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Have you ever heard of Quantum Chess? If not, we are confident you are in for a real treat.

Read on to find out more about this interesting take on a very ancient strategy game. But brace yourself, things are about to get a little "spooky".

RELATED: WINNER OF THE WORLD'S FIRST QUANTUM CHESS TOURNAMENT ANNOUNCED

Quantum Chess is a variant of the classical strategy game. It incorporates the principles of quantum physics. For example, unlike traditional chess, the piecescan be placed into a superposition of two locations, meaning that a piece can occupy more than one square.

Unlike chesspieces in the conventional game where, for example, a pawn is always a pawn, aquantum chesspiece is a superposition of "states", with each state representing a different conventional piece.

Conventional chess is a very complex game, although it is possible for computer algorithmsto beat the world's greatest chess playersby accurately determining the moves necessary to win the game at any point.

The main rationale behind the creation of Quantum Chess is to introduce an element of unpredictability into the game, and thereby place the computer and the human on a more equal footing. The game can also help "level the playing field" somewhat between human players of widely different skills and experience with chess.

Its like youre playing in a multiverse but the different boards [in different universes] are connected to each other, said Caltech physicist Spiros Michalakis during aLivestreamof a recent Quantum Chess tournament. It makes 3D chess fromStar Treklook silly.

But don't let the term intimidate you. New players to the game don't need to be experts in quantum physics a basic understanding of chess is more important actually.

While it might sound like something of a gimmick, Quantum Chess is an interesting and entertaining spin on the classic game that many find enjoyable. Unless, of course, you cannot live without knowing for sure what and where each piece is at any given time.

If that is the case, you might find this one of the most frustrating games ever created!

Quantum Chess, as you have probably already worked out, is not like any game of classical chess you have ever played. But, it is important to note that there are also several variants of Quantum Chess.

The best known is probably the one created by Chris Cantwell when he was a graduate student at theUniversity of Southern California.This variant differs from other examples by the fact that it is more "truly quantum" than others.

My initial goal was to create a version of quantum chess that was truly quantum in nature, so you get to play with the phenomenon,Cantwell said in an interview with Gizmodoback in 2016.

I didnt want it to just be a game that taught people, quantum mechanics. The idea is that by playing the game, a player will slowly develop an intuitive sense of the rules governing the quantum realm. In fact, I feel like Ive come to more intuitively understand quantum phenomena myself, just by making the game, he added.

In Cantwell's version of Quantum Chess, this superposition of pieces is indicated by a ring that details the probability that the piece can actually be found in a given square. Not only that, but when moving a piece, each action can also be governed by probability.

You can think of the pieces of the game existing on multiple boards in which their numbers are also not fixed. The board you see is a kind of overview of all of these other boards and a single move acts on other boards at the same time.

Whenever a piece moves, many calculations are made behind the scenes to determine the actual outcome, which could be completely unexpected.

That being said, moves do follow the basic rules of traditional chess, including things like castling and en passant. However, there are a few important differences:

Pieces in this version of Quantum Chess can make a series of either "quantum moves" (except for pawns) or regular chess moves. In this sense, the pieces can occupy more than one square on the multiverse of boards simultaneously.

These moves also come in a variety of "flavors".

The first is a move called a "split move". This can be performed by all non-pawn pieces and allows a piece to actually occupy two different target squares that it could traditionally reach in normal chess.

But, this can only be done if the target square is unoccupied or is occupied by pieces of the same color and type. A white knight, for example, could use this kind of move to occupy the space of another white knight.

Such a move cannot; however, be used to capture an opponent's piece.

Another interesting move is called a "merge move". This can be performed by all pieces except pawns and, like a split move, can only be performed on an unoccupied square or one occupied by a piece of the same type and color.

Using our previous example of a white knight, this would mean that two white knights could merge together on the same square. Again, this move cannot be used to capture enemy pieces.

So how do you take pieces in Quantum Chess?

Well, when two pieces of different colors meet on the same square the game makes a series of measurements.These measurements are designed to answer a specific yes or no question.

For example, the game's mechanics will look at certain squares to determine if they are occupied or not.The outcome of this can be to cause a piece's "superposition" state to "collapse".

If the superposition state collapses, then the desired move will be performed. If not, the move is not made and the player's turn ends.

Capturing is also very different in a game of Quantum Chess. When a player attempts to do this, the game will make calculations for the square where the piece is situated and for its target square, as well as any other squares in its path, to answer the question, "is the attacking piece present and can it reach the target?".

