Of all the reasons for wanting to time-travel—saving someone from a fatal mistake, exploring ancient civilizations, gathering evidence about unsolved crimes—recovering lost information isn’t the most exciting. But even if a quest to recover the file that didn’t auto-save doesn't sound like a Hollywood movie plot, we’ve all had moments when we’ve longed to go back in time for exactly that reason.

Theories of time and time-travel have highlighted an apparent stumbling block: time travel requires changing the past, even simply by adding in the time traveller. The problem, according to chaos theory, is that the smallest of changes can cause radical consequences in the future. In this conception of time travel, it wouldn’t be advisable to recover your unsaved document since this act would have huge knock-on effects on everything else.

New research in quantum physics from Los Alamos National Laboratory has shown that the so-called butterfly effect can be overcome in the quantum realm in order to “unscramble” lost information by essentially reversing time.

In a paper published in July, researchers Bin Yan and Nikolai Sinitsyn write that a thought experiment in “unscrambling” information with time-reversing operations would be “expected to lead to the same butterfly effect as the one in the famous Ray Bradbury’s story ‘A Sound of Thunder’” In that short story, a time traveler steps on an insect in the deep past and returns to find the modern world completely altered, giving rise to the idea we refer to as the butterfly effect.

“In contrast," they wrote, "our result shows that by the end of a similar protocol the local information is essentially restored.”

"The primary focus of this work is not 'time travel'—physicists do not have an answer yet to tell whether it is possible and how to do time travel in the real world,” Yan clarified.

“[But] since our protocol involves a 'forward' and a 'backward' evolution of the qubits, achieved by changing the orders of quantum gates in the circuit, it has a nice interpretation in terms of Ray Bradbury's story for the butterfly effect. So, it is an accurate and useful way to understand our results."

What is the butterfly effect?

The world does not behave in a neat, ordered way. If it did, identical events would always produce the same patterns of knock-on effects, and the future would be entirely predictable, or deterministic. Chaos theory claims that the opposite: total randomness is not our situation either. We exist somewhere in the middle, in a world that often appears random but in fact obeys rules and patterns.

Patterns within chaos are hidden because they are highly sensitive to tiny changes, which means similar but not identical situations can produce wildly different outcomes. Another way of putting it is that in a chaotic world, effects can be totally out of proportion to their causes, like the metaphor of a flap of butterfly wings causing a tornado on the other side of the world. On the tornado side of the world, the storm would seem random, because the connection between the butterfly-flap and the tornado is too complex to be apparent. While this butterfly effect is the classic poetic metaphor illustrating chaos theory, chaotic dynamics also play out in real-world contexts, including population growth in the Canadian lynx species and the rotation of Pluto’s moons.

Another feature of chaos is that, even though the rules are deterministic, the future is not predictable in the long-term. Since chaos is so sensitive to small variations, there are near-infinite ways the rules could play out and we would need to know an impossible amount of detail about the present and past to map out exactly how the world will evolve.

Similarly, you can’t reverse-engineer some piece of information about the past simply by knowing the current and even future situations; time-travel doesn’t help retrieve past information, because even moving backwards in time, the chaotic system is still in play and will produce unpredictable effects.

__Information scrambling__

Unscrambling information which has previously been scrambled is not straightforward in a chaotic system. Yan and Sinitsyn’s key discovery is that it is nonetheless possible in quantum computing to get enough information via time-reversal which will then enable information unscrambling.

According to Yan, the fact that the butterfly effect does not occur in quantum realms is not a surprising result, but demonstrating information unscrambling is both novel and important.

In quantum information theory, scrambling occurs when the information encoded in each quantum particle is split up and redistributed across multiple quantum particles in the same quantum system. The scrambling is not random, since information redistribution relies on quantum entanglement, which means that the states of some quantum particles are dependent on each other. Although the scrambled result is seemingly chaotic, the information can be put back together, at least in principle, using the entangled relationships.

