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Creating time crystals with a quantum computer

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This November 30, 2021 news item on phys.org about time crystals caught my attention,

There is a huge global effort to engineer a computer capable of harnessing the power of quantum physics to carry out computations of unprecedented complexity. While formidable technological obstacles still stand in the way of creating such a quantum computer, today’s early prototypes are still capable of remarkable feats.

For example, the creation of a new phase of matter called a “time crystal.” Just as a crystal’s structure repeats in space, a time crystal repeats in time and, importantly, does so infinitely and without any further input of energy—like a clock that runs forever without any batteries. The quest to realize this phase of matter has been a longstanding challenge in theory and experiment—one that has now finally come to fruition.

In research published Nov. 30 [2021] in Nature, a team of scientists from Stanford University, Google Quantum AI, the Max Planck Institute for Physics of Complex Systems and Oxford University detail their creation of a time crystal using Google’s Sycamore quantum computing hardware.

The Google Sycamore chip used in the creation of a time crystal. Credit: Google Quantum AI [downloaded from https://phys.org/news/2021-11-physicists-crystals-quantum.html]

A November 30, 2021 Stanford University news release (also on EurekAlert) by Taylor Kubota, which originated the news item, delves further into the work and into the nature of time crystals,

“The big picture is that we are taking the devices that are meant to be the quantum computers of the future and thinking of them as complex quantum systems in their own right,” said Matteo Ippoliti, a postdoctoral scholar at Stanford and co-lead author of the work. “Instead of computation, we’re putting the computer to work as a new experimental platform to realize and detect new phases of matter.”

For the team, the excitement of their achievement lies not only in creating a new phase of matter but in opening up opportunities to explore new regimes in their field of condensed matter physics, which studies the novel phenomena and properties brought about by the collective interactions of many objects in a system. (Such interactions can be far richer than the properties of the individual objects.)

“Time-crystals are a striking example of a new type of non-equilibrium quantum phase of matter,” said Vedika Khemani, assistant professor of physics at Stanford and a senior author of the paper. “While much of our understanding of condensed matter physics is based on equilibrium systems, these new quantum devices are providing us a fascinating window into new non-equilibrium regimes in many-body physics.”

What a time crystal is and isn’t

The basic ingredients to make this time crystal are as follows: The physics equivalent of a fruit fly and something to give it a kick. The fruit fly of physics is the Ising model, a longstanding tool for understanding various physical phenomena – including phase transitions and magnetism – which consists of a lattice where each site is occupied by a particle that can be in two states, represented as a spin up or down.

During her graduate school years, Khemani, her doctoral advisor Shivaji Sondhi, then at Princeton University, and Achilleas Lazarides and Roderich Moessner at the Max Planck Institute for Physics of Complex Systems stumbled upon this recipe for making time crystals unintentionally. They were studying non-equilibrium many-body localized systems – systems where the particles get “stuck” in the state in which they started and can never relax to an equilibrium state. They were interested in exploring phases that might develop in such systems when they are periodically “kicked” by a laser. Not only did they manage to find stable non-equilibrium phases, they found one where the spins of the particles flipped between patterns that repeat in time forever, at a period twice that of the driving period of the laser, thus making a time crystal.

The periodic kick of the laser establishes a specific rhythm to the dynamics. Normally the “dance” of the spins should sync up with this rhythm, but in a time crystal it doesn’t. Instead, the spins flip between two states, completing a cycle only after being kicked by the laser twice. This means that the system’s “time translation symmetry” is broken. Symmetries play a fundamental role in physics, and they are often broken – explaining the origins of regular crystals, magnets and many other phenomena; however, time translation symmetry stands out because unlike other symmetries, it can’t be broken in equilibrium. The periodic kick is a loophole that makes time crystals possible.

The doubling of the oscillation period is unusual, but not unprecedented. And long-lived oscillations are also very common in the quantum dynamics of few-particle systems. What makes a time crystal unique is that it’s a system of millions of things that are showing this kind of concerted behavior without any energy coming in or leaking out.

“It’s a completely robust phase of matter, where you’re not fine-tuning parameters or states but your system is still quantum,” said Sondhi, professor of physics at Oxford and co-author of the paper. “There’s no feed of energy, there’s no drain of energy, and it keeps going forever and it involves many strongly interacting particles.”

