Helping quantum computing by reversing time

Reversing time
CREDIT: @TSARCYANIDE/MIPT PRESS OFFICE

Researchers from the Moscow Institute of Physics and Technology teamed up with colleagues from the U.S. and Switzerland and returned the state of a quantum computer a fraction of a second into the past. They also calculated the probability that an electron in empty interstellar space will spontaneously travel back into its recent past.

The study comes out March 13 in Scientific Reports.

“This is one in a series of papers on the possibility of violating the second law of thermodynamics. That law is closely related to the notion of the arrow of time that posits the one-way direction of time: from the past to the future,” commented the study’s lead author Gordey Lesovik, who heads the Laboratory of the Physics of Quantum Information Technology at MIPT.

“We began by describing a so-called local perpetual motion machine of the second kind. Then, in December, we published a paper that discusses the violation of the second law via a device called a Maxwell’s demon,” Lesovik said. “The most recent paper approaches the same problem from a third angle: We have artificially created a state that evolves in a direction opposite to that of the thermodynamic arrow of time.”

What makes the future different from the past

Most laws of physics make no distinction between the future and the past. For example, let an equation describe the collision and rebound of two identical billiard balls. If a close-up of that event is recorded with a camera and played in reverse, it can still be represented by the same equation. Moreover, one could not tell from the recording if it has been doctored. Both versions look plausible. It would appear that the billiard balls defy the intuitive sense of time.

However, imagine that someone has recorded a cue ball breaking the pyramid, the billiard balls scattering in all directions. One need not know the rules of the game to tell the real-life scenario from reverse playback. What makes the latter look so absurd is our intuitive understanding of the second law of thermodynamics: An isolated system either remains static or evolves toward a state of chaos rather than order.

Most other laws of physics do not prevent rolling billiard balls from assembling into a pyramid, infused tea from flowing back into the tea bag, or a volcano from “erupting” in reverse. But we do not see any of this happening, because that would require an isolated system to assume a more ordered state without any outside intervention, which runs contrary to the second law. The nature of that law has not been explained in full detail, but researchers have made great headway in understanding the basic principles behind it.

Spontaneous time reversal

Quantum physicists from MIPT decided to check if time could spontaneously reverse itself at least for an individual particle and for a tiny fraction of a second. That is, instead of colliding billiard balls, they examined a solitary electron in empty interstellar space.

“Suppose the electron is localized when we begin observing it. This means that we’re pretty sure about its position in space. The laws of quantum mechanics prevent us from knowing it with absolute precision, but we can outline a small region where the electron is localized,” says study co-author Andrey Lebedev from MIPT and ETH Zurich.

The physicist explains that the evolution of the electron state is governed by Schrödinger’s equation. Although it makes no distinction between the future and the past, the region of space containing the electron will spread out very quickly. That is, the system tends to become more chaotic. The uncertainty of the electron’s position is growing. This is analogous to the increasing disorder in a large-scale system — such as a billiard table — due to the second law of thermodynamics.

“However, Schrödinger’s equation is reversible,” adds Valerii Vinokur, a co-author of the paper, from the Argonne National Laboratory, U.S. “Mathematically, it means that under a certain transformation, called complex conjugation, the equation will describe a ‘smeared’ electron localizing back into a small region of space over the same time period.” Although this phenomenon is not observed in nature, it could theoretically happen due to a random fluctuation in the cosmic microwave background permeating the universe.

The team set out to calculate the probability to observe an electron “smeared out” over a fraction of a second spontaneously localizing into its recent past. It turned out that even if one spent the entire lifetime of the universe — 13.7 billion years — observing 10 billion freshly localized electrons every second, the reverse evolution of the particle’s state would only happen once. And even then, the electron would travel no more than a mere one ten-billionth of a second into the past.

Large-scale phenomena involving billiard balls, volcanoes, etc. obviously unfold on much greater timescales and feature an astounding number of electrons and other particles. This explains why we do not observe old people growing younger or an ink blot separating from the paper.

Reversing time on demand

The researchers then attempted to reverse time in a four-stage experiment. Instead of an electron, they observed the state of a quantum computer made of two and later three basic elements called superconducting qubits.

Stage 1: Order. Each qubit is initialized in the ground state, denoted as zero. This highly ordered configuration corresponds to an electron localized in a small region, or a rack of billiard balls before the break.

