{"id":138423,"date":"2022-04-22T01:06:54","date_gmt":"2022-04-22T06:06:54","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2022\/04\/parallel-quantum-simulation-of-large-systems-on-small-nisq-computers"},"modified":"2022-04-22T01:06:54","modified_gmt":"2022-04-22T06:06:54","slug":"parallel-quantum-simulation-of-large-systems-on-small-nisq-computers","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2022\/04\/parallel-quantum-simulation-of-large-systems-on-small-nisq-computers","title":{"rendered":"Parallel quantum simulation of large systems on small NISQ computers"},"content":{"rendered":"

<\/a><\/p>\n

Basically all this says is that a basic quantum computer made of a simulation of an infinite quantum computer. So essentially infinite quantum computers could make the internet much more instant.<\/p>\n

\n

To parallelise our simulation on a small NISQ machine, we first identify partitions of the system where the effect of one partition upon the other can be summarised by a small amount of information. This is achieved by making Schmidt decompositions across the cut: \\(\\left|\\psi \\right\\rangle =\\mathopsum
olimits_alpha = 1Dlambda<\/sup> ^alpha \\left|phi _L^alpha \\right\\rangle \\left|phi _R^alpha \\right\\rangle,\\) where \\(\\left|phi _L^alpha \\right\\rangle\\) are an orthonormal set of states to the left of the cut and \\(\\left|phi _R^alpha \\right\\rangle\\) the same on the right. The \u03bb<\/i>\u03b1<\/i><\/sup> are known as the Schmidt coefficients and D<\/i> the Schmidt rank or bond order. Retaining \u03bb<\/i>\u03b1<\/i><\/sup> only above some threshold value provides a way to compress representations of a quantum state; the MPS construction can be obtained by applying this procedure sequentially along a spin chain4<\/a><\/sup>.<\/p>\n

If an observation is made on the right-hand-side of such a cut, the effect of the quantum state on the left upon the observation can be summarised by just D<\/i> variables corresponding to the Schmidt coefficients. This same effect can be achieved by an effective state on a spin chain of length \\(log\\,_2D\\) \u2014see Fig. 1 <\/a>\u2014which can be parametrised on the quantum circuit by an S<\/i>U <\/i>(D<\/i>2<\/sup>) unitary V<\/i>L<\/i><\/sub>. This encodes both the Schmidt coefficients \u03bb<\/i>\u03b1<\/i><\/sub> and the orthonormal states \\(\\left|phi _L^alpha \\right\\rangle\\). The latter does not contribute to observables on the right and so in principle, V<\/i>L<\/i><\/sub> can be parametrised by just D<\/i> variational parameters. The precise numerical values must be determined by solving a quantum mechanical problem on the left of the system. Similarly, for observations made to the left of the cut, the effect of the right-hand side can be summarised by a unitary V<\/i>R<\/i><\/sub>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Basically all this says is that a basic quantum computer made of a simulation of an infinite quantum computer. So essentially infinite quantum computers could make the internet much more instant. To parallelise our simulation on a small NISQ machine, we first identify partitions of the system where the effect of one partition upon the [\u2026]<\/p>\n","protected":false},"author":513,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1523,418,1617],"tags":[],"class_list":["post-138423","post","type-post","status-publish","format-standard","hentry","category-computing","category-internet","category-quantum-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/138423","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/513"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=138423"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/138423\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=138423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=138423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=138423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}