Quantum circuit lower bounds in the magic hierarchy<\/p>\n
Natalie Parham |\u00a0 Columbia University<\/p>\n
In this talk I\u2019ll introduce the magic hierarchy, a quantum circuit model alternating between arbitrary Clifford circuits and constant-depth circuits with two-qubit gates (QNC0). This framework unifies several existing models, including those with adaptive measurements. I\u2019ll present new lower bounds at the first level of the hierarchy and explain how extending these bounds above a certain level would imply major breakthroughs in classical complexity theory\u2014making the hierarchy a natural testing ground for lower bound techniques.<\/p>\n
In particular, I\u2019ll show that certain explicit quantum states\u2014such as ground states of topological Hamiltonians and non-stabilizer codes\u2014cannot be approximately prepared by a Clifford circuit followed by QNC0. These proofs go beyond standard light cone arguments and reveal an infectiousness property: approximating even one state in a high-distance code forces the entire code space to lie near a perturbed stabilizer code. Based on this paper: Quantum circuit lower bounds in the magic hierarchy<\/a><\/p>\n Location<\/p>\n","protected":false},"excerpt":{"rendered":"Quantum circuit lower bounds in the magic hierarchy Natalie Parham |\u00a0 Columbia University In this talk I\u2019ll introduce…\n","protected":false},"author":2,"featured_media":5161,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46],"tags":[191,74],"class_list":{"0":"post-5160","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-computing","8":"tag-computing","9":"tag-technology"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/5160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/comments?post=5160"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/5160\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media\/5161"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media?parent=5160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/categories?post=5160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/tags?post=5160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}