While this may sound suspiciously close to a “perpetual motion machine,” a closer look reveals that time crystals don’t break any laws of physics. Entropy – a measure of disorder in the system – remains stationary over time, marginally satisfying the second law of thermodynamics by not decreasing.

Between the development of this plan for a time crystal and the quantum computer experiment that brought it to reality, many experiments by many different teams of researchers achieved various almost-time-crystal milestones. However, providing all the ingredients in the recipe for “many-body localization” (the phenomenon that enables an infinitely stable time crystal) had remained an outstanding challenge.

For Khemani and her collaborators, the final step to time crystal success was working with a team at Google Quantum AI. Together, this group used Google’s Sycamore quantum computing hardware to program 20 “spins” using the quantum version of a classical computer’s bits of information, known as qubits.

Revealing just how intense the interest in time crystals currently is, another time crystal was published in Science this month [November 2021]. That crystal was created using qubits within a diamond by researchers at Delft University of Technology in the Netherlands.

Quantum opportunities

The researchers were able to confirm their claim of a true time crystal thanks to special capabilities of the quantum computer. Although the finite size and coherence time of the (imperfect) quantum device meant that their experiment was limited in size and duration – so that the time crystal oscillations could only be observed for a few hundred cycles rather than indefinitely – the researchers devised various protocols for assessing the stability of their creation. These included running the simulation forward and backward in time and scaling its size.

“We managed to use the versatility of the quantum computer to help us analyze its own limitations,” said Moessner, co-author of the paper and director at the Max Planck Institute for Physics of Complex Systems. “It essentially told us how to correct for its own errors, so that the fingerprint of ideal time-crystalline behavior could be ascertained from finite time observations.”

A key signature of an ideal time crystal is that it shows indefinite oscillations from all states. Verifying this robustness to choice of states was a key experimental challenge, and the researchers devised a protocol to probe over a million states of their time crystal in just a single run of the machine, requiring mere milliseconds of runtime. This is like viewing a physical crystal from many angles to verify its repetitive structure.

“A unique feature of our quantum processor is its ability to create highly complex quantum states,” said Xiao Mi, a researcher at Google and co-lead author of the paper. “These states allow the phase structures of matter to be effectively verified without needing to investigate the entire computational space – an otherwise intractable task.”

Creating a new phase of matter is unquestionably exciting on a fundamental level. In addition, the fact that these researchers were able to do so points to the increasing usefulness of quantum computers for applications other than computing. “I am optimistic that with more and better qubits, our approach can become a main method in studying non-equilibrium dynamics,” said Pedram Roushan, researcher at Google and senior author of the paper.

“We think that the most exciting use for quantum computers right now is as platforms for fundamental quantum physics,” said Ippoliti. “With the unique capabilities of these systems, there’s hope that you might discover some new phenomenon that you hadn’t predicted.”

A view of the Google dilution refrigerator, which houses the Sycamore chip. Credit: Google Quantum AI [downloaded from https://scitechdaily.com/stanford-and-google-team-up-to-create-time-crystals-with-quantum-computers/]

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

Time-Crystalline Eigenstate Order on a Quantum Processor by Xiao Mi, Matteo Ippoliti, Chris Quintana, Ami Greene, Zijun Chen, Jonathan Gross, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Alexander Bilmes, Alexandre Bourassa, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Benjamin Chiaro, Roberto Collins, William Courtney, Dripto Debroy, Sean Demura, Alan R. Derk, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Alan Ho, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Tanuj Khattar, Seon Kim, Alexei Kitaev, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Joonho Lee, Kenny Lee, Aditya Locharla, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Matt McEwen, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Michael Newman, Murphy Yuezhen Niu, Thomas E. O’Brien, Alex Opremcak, Eric Ostby, Balint Pato, Andre Petukhov, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vladimir Shvarts, Yuan Su, Doug Strain, Marco Szalay, Matthew D. Trevithick, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Adam Zalcman, Hartmut Neven, Sergio Boixo, Vadim Smelyanskiy, Anthony Megrant, Julian Kelly, Yu Chen, S. L. Sondhi, Roderich Moessner, Kostyantyn Kechedzhi, Vedika Khemani & Pedram Roushan. Nature (2021) DOI: https://doi.org/10.1038/s41586-021-04257-w Published 30 November 2021

This is a preview of the unedited paper being provided by Nature. Click on the Download PDF button (to the right of the title) to get access.