If the answer is no, it is important to note that this doesn't necessarily mean the attacking piece is not present. Nor does it mean that its path is blocked.

Another interesting concept of Quantum Chess is called "exclusion". If a moving target is occupied and is in superposition by a piece that cannot be captured by the move, it is called an exclusion move.

Again, calculations are made for the target square and any squares in the path of an allowed move by a piece in superposition. This is done to answer the same question as capturing, with similar outcomes.

Castling is also very different in Quantum Chess. This move always involves two targets, and the same measurements are made for both targets. Castling cannot be used to capture, and will always be an exclusion move.

So, you might be wondering how you actually win a game of Quantum Chess?

Just like traditional chess, the aim of the game is to capture the opponent's king. However, unlike in traditional chess, the concept of checkmate does not exist.

To win, the enemy king must no longer actually exist on the board. As any piece, including the king, exist in a state of superposition, they can either be captured or not which further complicates the issue.

The game, therefore, continues until it is known, with certainty, that a particular player has no king left. For this reason, it is possible for both players to lose their king at the same time and the game would then be considered a draw.

Another important thing to note is that each player has a set amount of time for the game. For this reason, you can also win by running an opponent's time out.

How you play Quantum Chess depends on the variant of the game you are playing. We have already covered the rules of one variant above, and that game can be played throughQuantum Realm Games. But another version created byAlice Wismath at theSchool of Computing at Queen's University in Californiahas some slightly different rules.

You can try that game for yourself here.

In her version, each player has sixteen pieces. These pieces are in a quantum state of superposition of two types: a primary and a secondary type.

They are also in an unknown (quantum) type or a known (classical) type.When a piece is "touched" it collapses into its classical state and has an equal probability of becoming either a primary or secondary type. The king, however, is an exception, and is always in a classical state.

Each player has one king and its position is always known.

All other pieces are assigned the following primary piece types: left rook, left bishop, left knight, queen, right knight, right bishop, right rook, and pawns one through eight. Secondary piece types are then randomly assigned from this same list of piece types so that each type occurs exactly twice in the player's pieces.

Each piece is created at the start of each game and superpositions are not changed throughout the game. Pieces also start as they would in regular chess, on the first two rows, according to their primary piece type with all, except the king, in a state of superposition.

Once a quantum state piece is touched (i.e. chosen to move), it collapses into one of its two predetermined states, and this state is suddenly revealed to both players.

This can mean that a pawn in the front row can suddenly become a white knight once the piece has been "touched". You won't know until the piece's quantum state collapses.

Quantum Chess boards are the same as regular chess boards except that when a piece lands on a white square it remains in its classical state. When pieces land on black squares, however, they undergo a quantum transformation and regain, if lost, their quantum superposition.

This means that a previously "revealed" pawn can also suddenly transform into a queen if that was one of its predetermined primary or secondary types. A very interesting concept indeed.

To play the game, each player chooses a piece to move and must move it. If the quantum piece collapses into a piece type with no possible moves, then the player's move is over.

Pieces in classical states with no possible moves cannot be chosen. All pieces move as they would in classical chess with some of the following exceptions:

Pieces can also be captured as normal, and quantum pieces collapse from their superposition state and are removed from play.

If a player touches a quantum piece that collapses into a state that puts the opponent's king in check, their move is over. The opponent, however, is not required to get out of check in such circumstances.

Pawns that reach the opposite side of the board can be promoted to aqueen, bishop, rook, or knight, regardless of the number of pieces of that type already in the game. Also, if a piece in the quantum state on the far row is touched and revealed to be a pawn, it is promoted, but the promotion takes up the turn. The superimposed piece type is not affected.

To win the game, each player must capture the enemy's king, as a checkmate does not happen in Quantum Chess. For this reason, kings can actually move into a position that would normally be considered check.

Games are considered a draw if both opponents are left with only their king in play or 100 consecutive moves have been made with no captures or pawn movements by either player.

It was recently announced that the world's first Quantum Chess tournament had been won by Aleksander Kubica, a postdoctoral fellow at Canada's Perimeter Institute for Theoretical Physics and Institute for Quantum Computing. The tournament was held on the 9th of December 2020 at the Q2B 2020 conference.

The tournament games are timed, and Kubica managed to beat his opponent, Google's Doug Strain, by letting him run out of time. This currently makes Kubica officially the best Quantum Chess player in the world.