Importantly, information scrambling is not the same as information loss. To continue the earlier analogy: information loss occurs when a document is permanently deleted from your computer. For information scrambling, imagine cutting and pasting tiny bits of one computer file into every other file on your machine. Each file now contains a mess of information snippets. You could reconstruct the original files, if you remembered exactly which bits were cut and pasted, and did the entire process in reverse.

Physicists are interested in information scrambling for two main reasons. On the theoretical side, it’s been proposed as a way to explain what happens to information sucked into a black hole. On the more applied side, it could be an important mechanism for quantum computers to store and hide information, and could produce fast and efficient quantum simulators, which are used already to perform complex experiments including new drug discovery.

Yan and Sinitsyn fall into the second camp, and construct what they call a “practically accessible scenario” to test unscrambling by time-travel. This scenario is still hypothetical, but explores the mathematics of the actual quantum processor used by Google to demonstrate quantum supremacy in 2019.

Yan says: “Another potential application is to use this effect to protect information. A random evolution on a quantum circuit can make the qubit robust to perturbations. One may further exploit the discovered effect to design protocols in quantum cryptography.”

__The set-up__

In Yan and Sinitsyn's quantum thought experiment, Alice and Bob are the protagonists. Alice is using a simplified version of Google’s quantum processor to hide just one part of the information stored on the computer (called the “central qubit”) by scrambling this qubit’s state across all the other qubits (called the “qubit bath”). Bob is cast as the “intruder”, much like a malicious computer hacker. He wants the important information originally stored on the central qubit, now distributed across entangled quantum particles in the bath.

Unfortunately, Bob’s hack, while successful in getting the information he wanted, leaves a trail of destruction.

“If her processor has already scrambled the information, Alice is sure that Bob cannot get anything useful,” the authors write. “However, Bob’s measurement changes the state of the central qubit and also destroys all quantum correlations between this qubit and the rest of the system.”

Bob's method of information theft has altered the computer state so that Alice can also no longer access the hidden information. In this case, the damage occurs because quantum states contain all possible values they could have, with assigned probabilities of each value, but these possibilities (represented by the wave function) “**collapse**” down to just one value when a measurement is taken. Quantum computing relies on unmeasured quantum systems to store even more information in multiple possible states, and Bob’s intrusion has totally altered the computer system.

__Reversing time__

Theoretically, the behaviour of a quantum system moving backwards in time can be demonstrated mathematically using what’s called a time-reversed evolution operator, which is exactly what Alice uses to de-scramble the information.

Her time-reversal is not actually time travel the way we understand it from science fiction, it is literally a reversal of time’s direction; the system evolves backwards following whatever dynamics are in play, rather than Alice herself revisiting an earlier time. If the butterfly effect held in the quantum world, then this backwards evolution would actually increase the damage Bob had caused, and Alice would only be able to retrieve the hidden information if she knew exactly what that damage was and could correct her calculations accordingly.

Luckily for Alice, quantum systems behave totally differently to non-quantum (classical or semiclassical) chaotic systems. What Yan and Sinitsyn found is that she can apply her time-reversal operation and end up at an "earlier" state which will not be identical with the initial system she set up, but it will also not have increased the damage which occurred later. Alice can then reconstruct her initial system using a method of quantum unscrambling called quantum state tomography.

What this means is that a quantum system can effectively heal and even recover information that was scrambled in the past, without the chaos of the butterfly effect.

“Classical chaotic evolution magnifies any state damage exponentially quickly, which is known as the butterfly effect,” explain Yan and Sinitsyn. “The quantum evolution, however, is

linear. This explains why, in our case, the uncontrolled damage to the state is not magnified by the subsequent complex evolution. Moreover, the fact that Bob’s measurement does not damage the useful information follows from the property of entanglement correlations in the scrambled state.”

Hypothetical though this scenario may be, the result already has a practical use: verifying whether a quantum system has achieved quantum supremacy. Quantum processors can simulate time-reversal in a way that classical computers cannot, which could provide the next important test for the quantum race between Google and IBM.

So, while time travel is still not in the cards, the quantum world continues to mess with our classical conception of how the world evolves in time, and pushes the limits of computing information.

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