The quantum Hamming distance is hard to reliably measure. It tends to ignore the quantum complexity of the quantum phase. The inner space is a hyperbolic space that is a type of moduli of curves or paths. This approach may in the long run be preferable.
LC On Wednesday, October 6, 2021 at 6:58:50 AM UTC-5 johnk...@gmail.com wrote: > The difficulty in maintaining quantum coherence is the only reason we > don't have practical quantum computers today, but Monday's issue of the > journal Nature reported on a major advance in solving that problem. For > the first time it has been proven that a quantum error correcting code > called the "Bacon-Shor code" actually works in practice and not just in > theory. They combined 9 physical Qubits that work correctly 98.9% of the > time to make one virtual logic Qubit that works correctly 99.4% of the > time, and that virtual logic Qubit would be the one you would use in an > actual computation. Until now nobody has been able to prove that a logical > Qubit can be made that is more reliable than any of the parts it is made > out of. This illustrates how different the quantum world is from the macro > world we're accustomed to. If 9 people on an assembly line install a part > into a machine and install the part correctly 98.9% of the time then the > probability the entire finished machine will work correctly is only > (0.989)^9 = 90.5% , but if the workers lived in the quantum world and they > assemble the parts the way that Bacon-Shor tells them to then the finish > machine will work correctly 99.4% of the time not 90.5%. The best thing is > that although there are still engineering problems to solve there doesn't > seem to be any fundamental reason Bacon-Shor can't be scaled up. > > Kenneth Brown, what are the authors of the paper, says: > > *"What's amazing about fault tolerance is it's a recipe for how to take > small unreliable parts and turn them into a very reliable device. And > fault-tolerant quantum error correction will enable us to make very > reliable quantum computers from faulty quantum parts. The key part of > quantum error correction is redundancy, which is why we needed 9 qubits in > order to get one logical qubit. That redundancy helps us look for errors > and correct them, because an error on a single qubit can be protected by > the other eight."* > > Laird Egan, another author of the paper says: > > "This is really a demonstration of quantum error correction improving > performance of the underlying components for the first time. It's really > a proof of concept that quantum error correction works. It shows that we > can get all the pieces together and do all the steps. And there's no > reason that other platforms can't do the same thing as they scale up." > > Fault-tolerant control of an error-corrected qubit > <https://www.nature.com/articles/s41586-021-03928-y> > > John K Clark See what's on my new list at Extropolis > <https://groups.google.com/g/extropolis> > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/97605808-2db1-4d16-b012-56db91046e30n%40googlegroups.com.
