{"id":920,"date":"2011-05-26T12:46:08","date_gmt":"2011-05-26T16:46:08","guid":{"rendered":"http:\/\/michaelnielsen.org\/blog\/?p=920"},"modified":"2011-05-26T12:53:28","modified_gmt":"2011-05-26T16:53:28","slug":"survey-notes-on-fermi-algebras-and-the-jordan-wigner-transform-now-on-github","status":"publish","type":"post","link":"https:\/\/michaelnielsen.org\/blog\/survey-notes-on-fermi-algebras-and-the-jordan-wigner-transform-now-on-github\/","title":{"rendered":"Survey notes on fermi algebras and the Jordan-Wigner transform now on GitHub"},"content":{"rendered":"

Continuing the theme of my last post<\/a>, I’ve now put my old survey notes<\/a> on fermi algebras and the Jordan-Wigner transform up on GitHub<\/a>.<\/p>\n

The Jordan-Wigner transform is an amazing tool. It let’s you move back and forth between two seemingly very different ways of describing a physical system, either as a collection of qubits, or as a collection of fermions. To give you an idea of the power of the Jordan-Wigner transform, in his famous 1982 paper on quantum computing<\/a>, Richard Feynman wrote the following:<\/p>\n

\ncould we [use a quantum computer to] imitate every quantum mechanical system which is discrete and has a finite number of degrees of freedom? I know, almost certainly, that we could do that for any quantum mechanical system which involves Bose particles. I’m not sure whether Fermi particles could be described by such a system. So I leave that open.\n<\/p><\/blockquote>\n

As shown in the notes, once you understand the Jordan-Wigner transform, the answer to Feynman’s question is obvious: yes, we can use quantum computers to simulate systems of fermions. The reason is that the Jordan-Wigner transforms lets us view the fermi system as a system of qubits which is easy to simulate using standard simulation techniques. Obviously, the point here isn’t that Feynman was silly: it’s that tools like the Jordan-Wigner transform can make formerly hard things very simple.<\/p>\n

The notes assume familiarity with elementary quantum mechanics, comfort with elementary linear algebr, and a little familiarity with the basic nomenclature of quantum information science (qubits, the Pauli matrices).<\/p>\n

I’m releasing the notes under a Creative Commons Attribution license (CC BY 3.0). That means anyone can copy, distribute, transmit and adapt\/remix the work, provided my contribution is attributed. The notes could be used, for example, to help flesh out Wikipedia’s article<\/a> about the Jordan-Wigner transform. Or perhaps they could usefully be adapted into course notes, or part of a review article.<\/p>\n","protected":false},"excerpt":{"rendered":"

Continuing the theme of my last post, I’ve now put my old survey notes on fermi algebras and the Jordan-Wigner transform up on GitHub. The Jordan-Wigner transform is an amazing tool. It let’s you move back and forth between two seemingly very different ways of describing a physical system, either as a collection of qubits,… Continue reading Survey notes on fermi algebras and the Jordan-Wigner transform now on GitHub<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-920","post","type-post","status-publish","format-standard","hentry","category-uncategorized","entry"],"_links":{"self":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts\/920","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/comments?post=920"}],"version-history":[{"count":5,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts\/920\/revisions"}],"predecessor-version":[{"id":924,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/posts\/920\/revisions\/924"}],"wp:attachment":[{"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/media?parent=920"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/categories?post=920"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/michaelnielsen.org\/blog\/wp-json\/wp\/v2\/tags?post=920"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}