The cited paper[1] references "random circuit sampling" which is defined in [2] which then gets so heavy into abstract math, and I give up.
Can someone explain this in terms an EE or programmer can understand?
Can someone explain this in terms an EE or programmer can understand?
At the end of the day, people writing these papers are also human. The very same sorts of humans who pad resumes with shiny technology and self-serving complexity.
This might be a case of a rabbit you do not want to chase.
I'm sure the researchers will all collectively realize this, if it were to be the case, and disregard their 12 year academic journey with their great salaries in favor of research into more important topics like world hunger, renewable energy, etc.
I'm so sure that the percentage of sureness is an imaginary, quantum-entangled value between -7 and 13 billion percent.
You may just be spouting off, but I genuinely am asking. If someone else dissing QC research wants to make a pitch for a concrete plan on how to make a difference in the world with a physics PhD and years of experience in scientific computing, drop me a message.
First, it's important to know that a quantum state (written as |letter>) is not directly observable. We can think of it as some vector, for which we can only apply an operation to to get out a scalar observable.
A quantum circuit is a series of operations on a quantum state to create a different quantum state, which can be modeled as a matrix U, which is unitary (meaning U*U=1).
The goal of "sampling a random quantum circuit" is trying to find the probability of observing some given observable if you keep applying random quantum circuits to a given input state.
Yeah, if someone could please do that.
Quantum circuits are made of quantum logic gates like Hadamard, CNOT, Z, CZ, etc. Instead of bits as inputs and outputs, quantum logic gates have qubits. Unlike boolean logic where bits are 0 and 1, a qubit is a 2D vector [α β] where α and β are complex numbers, corresponding to a superposition of the zero and one bases: α * |0> + β * |1>. You can visualise a qubit as a point on a sphere, the so called Bloch sphere [1]
There are multiple ways to implement a qubit, but you need to start with some quantum phenomenon. An example is the polarisation of a photon, so horizontal could be |0> and vertical polarisation could be |1> and the qubit is represented as complex vector of these two. If you've studied linear algebra you know manipulating a vector often involves linear transformations. Any linear transformation can be represented as a matrix - so applying gates is just doing matrix multiplication. Unary gates are 2x2 matrices and binary gates are 4x4 matrices - for photons they would be implemented with mirrors and optical waveplates. Measuring the polarisation at the end is the output. The output is not deterministic but it always follows the same distribution, so you could design a circuit that has |001> X% of the time, |010> Y%, |111> Z% of the time, etc. such that X + Y + Z + .. = 100%.
I'm not too familiar with the details of random circuit sampling, but the idea is that you start with a big circuit that wasn't intentionally designed and therefore has no known properties we can exploit - instead it's a random mess of transformations to the qubits. A classical computer cannot run big quantum circuits - N gates with the 49 Google qubits requires like 2^49 * N^3 classical gates, so it won't be able to calculate the output distribution. However, what we can do is run the quantum circuit many times (do measurements on the quantum computer) and collect many samples. Given enough samples, a classical computer can verify whether there's consistency between them and whether an actual transformation produced them (and therefore quantum computation happened) or its just pure noise / garbage using cross entropy benchmarks [2].
Note that the purpose of the "random" in the random circuit is to introduce hardness and prevent cheating (assume that the classical computer is the "opponent" of the quantum computer); the circuits don't calculate anything useful / of human value.
What's interesting is that once people with supercomputers saw the benchmark formula and analysed the constant factors, they found a loophole which let them run a classical algorithm which generates measurements/samples that satisfy the benchmark with 40K classical CPUs for a week, or even a single A100 within 140 days. Some of their success was due to the sheer power available and some is due to algorithmic cleverness (see: tensor networks). In my opinion, they are only disproving the Sycamore supremacy in a fussy way.
[1] - https://en.wikipedia.org/wiki/Bloch_sphere
[2] - https://en.wikipedia.org/wiki/Cross-entropy_benchmarking
Unfortunately not. The physicists who are behind quantum computing don't think the same way, and go straight for the abstract math to solve any problem. I am pretty sure they don't understand that most of our progress on computing up to this point is because you don't need to go into Galois fields or discrete math to describe what a computer or algorithm does. I'm also pretty sure that they don't know of another way to think about it.
It's either Monte Carlo or bullshit.