Stage 2: Degradation. The order is lost. Just like the electron is smeared out over an increasingly large region of space, or the rack is broken on the pool table, the state of the qubits becomes an ever more complex changing pattern of zeros and ones. This is achieved by briefly launching the evolution program on the quantum computer. Actually, a similar degradation would occur by itself due to interactions with the environment. However, the controlled program of autonomous evolution will enable the last stage of the experiment.

Stage 3: Time reversal. A special program modifies the state of the quantum computer in such a way that it would then evolve “backwards,” from chaos toward order. This operation is akin to the random microwave background fluctuation in the case of the electron, but this time it is deliberately induced. An obviously far-fetched analogy for the billiards example would be someone giving the table a perfectly calculated kick.

Stage 4: Regeneration. The evolution program from the second stage is launched again. Provided that the “kick” has been delivered successfully, the program does not result in more chaos but rather rewinds the state of the qubits back into the past, the way a smeared electron would be localized or the billiard balls would retrace their trajectories in reverse playback, eventually forming a triangle.

The researchers found that in 85 percent of the cases the two-qubit quantum computer indeed returned back into the initial state. When three qubits were involved, more errors happened, resulting in a roughly 50 percent success rate. According to the authors, these errors are due to imperfections in the actual quantum computer. As more sophisticated devices are designed, the error rate is expected to drop.

Interestingly, the time reversal algorithm itself could prove useful for making quantum computers more precise. “Our algorithm could be updated and used to test programs written for quantum computers and eliminate noise and errors,” Lebedev explained.

Learn more: Physicists reverse time using quantum computer

 

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Argonne researchers posit way to locally circumvent Second Law of Thermodynamics

Argonne scientists Ivan Sadovskyy (left) and Valerii Vinokur published a paper showing a mathematical construction to a possible local violation of the Second Law of the Thermodynamics. One implication for the research could be a way to one day remotely power a device — that is, the energy expended to light the lamp could take place anywhere. (Image by Mark Lopez/Argonne National Laboratory.)

Argonne scientists Ivan Sadovskyy (left) and Valerii Vinokur published a paper showing a mathematical construction to a possible local violation of the Second Law of the Thermodynamics. One implication for the research could be a way to one day remotely power a device — that is, the energy expended to light the lamp could take place anywhere. (Image by Mark Lopez/Argonne National Laboratory.)

For more than a century and a half of physics, the Second Law of Thermodynamics, which states that entropy always increases, has been as close to inviolable as any law we know. In this universe, chaos reigns supreme.

But researchers with the U.S. Department of Energy’s (DOE’s) Argonne National Laboratory announced recently that they may have discovered a little loophole in this famous maxim.

Their research, published in Nature Scientific Reports, lays out a possible avenue to a situation where the Second Law is violated on the microscopic level.

The Second Law is underpinned by what is called the H-theorem, which says that if you open a door between two rooms, one hot and one cold, they will eventually settle into lukewarm equilibrium; the hot room will never end up hotter.

But even in the twentieth century, as our knowledge of quantum mechanics advanced, we didn’t fully understand the fundamental physical origins of the H-theorem.

“What we did was formulate how these beautiful abstract mathematical theories could be connected to our crude reality.” 

Recent advancements in a field called quantum information theory offered a mathematical construction in which entropy increases.

“What we did was formulate how these beautiful abstract mathematical theories could be connected to our crude reality,” said Valerii Vinokur, an Argonne Distinguished Fellow and corresponding author on the study.

The scientists took quantum information theory, which is based on abstract mathematical systems, and applied it to condensed matter physics, a well-explored field with many known laws and experiments.

“This allowed us to formulate the quantum H-theorem as it related to things that could be physically observed,” said Ivan Sadovskyy, a joint appointee with Argonne’s Materials Science Division and the Computation Institute and another author on the paper. “It establishes a connection between well-documented quantum physics processes and the theoretical quantum channels that make up quantum information theory.”

The work predicts certain conditions under which the H-theorem might be violated and entropy — in the short term — might actually decrease.

As far back as 1867, physicist James Clerk Maxwell described a hypothetical way to violate the Second Law: if a small theoretical being sat at the door between the hot and cold rooms and only let through particles traveling at a certain speed. This theoretical imp is called “Maxwell’s demon.”

“Although the violation is only on the local scale, the implications are far-reaching,” Vinokur said. “This provides us a platform for the practical realization of a quantum Maxwell’s demon, which could make possible a local quantum perpetual motion machine.”

For example, he said, the principle could be designed into a “refrigerator” which could be cooled remotely — that is, the energy expended to cool it could take place anywhere.

Learn more: Argonne researchers posit way to locally circumvent Second Law of Thermodynamics

 

 

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