<story><title>New quantum algorithms finally crack nonlinear equations</title><url>https://www.quantamagazine.org/new-quantum-algorithms-finally-crack-nonlinear-equations-20210105/</url></story><parent_chain><item><author>ur-whale</author><text>The article seem to imply that quantum computers are a solution to the problem that non-linear differential equations are chaotic (as in: tiny changes in initial conditions lead to vastly different solutions).&lt;p&gt;My impression of quantum computers are they will allow us to get to solutions to algorithmic problems &lt;i&gt;faster&lt;/i&gt;.&lt;p&gt;I fail to see how they could possibly work around the chaos inherent to some diffeqs (e.g. N-body problems).&lt;p&gt;[edit]:and after reading the article more carefully, I&amp;#x27;m still not sure how QC has &lt;i&gt;any&lt;/i&gt; effect on the chaotic nature of non-linear diffeqs . All I see in here is that they&amp;#x27;re trying to map non-linear diffeqs to linear systems via approximations so they  can run it on a QC.</text></item></parent_chain><comment><author>conformist</author><text>Yes, essentially that&amp;#x27;s right (regarding Child&amp;#x27;s paper), as far as I can tell.
Child&amp;#x27;s article seems to be about a smart way to approximate sufficiently dissipative, non-linear, n-dimensional ODEs (or spatially discretised PDEs for that matter), such that you can apply good old forward Euler. They do that in such a manner that you end up solving a linear system for time-stepping for which a log(n) quantum algo is known. 
This is pretty cool, because they basically use standard numerical analysis tools and manage to plug in the quantum computing part to show that, e.g., as you increase the spatial &amp;quot;resolution&amp;quot; with which you solve a PDE, the cost only increases logarithmically.
This feels useful from a computational fluid  dynamics perspective, say, if you&amp;#x27;re not interested in super turbulent flows.
So this is more about &amp;quot;how do we make solving hard PDEs faster&amp;quot; than &amp;quot;finally cracking non-linear PDEs&amp;quot;.</text></comment>
<story><title>New quantum algorithms finally crack nonlinear equations</title><url>https://www.quantamagazine.org/new-quantum-algorithms-finally-crack-nonlinear-equations-20210105/</url></story><parent_chain><item><author>ur-whale</author><text>The article seem to imply that quantum computers are a solution to the problem that non-linear differential equations are chaotic (as in: tiny changes in initial conditions lead to vastly different solutions).&lt;p&gt;My impression of quantum computers are they will allow us to get to solutions to algorithmic problems &lt;i&gt;faster&lt;/i&gt;.&lt;p&gt;I fail to see how they could possibly work around the chaos inherent to some diffeqs (e.g. N-body problems).&lt;p&gt;[edit]:and after reading the article more carefully, I&amp;#x27;m still not sure how QC has &lt;i&gt;any&lt;/i&gt; effect on the chaotic nature of non-linear diffeqs . All I see in here is that they&amp;#x27;re trying to map non-linear diffeqs to linear systems via approximations so they  can run it on a QC.</text></item></parent_chain><comment><author>marius_k</author><text>I am not sure if this is related but during the past year I noticed few articles describing about how quantum systems are immune to butterfly effect [0]. I can&amp;#x27;t tell more details as those articles are still on my backlog.&lt;p&gt;[0] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;news.ycombinator.com&amp;#x2F;item?id=24167691&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;news.ycombinator.com&amp;#x2F;item?id=24167691&lt;/a&gt;</text></comment>