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Does someone know for reference how big of a number that computer can factor? Or some other complex problem that is not highly theoretical...
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? [1] https://arxiv.org/abs/2304.11119 [2] https://arxiv.org/abs/2007.07872
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
"This is a very nice demonstration of quantum advantage. While a great achievement academically, the algorithm used does not really have real world practical applications, though." Not having real world applications is not necessarily damning, of course. Curious to know what implications this has for general algorithms. Reading this, it almost makes it sound like there will be some algorithms that quantum is better a…
My understanding is that quantum computers only have two real use cases, as of today: 1. Breaking crypto. 2. Simulating other quantum systems. For (1) it's basically all downsides. For (2) unless you're a particle phycisist you'll never need quantum computers. But that's now. Maybe there will be a killer app for it some day, changing everything. Or indeed, we could get it indirectly. Maybe simulating quantum systems…
Dumb question: Say I have a wooden stick and I break it in half in less than a second. Assume a computer would need several minutes to simulate everything that would've happened in the stick. I clearly got the output faster than a computer (and with more precision), so does this imply I'm doing anything particularly fascinating? I assume the same scenario is possible to concoct for a quantum computer. I assume it wou…
> He said: “This is a very nice demonstration of quantum advantage. While a great achievement academically, the algorithm used does not really have real world practical applications, though. > “We really must get to utility quantum computing – an era where quantum computers with many thousand qubits actually begin to deliver value to society in a way that classical computers never will be able to.” This seems to be t…
A potential hidden bonus: if quantum computing theories get enough attention, maybe people will start to consider using the quantum computing abilities of the human mind with conscious intentionality (since by the time we get computers to be able to do it, it may be too late)!
Dumb question: Say I have a wooden stick and I break it in half in less than a second. Assume a computer would need several minutes to simulate everything that would've happened in the stick. I clearly got the output faster than a computer (and with more precision), so does this imply I'm doing anything particularly fascinating? I assume the same scenario is possible to concoct for a quantum computer. I assume it wou…
The difference between you breaking a stick and the computer modeling it is that you've measured nothing. You don't know, with any precision, the amount of force you used, the rate the stick broke at, how much mass remains in the two pieces and how much was lost to splintering, etc. In other words, assuming the computer model has sufficiently accurate data as an input, it can produce significantly more refined output…
Earlier quoted context omitted.
A potential hidden bonus: if quantum computing theories get enough attention, maybe people will start to consider using the quantum computing abilities of the human mind with conscious intentionality (since by the time we get computers to be able to do it, it may be too late)!
What are these capabilities of which you speak? Or have i missed the sarcasm
> He said: “This is a very nice demonstration of quantum advantage. While a great achievement academically, the algorithm used does not really have real world practical applications, though. > “We really must get to utility quantum computing – an era where quantum computers with many thousand qubits actually begin to deliver value to society in a way that classical computers never will be able to.” This seems to be t…
I don't think it's that the concepts are contrived (although the test cases certainly are), it's just that our quantum computers are really early in their development and can't do the more complicated things yet. It's like if we had calculators that took an hour to do each arithmetic operation- the fact that people wouldn't use it doesn't mean arithmetic is contrived, just that it isn't as powerful as better alternat…
Earlier quoted context omitted.
A potential hidden bonus: if quantum computing theories get enough attention, maybe people will start to consider using the quantum computing abilities of the human mind with conscious intentionality (since by the time we get computers to be able to do it, it may be too late)!
What are these capabilities of which you speak? Or have i missed the sarcasm
Someone may venture into this territory some day, and perhaps that someone will find some travelling companions to make the journey more exciting and productive....time will tell!
Google's and IBM's previous "quantum supremacy" demonstrations were quickly crushed by improved classical simulations. Let's see if it survives this time.
The main issue I had with their demonstrations were that the problems they chose were essentially "let's show that a quantum computer is better at being a quantum computer than a classical computer". Obviously they are, just like I'm better at being a human than ChatGPT is. I'm not saying they suck, but to proclaim that "quantum computers are superior" you need an actual use-case, IMO.