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Breaking Laws For Better Computing Power

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@RakamtlAudrey Raby

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As Moore’s Law lies on its death bed, scientists wonder if time crystals could solve one of quantum computing’s greatest problem.

Moore’s law is one of economics — not physics. If you want to know the difference, ask John Searle (it’s quite entertaining).

Meanwhile, laws of physics are supposed to be applicable everywhere and anytime. For instance, a ball thrown at a certain speed in a certain direction will inevitably go the same distance, no matter where it’s being thrown (assuming the conditions are the same).

However, a few things do not respect space symmetry. Some atoms in crystals (sugar, salt and diamonds) for instance have preferred positions which make them look different based on the position of the observer.

This is salt.

Time symmetry though was said to be unbreakable. The more Nobel laureate Frank Wilczek thought about it, the more questions he had. Time and space being similar in many ways, why shouldn’t we be able to break symmetry in the fourth dimension?

His idea of ‘time crystals’ was first proposed in 2012, although the term had been used before in biology to refer to a regularly repeating system. Wilczek and his colleagues at MIT used the analogy to describe a type of matter that could break conservation of momentum.

In its introduction, Wilczek’s paper “Quantum Time Crystals” considers the question “whether time translation symmetry might be spontaneously broken in a closed quantum-mechanical system”. Translation: can we create matter that breaks another law of physics. Pretty exciting stuff, right?

Breaking time symmetry

Ok, but that’s a lot of big words. What the heck is time translation symmetry to begin with? Symmetry in physics has its own specific meaning. It describes all kinds of physical phenomena where you can change the variables (where you are when throw the ball) without changing the dynamics (where it ends up).

This is the backbone of classical and quantum mechanics. If you find something that works the same in all places at all times, you’ve found symmetry. So, can something break this rule by not working the same at all times, in a closed system?

Thermal equilibrium

Normal, stable matter in thermal equilibrium only has random internal motion. In solid matter, that would be the vibration of its constituting atoms. That buzz remains random over time.

Reminder: time is a construct which relies on cause and effect. One thing precedes the other, always trying to reach a state of equilibrium, or “zero-point energy” (or so we thought).

In such “closed system”, where there is no exchange of matter or external forces implied (no energy in or out), the total momentum should be constant.

If you could dream of a particular type of matter that could move without using any energy, you might make a few physicists nervous, as it would break time translation symmetry. This is what Wilczek’s team tried to do.

Their paper describes a ‘simple’ model in which charged particles in a superconducting ring break continuous time translation symmetry by creating a system that’s different on a global level, from an instant to the next.

First theory

Wilczek proposed a substance that would be in perpetual motion while in equilibrium. Oscillations would be the most fundamental lowest energy (or ground) state.

This imaginary system would break symmetry, because there would be global differences in the state of the matter; non-random patterns that change over time. Not in fluid or continuous way, in a periodic way.

There’s only one problem: how might we jiggle the Jell-O without an initial energy input?

Wilczek‘s theory lacked a dinosaur to make his Jell-O jiggle.

In 2015, another paper, by Haruki Watanabe (University of Tokyo) and Masaki Oshikawa (UC Berkeley), showed by theoretical arguments that time translational symmetry can’t be broken by quantum systems in equilibrium. Nice try, Frank.

The answer? Ditch the equilibrium element, suggested theoretical physicists at Princeton University and Microsoft’s Station Q.

Coming up with a recipe

Regular crystals have a periodic cycle through space, meaning their atoms bond in such a way that they repeat in patterns indefinitely.

A Diamond Lattice Model, by pmoews, found on Thingiverse.

Meanwhile, time crystals describe a type of matter that displays the same properties, but have an atomic structure that’s also repeating with constant separations in time.

In the end, it’s Norman Yao’s team at UC Berkeley who bridged the gap between the idea and the experimentation in their paper called “Discrete Time Crystals: Rigidity, Criticality, and Realizations” It turns out by using an external input of energy to force the oscillating states, time crystals can be created.

Imagine a chain of ions (electrically charged atoms, produced by either removing or adding electrons) in a crystal. These ions have spin values (jargon: quantum mechanical intrinsic angular momenta) from their electrons.

Spins in nearby ions line up with each other due to interacting magnetic fields. Whether direct or opposite alignment, both require less energy than random alignment. This is the same effect that results in magnetic materials.

This is what a chain of ions and a laser look like. I guess.

If you force the spins to flip back and forth using a laser, the spin flip oscillation will be determined by the frequency of the laser (which, as you know, is just a well ordered electromagnetic wave with a known frequency). This is what takes the system out of equilibrium, because you’re basically pumping in energy.

Normally, the energy would pass through one atom to the next until the chain returns to equilibrium, or zero-point energy.

Yao’s paper proposed that if you let go of the electrons after the system has been taken out of equilibrium (removing the cause), it can never return to it, because the ions are connected through quantum entanglement in repeating patterns, so that ions down the chain feel the effects before the cause.

Yao’s predictions. Image credit: Norman Y. Yao, Andrew C. Potter, Ionut-Dragos Potirniche, Ashvin Vishwanath.

The spin oscillation (movement) therefore continues eternally, without further energy input. This challenges the “common wisdom” among physicists that all systems eventually settle down. And there you have it: a new form of matter, in perpetual motion!

Although the 2015 paper was theoretical, it basically laid out a practical approach for others to try and build time crystals. Which, of course, they did.

Ten yttrium atoms with entangled electron spins. Image credit: Chris Monroe, University of Maryland.

A new type of matter

Two different teams of scientists managed to prove Yao’s theory by synthesizing time crystals in their lab, using two wildly disparate systems.

Chris Monroe’s team at Maryland University followed Yao’s blueprint by setting up a chain of ions using ytterbium, while Harvard’s team tried something completely different (and quite elegant): a time crystal in a space crystal.

The second team, led by Mikhail Lukin, used microwaves to generate oscillations in the spins of nitrogen impurities inside of a diamond (nothing less). Their results have been published recently in Nature.

The Harvard Diamond. Image credit: Georg Kucsko.

Bam! Time crystals can exist, say peer reviews. Of course, there is still some skepticism in the scientific community, and some believe the effects might not last forever, but seeing that two different methods have confirmed the predicted results is quite promising.

“Time crystals are a broad new phase of matter, not simply a curiosity relegated to small or narrowly specific systems,” wrote Phil Richerme from Indiana University in Physical Review Letters.

“Observation of the discrete time crystal… confirms that symmetry breaking can occur in essentially all natural realms, and clears the way to several new avenues of research.” he added.

Maintaining quantum state with time crystals

Even if the practical applications seem far off, non-equilibrium matter could bring us closer to making quantum computing a reality.

The most popular approach to building a quantum memory element is to use electron spins instead of zeros and ones.

One of the biggest challenges is that these quantum states are very hard to maintain. Too much random motion from heat, and you can completely mess up your calculations. Therefore, most prototypes today need to be heavily shielded from the tiniest interference from the outside world.

Since time crystals have resilient spin flip cycles, they could help in building stable quantum memory, overcoming one of the greatest obstacle to the widespread use of a technology millions of times faster than what we have today.

Audrey Raby is a strategist, a storyteller a speaker and a mom. She’s also COO of innovation consulting firm Nash, in Montreal.

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