alt Hacker NewsVery interesting article.
This makes me wonder: Would it be possible to implement an equivalent to Shor's algorithm on a p-computer. Maybe the quantumness isn't necessary at all
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That's a cool thought! For those who may not know, Shor's algorithm is fundamentally quantum because it relies on the interference of probability amplitudes, which can be both positive and negative. It could not be directly implemented on a p-computer because you could only simulate this interference, which removes the exponential advantage.
It's possible that an entirely different approach is made possible by p-computers, but this would be tricky to find. Furthermore, it seems that the main advantage of p-computers is sampling from a Boltzmann-like distribution, and I'm not aware that this is the bottleneck in any known factorisation algorithm.
A direct equivalent, no, as stated in the introduction.
"Notably, while probabilistic computers can emulate quantum interference with polynomial resources, their convergence is in general believed to require exponential time [10]. This challenge is known as the signproblem in Monte Carlo algorithms [11]."
I doubt it. Shor's algorithm relies on the quantum Fourier transform, which requires the complex phase information encoded in the quantum wavefunctions. The quantum probability norm (L2) accounts for interference between the complex amplitudes of these wavefunctions; the classical L1 probability norm does not.
The paper compares p-computers with D-Wave's quantum annealing machine, which is limited to only solving certain problems (as opposed to universal QC such as Google or IonQ's, that could in theory implement Shor's)
The power of quantum computing is constructing the solution to a problem out of an interference pattern. Classical probabilities don’t interfere, but quantum probabilities do. Loosely, quantum probabilities can be constructed to cancel, since their amplitudes can be negative.
Shor’s algorithm works on the quantum Fourier transform. The quantum Fourier transform works because you can pick a frequency out of a signal using a “test wave.” The test wave can select out the amplitude of interest because the information of the test wave constructively interferes, whereas every other frequency cancels. This is the interference effect that can only happen with complex/negative probability amplitudes.