I remember seeing a lecture by Aaronson where he described the idea of a “relativity computer” where you set a computer running on some exponential task, but th

I remember seeing a lecture by Aaronson where he described the idea of a “relativity computer” where you set a computer running on some exponential task, but then hop in a spaceship and fly off at nearly the speed of light, and come back to find the answer in an amount of time only polynomial for you. He “debunked” this by mentioning to do it you’d potentially need an exponentially large supply of fuel to accelerate yourself to a speed exponentially close to the speed of light as the problem to solve grows more complex. I wonder if something similar could be true about quantum computing. Maybe it is theoretically possible to solve problems polynomially that can only be solved exponentially in a classical computer. But maybe it requires “exponentially more” of some resource, like a power supply to power the physical devices needed to do an amount of error correction to make it physically realizable as the problem size grows. Would it be possible for the Church-Turing thesis to be false mathematically, but for the amount of quantum error correction to require an amount of physical resources that grow prohibitively and prevent it from being practically possible (like the fuel limitation prevents the otherwise physically possible relativity computer)?