Here is a way to see the fallacy of the
OMG, its 10^300 variables, thats crazy style of “argument”.
Consider a probabilistic classical algorithm on 500 bits. Perhaps a Monte Carlo simulation of an Ising model for example.
Note first that the most general probability distribution over the 500 classical bits takes 2^500 real numbers to specify. (You have to specify P(000…0) and P(000…1) and… P(111…1)). [You should compare this to the 2^501 real parameters it takes to specify the quantum state of 500 qubits.]
To generate the most general such distribution perhaps you are restricted to using circuits where the gates act on at most n-bits at a time. Each gate can be described by a 2^n x 2^n bistochastic matrix comprised of (n-1)^2 real parameters. [You should compare this to the n^2 real parameters it takes to specify a 2^n x 2^n unitary matrix for a quantum gate acting on n qubits.]
Obviously its nuts to imagine you can generate all classical probability distributions over the 2^500 real parameters, particularly if you’re so mad as to think you are going to do it using a circuit comprised only of these n-bit gates!
Therefore useful classical monte carlo computing is obviously decades away.
(Oh and please trust me, I'm well know in stuff that isn't quantum computing.)
Consider a probabilistic classical algorithm on 500 bits. Perhaps a Monte Carlo simulation of an Ising model for example.
Note first that the most general probability distribution over the 500 classical bits takes 2^500 real numbers to specify. (You have to specify P(000…0) and P(000…1) and… P(111…1)). [You should compare this to the 2^501 real parameters it takes to specify the quantum state of 500 qubits.]
To generate the most general such distribution perhaps you are restricted to using circuits where the gates act on at most n-bits at a time. Each gate can be described by a 2^n x 2^n bistochastic matrix comprised of (n-1)^2 real parameters. [You should compare this to the n^2 real parameters it takes to specify a 2^n x 2^n unitary matrix for a quantum gate acting on n qubits.]
Obviously its nuts to imagine you can generate all classical probability distributions over the 2^500 real parameters, particularly if you’re so mad as to think you are going to do it using a circuit comprised only of these n-bit gates!
Therefore useful classical monte carlo computing is obviously decades away.
(Oh and please trust me, I'm well know in stuff that isn't quantum computing.)