 (v1), last revised 23 Dec 2016 (this version, v2))  arXiv:1606.00687 [cond-mat.soft] (or arXiv:1606.00687v2

This paper is open access and open to public peer review.