The Butterfly Effect Disproved in Quantum Time Travel

The butterfly effect is one of the most important elements that form the chaos theory. Now, a team of researchers has proven that, in quantum realm, there is no ‘butterfly effect’ by using a quantum computer to mimic time travel.

In the study, information – qubits or quantum bits – time-travel into the simulated past. One of the qubits is then violently damaged, which may resemble stepping on a butterfly, and when all qubits return to the ‘present,’ they are mainly unaltered as if reality is somehow self-healing.

“On a quantum computer, there is no problem simulating opposite-in-time evolution, or simulating running a process backwards into the past,” said Nikolai Sinitsyn, a theoretical physicist at Los Alamos National Laboratory and co-author of the paper with Bin Yan, a post-doctorate in the Center for Nonlinear Studies, also at Los Alamos. “So we can actually see what happens with a complex quantum world if we travel back in time, add small damage, and return. We found that our world survives, which means there’s no butterfly effect in quantum mechanics.”

How Does the Butterfly Effect Theoretically Unfold

This theory and process are described best in Ray Bradbury’s 1952 story, ‘A Sound of Thunder,’ in which a character used a time machine to go back to the deep past, where he stepped on a butterfly. When he returned to the present time, he found a completely different world.

The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other. [Credit: Wikipedia]
This story is believed to have coined the term ‘butterfly effect,’ which relates to the incredibly high sensitivity of an intricate, dynamic system to its initial conditions. In such a mechanism, early and small factors go on to very much impact the evolution of the entire system.

Rather, Yan and Sinitsyn discovered that simulating a return to the past to create small local damage in a quantum system only leads to small and trivial local damage in the present. This impact has feasible applications in information-hiding hardware and testing quantum information devices. Information can be covered by a computer by converting the initial state into a powerfully entangled one.

“We found that even if an intruder performs state-damaging measurements on the strongly entangled state, we still can easily recover the useful information because this damage is not magnified by a decoding process,” Yan said. “This justifies talks about creating quantum hardware that will be used to hide information.”

The new discovery could also be employed to test whether a quantum processor is, actually, working by quantum principles. Since the newfound no butterfly effect is entirely quantum, if a processor operates Yan and Sinitsyn’s systems and demonstrates this effect, then it must be a quantum processor.

The Butterfly Effect in Quantum Systems​

To test the butterfly effect in quantum systems, the two researchers used theory and simulations with the IBM-Q quantum processor to demonstrate how a circuit could develop an intricate system by applying quantum gates, with forwards and backwards cause and effect.

This can also be referred to as a quantum time-machine simulator.

In the experiment, the team had Alice, a stand-in agent they used for quantum thought experiments. Aline prepares one of her qubits​ in the present and runs it backwards through the quantum computer. In the past, an intruder, Bob, measures Alice’s qubit – this action deranges the qubit and destroys all its quantum links with the rest of the world. Then, the system is run forward to the present.

Alice prepares her qubit and applies the information scrambling unitary U to this and many other qubits altogether. Bob measures her qubit in any basis, flipping the qubit to the state not known to Alice. Alice still can reconstruct her information via a single decoding unitary U†. [Credit: Los Alamos National Laboratory]
As per Ray Bradbury, Bob’s small damage to the state and all those links in the past should be rapidly magnified during the intricate forward-in-time evolution. Therefore, Alice should be unable to access her information at the end.

However, that is not what happened. The scientists found that most of the presently local information was concealed in the deep past in the form of essentially quantum links that could not be messed up by minor tampering. They demonstrated that the information returns to Alice’s qubit without much damage in spite of Bob’s interference. Counter-intuitively, for deeper travels to the past and for larger ‘worlds,’ Alice’s final information goes back to her even less damaged.

“We found that the notion of chaos in classical physics and in quantum mechanics must be understood differently,” Sinitsyn said.

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