Not a bad way to see out one of the worst years in living memory.

And that, ladies and gentlemen, is a wrap.

If you like the sound of playing Quantum Chess, why not check out either of the versions we have discussed above in this article. Who knows, you might get proficient enough to challenge Kubica for the title in the not too distant future?

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What the Hell Is Quantum Chess? | IE - Interesting Engineering

Princeton University has discussed plans to create an additional campus across Lake Carnegie a campus that would potentially create an innovation center that could attract companies seeking the next great technological advancement. (More on that later.)

President Chris Eisgruber is just as excited to talk about the schools commitment to a different kind of expansion: One that would increase the number of low-income and first-generation students attending the nations premier university.

Its just such a passion for me, he said. One of the things Im proudest of is that we have become a national leader in terms of attracting students from low-income backgrounds and graduating them and seeing them go off and do spectacular things, with, I hope, many of them staying here in the state of New Jersey.

As we continue to look to elevate and nurture talent, it will be important to what Princeton University is doing going forward.

Going forward is a relative phrase these days. Princeton like all universities and much of society is eager to just return to the way it was. Few parts of society were as impacted as greatly by COVID-19 as higher education.

Princeton will bring its students back to campus next semester and do it with a rigorous testing system, while school officials await the day when everyone will be vaccinated. But, even then, Eisgruber knows the school will be different.

While the COVID-19 pandemic impacted how students learn, the murder of George Floyd led to a reexamination of how everyone thinks about racial equity and equality. At Princeton, that meant another look at the racist views of one of its former presidents, Woodrow Wilson, and the removal of his name from a number of prominent places.

Eisgruber discussed all of this and more in a recent chat for the Interview Issue, our annual year-end give-and-take with some of the most inspiring and intriguing people around the state.

Heres a look at the conversation, edited for space and clarity.

ROI-NJ: We have to start with COVID-19. Give us an overview of how that has impacted Princeton?

Chris Eisgruber: Education depends on engagement and personal interaction; thats what we try to provide. Thats the key to teaching that really inspires. But, the same kind of engagement and intimacy thats so valuable to education is also what spreads this virus. So, weve had the problem that the thing that is at our core of education has suddenly become dangerous in the midst of this pandemic, and weve had to adapt to that.

We made the tough decision to go online in the fall, and Ive been so impressed by the way our staff and our students and our faculty have worked together to find possibilities for making online education real and meaningful. And then, weve been working hard to find ways to bring back people to campus and do it safely. Im grateful to lots of people around this campus and to our alumni, who made it possible for us to set up a testing laboratory on the campus, so we can test our students twice a week, every week, even if the entire population looks asymptomatic.

We are working to de-densify, so that, in our housing system, well be able to have students one per room. Weve established a culture of masking and social distancing. So, Im confident that we can bring back students in the spring and bring them back safely. But Im among the many people who are looking forward to the day when we can get everybody vaccinated and we can go back to the in-person elements that add so much more to our education.

ROI: We have to think that virtual learning will continue in some fashion. How could that work?

CE: I think it will vary from institution to institution. I do think, for all of us, this will give us additional arrows in our quiver. The obvious place is in terms of guest speakers or when students are studying abroad or when a faculty member has to travel someplace. Its one thing when everything has to be on Zoom all the time. Its another if you suddenly realize, OK, distance doesnt have to be a barrier.

I still think in-person instruction will be the dominant mode of delivery, but, yes, you will still see (some virtual instruction) where we cant deliver the in-person experience.

ROI: Lets move to other big event of 2020, the killing of George Floyd and the long overdue discussion of racial equity, opportunity and justice that came about. The issue, of course, was reflected at Princeton in the removal of Woodrow Wilsons name from a number of key spots. Talk about how Princeton attempted to address all of these issues.

CE: I think we and other colleges and universities have a responsibility to be sites for honest confrontation with the right and wrongs of history and for conversations about very difficult subjects. And, obviously, race is a very hard subject to talk about in the United States and to talk about on our college campus. And we havent always done well with that.

Weve had to wrestle with Woodrow Wilsons legacy. I will say, personally, that, when I took office, I wasnt aware that he had resegregated the federal civil service. We talked about him on this campus in a way that didnt recognize that or acknowledge it. And I think that has been part of this problem of indifference thats held us back as a country and as a university as we reach for our highest aspirations.

