[HN Gopher] No distributed quantum advantage for approximate gra...
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       No distributed quantum advantage for approximate graph coloring
        
       Author : nabla9
       Score  : 61 points
       Date   : 2023-12-08 12:35 UTC (10 hours ago)
        
 (HTM) web link (arxiv.org)
 (TXT) w3m dump (arxiv.org)
        
       | flanfly wrote:
       | Good news for cryptographers in case we need an alternative to
       | LWE and coding-based PQC.
        
         | da-bacon wrote:
         | I'm not sure this implies much about PQC. The model here is
         | LOCAL distributed computing which is pretty far from what
         | you're concerned about in PQC.
        
       | nabla9 wrote:
       | It is not known if there is there any graph problem that someone
       | cares about for which there exist algorithm with distributed
       | quantum advantage?
       | 
       | For many graph problems it's possible show to show that there is
       | no quantum advantage by by defining a model so that it can do
       | anything except violating causality.
       | 
       | This paper shows that approximate graph coloring has not quantum
       | advantage.
        
       | jimsimmons wrote:
       | n00b question: what are some important problems for which quantum
       | computation has shown to have an advantage
        
         | mebassett wrote:
         | factoring large integers into primes (shor's algorithm). that
         | and grover's search promise to provide ways to crack a lot of
         | encryption.
         | 
         | also quantum computing should improve both classical and
         | quantum physical simulations.
        
           | vitus wrote:
           | The other side of Shor's algorithm is that you can use it to
           | solve discrete logarithm (which additionally breaks elliptic
           | curve crypto; factoring breaks RSA).
           | 
           | I don't agree that Grover's algorithm is as fundamental in
           | breaking encryption, since it "only" yields a quadratic
           | speed-up. You'd have similar effective security as in the
           | pre-quantum world by doubling the key length; you could do
           | this by, say, switching to AES-256 instead of AES-128.
           | Meanwhile, switching from RSA-2048 to RSA-4096 only helps if
           | it means the problem size now exceeds the size of the biggest
           | quantum computers.
        
         | erikaww wrote:
         | I think there is promise with tons of optimization problems
         | (machine learning, approximating differential equations). I
         | hope these would be significantly faster in practice.
         | 
         | It would be cool if we had quantum accelerated game physics
         | engines. Super realistic games that are fast.
         | 
         | Simulations could scale better, so we could make them a lot
         | more useful.
        
           | pclmulqdq wrote:
           | Unless you are simulating quantum effects, these sorts of
           | simulations are unlikely to be faster on a quantum computer.
           | Also, attempts at using the Ising model for general-purpose
           | optimization have found themselves somewhat limited in
           | application.
           | 
           | For people doing drug discovery and quantum physics/chemistry
           | research, they will see an exponential speedup from quantum
           | computing, but I think you're overstating how applicable this
           | technology is.
        
         | NooneAtAll3 wrote:
         | you aren't the first asking, so someone made a website listing
         | stuff
         | 
         | https://quantumalgorithmzoo.org/
        
       | cevi wrote:
       | At first, the results claimed here seem to clash with the fact
       | that we know, for instance, that it is NP-hard to 5-color a graph
       | which is promised to be 3-colorable [1]. Of course, the devil is
       | in the details - on page 11, where they describe the "LOCAL"
       | computation model they work in, they explain:
       | 
       | "In each round the processors may perform unbounded computations
       | on their respective local state variables and subsequently
       | exchange of messages of arbitrary size along the links given by
       | the underlying input graph."
       | 
       | Given this setup, it should be possible to solve any problem in
       | O(n) rounds, and indeed they point this out in the introduction:
       | 
       | "If the chromatic number of G is kh, in this setting it is
       | trivial to find a kh-coloring in T = O(n) rounds, as in O(n)
       | rounds all nodes can learn the full topology of their own
       | connected component and they can locally find an optimal coloring
       | by brute force without any further communication."
       | 
       | While this paper is very interesting from a theoretical
       | perspective, it is saying more about the LOCAL model of
       | distributed computing than it is about quantum computing. Nobody
       | should come away from this with the conclusion that we have
       | somehow proved that quantum algorithms are useless for real-world
       | problems.
       | 
       | [1] https://arxiv.org/abs/1811.00970
        
       | m3kw9 wrote:
       | Why are they trying to colour graphs with quantum computers? Just
       | reading the title
        
         | david_draco wrote:
         | I suspect the point is that all NP-hard problems are equivalent
         | to each other, often one can be transform one NP-hard problem
         | to another. This shows that quantum will not save us. This is
         | bad but also good for encryption. NP remains an important topic
         | post-quantum that cannot be hand-waved away.
        
           | cochne wrote:
           | NP hard problems aren't all equivalent, that's NP complete.
        
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