You shall not pass the speed of light,” said Albert Einstein. Although this was declared twenty years before Erwin Schrödinger postulated his famous equation, the same rule applies to quantum mechanics, setting an upper bound on the speed of information propagation and preserving causality.

In the quantum realm, everything exists in superposition—like a coin being both heads and tails—until an observation is made. In perhaps the most sci-fi interpretation, reality splits into different branches upon observation. Sadly, we don’t get to choose which reality we end up in, nor can we interact with other versions of ourselves.

But what if someone, like Neo from The Matrix, had the power to choose between a red or blue pill and knew which reality branches they would lead to? Not surprisingly, causality would be violated, allowing information to propagate faster than the speed of light! In some cases, we can simulate this faster-than-light behavior with a quantum computer, as we first demonstrated on Quantinuum’s H1 trapped-ion quantum computer in this paper. However, this is not universally true, and we provide an explicit example where this so-called ‘non-Hermitian’ quantum dynamics is too strong to be simulated, even with a quantum computer. (arxiv 2406.15557)