## quantum simulation or supremacy?

**N**ature this week contains a prominent paper by Arute et al. reporting an experiment on a quantum computer running a simulation on a state-space of dimension 2^{53} (which is the number of qubits in their machine, plus one dedicated to error correction if I get it right). With a million simulation of the computer state requiring 200 seconds. Which they claim would take 10,000 years (3 10¹¹ seconds) to run on a classical super-computer. And which could be used towards producing certified random numbers, an impressive claim given the intrinsic issue of qubit errors. (This part is not developed in the paper but I wonder how a random generator could handle such errors.)

“…a “challenger” generates a random quantum circuit C (i.e., a random sequence of 1-qubit and nearest-neighbor 2-qubit gates, of depth perhaps 20, acting on a 2D grid of n = 50 to 60 qubits). The challenger then sends C to the quantum computer, and asks it apply C to the all-0 initial state, measure the result in the {0,1} basis, send back whatever n-bit string was observed, and repeat some thousands or millions of times. Finally, using its knowledge of C, the classical challenger applies a statistical test to check whether the outputs are consistent with the QC having done this.” The blog of Scott Aaronson

I have tried reading the Nature paper but had trouble grasping the formidable nature of the simulation they were discussing, as it seems to be the reproduction by a simulation of a large quantum circuit of depth 20, as helpfully explained in the above quote. And checking the (non-uniform) distribution of the random simulation is the one expected. Which is the hard part and requires a classical (super-)computer to determine the theoretical distribution. And the News & Views entry in the same issue of Nature. According to Wikipedia, “the best known algorithm for simulating an arbitrary random quantum circuit requires an amount of time that scales exponentially with the number of qubits“. However, IBM (a competitor of Google in the quantum computer race) counter-claims that the simulation of the circuit takes only 2.5 days on a classical computer with optimised coding. (And this should be old news by the time this blog post comes out, since even a US candidate for the presidency has warned about it!)

November 11, 2019 at 2:54 pm

Just to point out that the number of qubits is 53 and that the corresponding Hilbert space has dimension 2^53.

The 54th qubit of the machine didn’t work properly so wasn’t used in the experiment.

For the random generation application, the idea is to use the output string of the quantum machine as an input to a randomness extractor, which will turn biased bits into a shorter random string approximately uniform (this also requires a short seed).

November 11, 2019 at 9:52 pm

Merci! I had thought the 54th qubit was like a validation bit…