ROI: How do we address this?

CE: This moment remains a moment of great challenge. These issues are so hard, and the problems have been so longstanding, but it also is a moment of opportunity for us. I think there is a greater and wider recognition of the need to do more affirmatively, even more than weve done. I know the state of New Jersey has been a leader in a lot of things. This university has tried to be a leader on a lot of things, but we need to do even more in order to reach our highest aspirations.

I assign a book to the incoming students every year. This year, it was a book by the historian Jill Lepore called This America: The Case for the Nation, which tries to tell the story of both the great triumphs and aspirations, but also the story of the failures. And she starts, to that end, with this quotation from W.E.B. Du Bois, which I now find myself quoting again and again to our students and alumni. In 1935, W.E.B. Du Bois said: Nations reel and stagger on their way. They make hideous mistakes. They commit frightful wrongs. They do great and beautiful things, and shall we not best guide humanity by telling the truth about all this so far as the truth is ascertainable?

And thats what I think we have tried to hold ourselves to do. And it is incredibly hard. And depending on who the audience is, they may hear or want to hear only one side of this. I think we have to tell it all, and thats the challenge.

Oswald Veblen. He was a mathematician here in the early 20th century. And he basically transformed the math and physics departments in this university and helped to start the Institute for Advanced Study. Hes not well known, but he should be. He realized early on what was happening in Nazi Germany and helped to bring over a number of Jewish refugees who otherwise would have perished. I think hes one of the unsung heroes. He just stands for so many things, from academic excellence to being a great citizen of the university to being somebody who helps the refugee in a time of need. So, he gets my vote.

Its humanity: One of the things that I love about New Jersey is that the people are real and theyre not pretentious.

One of the things were really going to want after this pandemic is to bring back the restaurants that have been badly affected. Thats going to matter to attracting young talent and keeping it here. One thing that stands in the way of aspiring chefs that might want to start interesting places that are cool and attractive to young people are the states liquor laws in particular, the difficulty that restaurants have in getting licenses in the state. I think it puts us at a real competitive disadvantage, by comparison to New York and Pennsylvania. So, Im going to put in a plug for our restaurant industry on that, and for the importance of having cool places that attract young people.

ROI: This challenge reaches all areas of the university. Sometimes in good ways. Princeton has had some successes in fundraising this year one was a gift from Mellody Hobson, a businesswomen, philanthropist and alumna that will have significance beyond the dollars and cents. Talk about her gift.

CE: Fundamentally, the process of fundraising at Princeton is about a desire of our friends and our alumni to pay it forward to future generations to do things that will make a difference at the university and beyond it. What we want to do right now, as we think about our current capital campaign, is to enable more students from more backgrounds to make a difference for the better in the world. And I think that message continues to resonate with our alumni.

One of our happiest moments during this difficult year was when we were able to announce the gift that will create Mellody Hobson College on the site where Wilson College was previously located. And I know, for many of our alumni and many of our students, the idea that they would be able to identify with an alum like Mellody Hobson, with her story of coming from Chicago as a first-generation Black student to Princeton University, then going on to this career of extraordinary national significance, means a lot. I think its a symbol for us. Its a symbol for students who will make a difference later in their lives. And its a symbol for higher education.

ROI: We are a business journal at heart. So, lets talk about how the university is connected to the business community in the state.

CE: Increasing Princetons connection to the New Jersey economic environment is important for us and the state of New Jersey because of its connections to our teaching and research mission. This is a change from the days when Albert Einstein was kind of the paradigmatic Princeton professor, thinking thoughts to win Nobel Prizes, but thoughts that didnt have immediate application in the business world. Nowadays, my top researchers, some of them who get whispered about in terms of winning Nobel Prizes, say their research is going to be better if they have more connection to the applied world, because theyre going to learn more about which problems need their attention, or where the really interesting issues are. And they want their research to have an application to the world.

One example of that, which really connects directly back to Einstein, is around quantum computing. We have an initiative in quantum computing. Some of our faculty are associated with a multiuniversity partnership that has a lot of government funding behind it. The Plasma Physics Laboratory is working on expanding into the area of nanochip technology. This is applying some of the most theoretical and worldly ideas that Einstein thought about. It is now the critical technology in terms of the next advances in computing. We would love to see all of that happen right here in central New Jersey. If we could be recognized as the place to go when it comes to quantum computing, thats going to be really good for the intellectual environment around Princeton University and really good for the state of New Jersey.

