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 [email protected] 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/97605808-2db1-4d16-b012-56db91046e30n%40googlegroups.com.
