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posted by martyb on Saturday October 20 2018, @06:27PM   Printer-friendly
from the quantum-improvement dept.

IBM finally proves that quantum systems are faster than classicals

In 1994, MIT professor of applied mathematics Peter Shor developed a groundbreaking quantum computing algorithm capable of factoring numbers (that is, finding the prime numbers for any integer N) using quantum computer technology. For the next decade, this algorithm provided a tantalizing glimpse at the potential prowess of quantum computing versus classical systems. However, researchers could never prove quantum would always be faster in this application or whether classical systems could overtake quantum if given a sufficiently robust algorithm of its own. That is, until now.

In a paper published Thursday in the journal Science, Dr. Sergey Bravyi and his team reveal that they've developed a mathematical proof which, in specific cases, illustrates the quantum algorithm's inherent computational advantages over classical.

[...] What's more, the proof shows that, in these cases, the quantum algorithm can solve the problem in a fixed number of steps, regardless of how many inputs are added. With a classical computer, the more inputs you add, the more steps it needs to take in order to solve. Such are the advantages of parallel processing.

There's now proof that quantum computers can outperform classical machines

In this paper, the researchers prove that a quantum computer with a fixed circuit depth is able to outperform a classical computer that's tackling the same problem because the classical computer will require the circuit depth to grow larger, while it can stay constant for the quantum computer.


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  • (Score: 2) by bzipitidoo on Sunday October 21 2018, @08:09PM (1 child)

    by bzipitidoo (4388) on Sunday October 21 2018, @08:09PM (#751759) Journal

    I read over the summary again, and realized it's more disconnected than I thought. It mentions the groundbreaking Integer Factorization algorithm that runs in polynomial time on a quantum computer. Then it says that some researchers have proven that a quantum computer needs less (algorithmically less) memory than a classic computer to solve a certain class of problems. It doesn't make it too clear they're now talking about another problem in a class that may or may not include Integer Factorization.

    I'd bet a large sum that their result includes the proviso that "if P≠NP" or a more specific "if P≠QP" or "if P≠BQP", and thus they haven't and weren't trying to prove that.

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  • (Score: 2) by maxwell demon on Sunday October 21 2018, @09:53PM

    by maxwell demon (1608) on Sunday October 21 2018, @09:53PM (#751780) Journal

    Well, no need to guess; the actual article is linked from the summary. Here's the abstract (direct copy/paste from arXiv):

    We prove that constant-depth quantum circuits are more powerful than their classical counterparts. To this end we introduce a non-oracular version of the Bernstein-Vazirani problem which we call the 2D Hidden Linear Function problem. An instance of the problem is specified by a quadratic form q that maps n-bit strings to integers modulo four. The goal is to identify a linear boolean function which describes the action of q on a certain subset of n-bit strings. We prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the 2D Hidden Linear Function problem with high probability must have depth logarithmic in n. In contrast, we show that this problem can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates acting locally on a two-dimensional grid.

    --
    The Tao of math: The numbers you can count are not the real numbers.