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.

D-Wave passes 1000-qubit barrier

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A local (Vancouver, Canada-based, quantum computing company, D-Wave is making quite a splash lately due to a technical breakthrough.  h/t’s Speaking up for Canadian Science for Business in Vancouver article and Nanotechnology Now for Harris & Harris Group press release and Economist article.

A June 22, 2015 article by Tyler Orton for Business in Vancouver describes D-Wave’s latest technical breakthrough,

“This updated processor will allow significantly more complex computational problems to be solved than ever before,” Jeremy Hilton, D-Wave’s vice-president of processor development, wrote in a June 22 [2015] blog entry.

Regular computers use two bits – ones and zeroes – to make calculations, while quantum computers rely on qubits.

Qubits possess a “superposition” that allow it to be one and zero at the same time, meaning it can calculate all possible values in a single operation.

But the algorithm for a full-scale quantum computer requires 8,000 qubits.

A June 23, 2015 Harris & Harris Group press release adds more information about the breakthrough,

Harris & Harris Group, Inc. (Nasdaq: TINY), an investor in transformative companies enabled by disruptive science, notes that its portfolio company, D-Wave Systems, Inc., announced that it has successfully fabricated 1,000 qubit processors that power its quantum computers.  D-Wave’s quantum computer runs a quantum annealing algorithm to find the lowest points, corresponding to optimal or near optimal solutions, in a virtual “energy landscape.”  Every additional qubit doubles the search space of the processor.  At 1,000 qubits, the new processor considers 21000 possibilities simultaneously, a search space which is substantially larger than the 2512 possibilities available to the company’s currently available 512 qubit D-Wave Two. In fact, the new search space contains far more possibilities than there are particles in the observable universe.

A June 22, 2015 D-Wave news release, which originated the technical details about the breakthrough found in the Harris & Harris press release, provides more information along with some marketing hype (hyperbole), Note: Links have been removed,

As the only manufacturer of scalable quantum processors, D-Wave breaks new ground with every succeeding generation it develops. The new processors, comprising over 128,000 Josephson tunnel junctions, are believed to be the most complex superconductor integrated circuits ever successfully yielded. They are fabricated in part at D-Wave’s facilities in Palo Alto, CA and at Cypress Semiconductor’s wafer foundry located in Bloomington, Minnesota.

“Temperature, noise, and precision all play a profound role in how well quantum processors solve problems.  Beyond scaling up the technology by doubling the number of qubits, we also achieved key technology advances prioritized around their impact on performance,” said Jeremy Hilton, D-Wave vice president, processor development. “We expect to release benchmarking data that demonstrate new levels of performance later this year.”

The 1000-qubit milestone is the result of intensive research and development by D-Wave and reflects a triumph over a variety of design challenges aimed at enhancing performance and boosting solution quality. Beyond the much larger number of qubits, other significant innovations include:

  •  Lower Operating Temperature: While the previous generation processor ran at a temperature close to absolute zero, the new processor runs 40% colder. The lower operating temperature enhances the importance of quantum effects, which increases the ability to discriminate the best result from a collection of good candidates.​
  • Reduced Noise: Through a combination of improved design, architectural enhancements and materials changes, noise levels have been reduced by 50% in comparison to the previous generation. The lower noise environment enhances problem-solving performance while boosting reliability and stability.
  • Increased Control Circuitry Precision: In the testing to date, the increased precision coupled with the noise reduction has demonstrated improved precision by up to 40%. To accomplish both while also improving manufacturing yield is a significant achievement.
  • Advanced Fabrication:  The new processors comprise over 128,000 Josephson junctions (tunnel junctions with superconducting electrodes) in a 6-metal layer planar process with 0.25μm features, believed to be the most complex superconductor integrated circuits ever built.
  • New Modes of Use: The new technology expands the boundaries of ways to exploit quantum resources.  In addition to performing discrete optimization like its predecessor, firmware and software upgrades will make it easier to use the system for sampling applications.