I think weve got the edge in terms of having the talent and the fundamentals here. And I think there are a number of other areas, like what were doing in bioengineering, what were doing in computer science. So, weve been really pleased that the New Jersey business community seems to have responded well to that. Its been a priority for Gov. (Phil) Murphys administration. And we hope that these initiatives will continue to grow.

ROI: Like the Princeton campus. This takes us back to an expansion across the lake.

CE: We want to expand gradually, because we want to make sure that were preserving the character of a Princeton education. So, one of the things were doing as were building these two new residential colleges is making sure that, as we start renovating some of our existing space, we will have the capacity to expand down the line.

We have land across the lake that is as large as our current campus. And part of what we have started to do is to put in place a general development plan for that land. Our belief is that the campus, as it develops over time, can be an important site for innovation and entrepreneurship. And part of what were thinking about is that the campus should develop with a character on the other side of the lake that provides a home to joint ventures of a sort that we cant quite imagine yet.

The example that I always give folks is, back in the 80s, Microsoft came to Cambridge University in England and said, Were interested in doing something jointly with your computer science department. And Cambridge, which has a lot of similarities to Princeton, was able to say Yes, because they had the equivalent of our land across the lake and they were ready to go and they were able to green-light it.

We want to be able to do that in New Jersey. If we get the right kind of project that advances our mission, and that could be good here for the innovation ecosystem, we want to be able to say, Yes, and that is one of the reasons why we are moving forward with planning for that.

Original post:
The Interview Issue: Eisgruber is trying to reshape the meaning of a Princeton education even as his school, and higher ed as a whole, grapples with...

Bitcoin evangelist and influencer Andreas Antonopoulos says Satoshi Nakamotos massive Bitcoin trove will be an easy target for quantum computers.

In a Bitcoin HARDTalk interview, Antonopoulos says that investors should keep a close watch on Nakamotos BTC fortune. If the dormant coins start moving, Antonopoulos says it is likely not the doing of the anonymous Bitcoin creator.

Especially with some of the early keys, they are pay-to-public keys, the public keys are visible and the money is sitting in them.

Therefore, a quantum computer, its first target, its juiciest target, its easiest to attack target is the Satoshi stash. How do we know if a quantum computer exists that can break ECDSA (elliptic curve digital algorithm). Simple, Satoshis coins start moving, and in fact at some point after a decade or so it might actually be the more likely explanation.

So you see the coins moving and youre like Did Satoshi come back from the dead? or Did a quantum computer emerge that can break [ECDSA keys]? As the years go by, I start leaning more towards, Okay, it appears a quantum computer has emerged that can do this, but I think were still a decade away from that.

However, the movement of Satoshis huge BTC stash is not a nail in the coffin for the leading cryptocurrency, says Antonopoulos.

It would cause a massive amount of volatility in the space by injecting an enormous amount of liquidity on the supply side of Bitcoin, but it would also once and for all resolve the question This is characteristic of markets which is, Sell the rumor, buy the fact

If something starts happening that is unexpected the market reacts badly, but as soon as that becomes expected, you get the opposite reaction. The markets go, Oh well, I guess Satoshis coins moved. Bitcoin didnt die completely, its price dipped. Well, now Bitcoin at whatever price its priced in now is a Bitcoin in which Satoshis coins have moved and are therefore part of the supply and priced in. Therefore, its future is now certain. That is no longer hanging over it

Sometimes having the bad news confirmed leads to a rally in the markets because you went from uncertainty to confirmation even though whats been confirmed is bad news.

I

Featured Image: Shutterstock/Gorgev

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Satoshis Bitcoin Fortune Will Be Easiest Batch for Quantum Computers to Hack, Says Andreas Antonopoulos - The Daily Hodl

Anyon Systems's Quantum Computer

Anyon System's superconducting quantum processor.

MONTREAL, Dec. 15, 2020 (GLOBE NEWSWIRE) -- Anyon Systems Inc. (Anyon), a quantum computing company based in Montreal, Canada, announced today that it is to deliver Canadas first gate-based quantum computer for the Department of National Defenses Defence Research and Development Canada (DRDC). The quantum computer will feature Anyons Yukon generation superconducting quantum processor. Named after Canadas westernmost territory, the quantum computer will enable DRDC researchers to explore quantum computing to solve problems of interest to their mission.

