"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 across 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 and volcanoes 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 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.