“Breaking the 1000 qubit barrier marks the culmination of years of research and development by our scientists, engineers and manufacturing team,” said D-Wave CEO Vern Brownell. “It is a critical step toward bringing the promise of quantum computing to bear on some of the most challenging technical, commercial, scientific, and national defense problems that organizations face.”

A June 20, 2015 article in The Economist notes there is now commercial interest as it provides good introductory information about quantum computing. The article includes an analysis of various research efforts in Canada (they mention D-Wave), the US, and the UK. These excerpts don’t do justice to the article but will hopefully whet your appetite or provide an overview for anyone with limited time,

A COMPUTER proceeds one step at a time. At any particular moment, each of its bits—the binary digits it adds and subtracts to arrive at its conclusions—has a single, definite value: zero or one. At that moment the machine is in just one state, a particular mixture of zeros and ones. It can therefore perform only one calculation next. This puts a limit on its power. To increase that power, you have to make it work faster.

But bits do not exist in the abstract. Each depends for its reality on the physical state of part of the computer’s processor or memory. And physical states, at the quantum level, are not as clear-cut as classical physics pretends. That leaves engineers a bit of wriggle room. By exploiting certain quantum effects they can create bits, known as qubits, that do not have a definite value, thus overcoming classical computing’s limits.

…

… The biggest question is what the qubits themselves should be made from.

A qubit needs a physical system with two opposite quantum states, such as the direction of spin of an electron orbiting an atomic nucleus. Several things which can do the job exist, and each has its fans. Some suggest nitrogen atoms trapped in the crystal lattices of diamonds. Calcium ions held in the grip of magnetic fields are another favourite. So are the photons of which light is composed (in this case the qubit would be stored in the plane of polarisation). And quasiparticles, which are vibrations in matter that behave like real subatomic particles, also have a following.

The leading candidate at the moment, though, is to use a superconductor in which the qubit is either the direction of a circulating current, or the presence or absence of an electric charge. Both Google and IBM are banking on this approach. It has the advantage that superconducting qubits can be arranged on semiconductor chips of the sort used in existing computers. That, the two firms think, should make them easier to commercialise.

…

Google is also collaborating with D-Wave of Vancouver, Canada, which sells what it calls quantum annealers. The field’s practitioners took much convincing that these devices really do exploit the quantum advantage, and in any case they are limited to a narrower set of problems—such as searching for images similar to a reference image. But such searches are just the type of application of interest to Google. In 2013, in collaboration with NASA and USRA, a research consortium, the firm bought a D-Wave machine in order to put it through its paces. Hartmut Neven, director of engineering at Google Research, is guarded about what his team has found, but he believes D-Wave’s approach is best suited to calculations involving fewer qubits, while Dr Martinis and his colleagues build devices with more.

It’s not clear to me if the writers at The Economist were aware of  D-Wave’s latest breakthrough at the time of writing but I think not. In any event, they (The Economist writers) have included a provocative tidbit about quantum encryption,

Documents released by Edward Snowden, a whistleblower, revealed that the Penetrating Hard Targets programme of America’s National Security Agency was actively researching “if, and how, a cryptologically useful quantum computer can be built”. In May IARPA [Intellligence Advanced Research Projects Agency], the American government’s intelligence-research arm, issued a call for partners in its Logical Qubits programme, to make robust, error-free qubits. In April, meanwhile, Tanja Lange and Daniel Bernstein of Eindhoven University of Technology, in the Netherlands, announced PQCRYPTO, a programme to advance and standardise “post-quantum cryptography”. They are concerned that encrypted communications captured now could be subjected to quantum cracking in the future. That means strong pre-emptive encryption is needed immediately.

I encourage you to read the Economist article.

Two final comments. (1) The latest piece, prior to this one, about D-Wave was in a Feb. 6, 2015 posting about then new investment into the company. (2) A Canadian effort in the field of quantum cryptography was mentioned in a May 11, 2015 posting (scroll down about 50% of the way) featuring a profile of Raymond Laflamme, at the University of Waterloo’s Institute of Quantum Computing in the context of an announcement about science media initiative Research2Reality.