Quantum computing is expected to be a disruptive technology and is of strategic importance to many industries and government agencies. Anyon is focused on delivering large-scale, fault-tolerant quantum computers to a wide group of early adopters including government agencies, high performance computing centers and universities in the near term, said Dr. Alireza Yazdi, founder and CEO of Anyon.

About Anyon Systems

Founded in 2014, Anyon Systems is the first Canadian company manufacturing gate-based quantum computing platform for universal quantum computation. Anyon Systems delivers turnkey gate-based quantum computers. The company is headquartered in Montreal, Quebec.

Media Contact:media@anyonsys.com

A photo accompanying this announcement is available at https://www.globenewswire.com/NewsRoom/AttachmentNg/7c776a6e-2ef8-4875-b33a-06c3ccf9f8df

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Anyon Systems to Deliver a Quantum Computer to the Canadian Department of National Defense - GlobeNewswire

Electrons inhabit a strange and topsy-turvy world. These infinitesimally small particles have never ceased to amaze and mystify despite the more than a century that scientists have studied them. Now, in an even more amazing twist, physicists have discovered that, under certain conditions, interacting electrons can create what are called topological quantum states. This finding, which was recently published in the journal Nature,holds great potential for revolutionizing electrical engineering, materials science and especially computer science.

Topological states of matter are particularly intriguing classes of quantum phenomena. Their study combines quantum physics with topology, which is the branch of theoretical mathematics that studies geometric properties that can be deformed but not intrinsically changed. Topological quantum states first came to the publics attention in 2016 when three scientists Princetons Duncan Haldane, who is Princetons Thomas D. Jones Professor of Mathematical Physics and Sherman Fairchild University Professor of Physics, together with David Thouless and Michael Kosterlitz were awarded the Nobel Prize for their work in uncovering the role of topology in electronic materials.

A Princeton-led team of physicists have discovered that, under certain conditions, interacting electrons can create what are called topological quantum states, which,has implications for many technological fields of study, especially information technology. To get the desired quantum effect, the researchersplaced two sheets of graphene on top of each other with the top layer twisted at the "magic" angle of 1.1 degrees, whichcreates a moir pattern. This diagram shows a scanning tunneling microscopeimaging the magic-angle twisted bilayer graphene.

Image courtesy of Kevin Nuckolls

The last decade has seen quite a lot of excitement about new topological quantum states of electrons, said Ali Yazdani, the Class of 1909 Professor of Physics at Princeton and the senior author of the study. Most of what we have uncovered in the last decade has been focused on how electrons get these topological properties, without thinking about them interacting with one another.

But by using a material known as magic-angle twisted bilayer graphene, Yazdani and his team were able to explore how interacting electrons can give rise to surprising phases of matter.

The remarkable properties of graphene were discovered two years ago when Pablo Jarillo-Herrero and his team at the Massachusetts Institute of Technology (MIT) used it to induce superconductivity a state in which electrons flow freely without any resistance. The discovery was immediately recognized as a new material platform for exploring unusual quantum phenomena.

Yazdani and his fellow researchers were intrigued by this discovery and set out to further explore the intricacies of superconductivity.

But what they discovered led them down a different and untrodden path.

This was a wonderful detour that came out of nowhere, said Kevin Nuckolls, the lead author of the paper and a graduate student in physics. It was totally unexpected, and something we noticed that was going to be important.

Following the example of Jarillo-Herrero and his team, Yazdani, Nuckolls and the other researchers focused their investigation on twisted bilayer graphene.

Its really a miracle material, Nuckolls said. Its a two-dimensional lattice of carbon atoms thats a great electrical conductor and is one of the strongest crystals known.

Graphene is produced in a deceptively simple but painstaking manner: a bulk crystal of graphite, the same pure graphite in pencils, is exfoliated using sticky tape to remove the top layers until finally reaching a single-atom-thin layer of carbon, with atoms arranged in a flat honeycomb lattice pattern.

To get the desired quantum effect, the Princeton researchers, following the work of Jarillo-Herrero, placed two sheets of graphene on top of each other with the top layer angled slightly. This twisting creates a moir pattern, which resembles and is named after a common French textile design. The important point, however, is the angle at which the top layer of graphene is positioned: precisely 1.1 degrees, the magic angle that produces the quantum effect.

Its such a weird glitch in nature, Nuckolls said, that it is exactly this one angle that needs to be achieved. Angling the top layer of graphene at 1.2 degrees, for example, produces no effect.

The researchers generated extremely low temperatures and created a slight magnetic field. They then used a machine called a scanning tunneling microscope, which relies on a technique called quantum tunneling rather than light to view the atomic and subatomic world. They directed the microscopes conductive metal tip on the surface of the magic-angle twisted graphene and were able to detect the energy levels of the electrons.

They found that the magic-angle graphene changed how electrons moved on the graphene sheet. It creates a condition which forces the electrons to be at the same energy, said Yazdani. We call this a flat band.

When electrons have the same energy are in a flat band material they interact with each other very strongly. This interplay can make electrons do many exotic things, Yazdani said.

One of these exotic things, the researchers discovered, was the creation of unexpected and spontaneous topological states.

This twisting of the graphene creates the right conditions to create a very strong interaction between electrons, Yazdani explained. And this interaction unexpectedly favors electrons to organize themselves into a series of topological quantum states.

The researchers discovered that the interaction between electrons creates topological insulators:unique devices that whose interiors do not conduct electricity but whose edges allow the continuous and unimpeded movement ofelectrons. This diagram depicts thedifferent insulating states of the magic-angle graphene, each characterized by an integer called its Chern number, which distinguishes between different topological phases.

Image courtesy of Kevin Nuckolls

Specifically, they discovered that the interaction between electrons creates what are called topological insulators. These are unique devices that act as insulators in their interiors, which means that the electrons inside are not free to move around and therefore do not conduct electricity. However, the electrons on the edges are free to move around, meaning they are conductive. Moreover, because of the special properties of topology, the electrons flowing along the edges are not hampered by any defects or deformations. They flow continuously and effectively circumvent the constraints such as minute imperfections in a materials surface that typically impede the movement of electrons.

During the course of the work, Yazdanis experimental group teamed up two other Princetonians Andrei Bernevig, professor of physics, and Biao Lian, assistant professor of physics to understand the underlying physical mechanism for their findings.

Our theory shows that two important ingredients interactions and topology which in nature mostly appear decoupled from each other, combine in this system, Bernevig said. This coupling creates the topological insulator states that were observed experimentally.

Although the field of quantum topology is relatively new, itcouldtransform computer science. People talk a lot about its relevance to quantum computing, where you can use these topological quantum states to make better types of quantum bits, Yazdani said. The motivation for what were trying to do is to understand how quantum information can be encoded inside a topological phase. Research in this area is producing exciting new science and can have potential impact in advancing quantum information technologies.

Yazdani and his team will continue their research into understanding how the interactions of electrons give rise to different topological states.

The interplay between the topology and superconductivity in this material system is quite fascinating and is something we will try to understand next, Yazdani said.

In addition to Yazdani, Nuckolls, Bernevig and Lian, contributors to the study included co-first authors Myungchul Oh and Dillon Wong, postdoctoral research associates, as well as Kenji Watanabe and Takashi Taniguchi of the National Institute for Material Science in Japan.

Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene, by Kevin P. Nuckolls, Myungchul Oh, Dillon Wong, Biao Lian, Kenji Watanabe, Takashi Taniguchi, B. Andrei Bernevig and Ali Yazdani, was published Dec. 14 in the journal Nature (DOI:10.1038/s41586-020-3028-8). This work was primarily supported by the Gordon and Betty Moore Foundations EPiQS initiative (GBMF4530, GBMF9469) and the Department of Energy (DE-FG02-07ER46419 and DE-SC0016239). Other support for the experimental work was provided by the National Science Foundation (Materials Research Science and Engineering Centers through the Princeton Center for Complex Materials (NSF-DMR-1420541, NSF-DMR-1904442) and EAGER DMR-1643312), ExxonMobil through the Andlinger Center for Energy and the Environment at Princeton, the Princeton Catalysis Initiative, the Elemental Strategy Initiative conducted by Japans Ministry of Education, Culture, Sports, Science and Technology (JPMXP0112101001, JSPS KAKENHI grant JP20H0035, and CREST JPMJCR15F3), the Princeton Center for Theoretical Science at Princeton University, the Simons Foundation, the Packard Foundation, the Schmidt Fund for Innovative Research, BSF Israel US foundation (2018226), the Office of Naval Research (N00014-20-1-2303) and the Princeton Global Network Funds.

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'Magic' angle graphene and the creation of unexpected topological quantum states - Princeton University