BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anirudh Krishna (Stanford University) DTSTART:20211028T000000Z DTEND:20211028T010000Z DTSTAMP:20260423T010336Z UID:UTSQSI/36 DESCRIPTION:Title: Abstract and physical constraints on quantum LDPC codes\nby Anirudh Kr ishna (Stanford University) as part of Centre for Quantum Software and Inf ormation Seminar Series\n\n\nAbstract\nDATE: 28 October\, 2021\nTIME: 11:0 0 am – 12:00 pm AEDT (Local Sydney time)\nTITLE: Abstract and physical c onstraints on quantum LDPC codes\nTOPIC: Quantum error correction\n\nSPEAK ER: Dr Anirudh Krishna\nAFFILIATION: Stanford University\, California\, US A\n\nABSTRACT:\nSeminal results by Bravyi\, Poulin and Terhal have shown t hat quantum codes are limited by locality. As a consequence\, all topologi cal codes witness sharp tradeoffs between their rate and distance. Quantum LDPC codes can be viewed as a generalization of topological codes constru cted using spatially-nonlocal connections. It is unclear what\, if any\, f undamental constraints these codes obey. The state-of-the-art code paramet ers are far from what their classical counterparts can achieve. We explore this question and present no-go results that shed some light on what is n ot possible.\n\nWe approach this question in two ways\, using abstract and physical constraints. First\, we use a graph-theoretic representation of a quantum code to show that the connectivity of this representation allows us to understand limitations of the associated code. We obtain generaliza tions of the Bravyi-Poulin-Terhal and Bravyi-Koenig bounds. We then study the complementary problem of embedding a code in D Euclidean dimensions. W e ask how many long-range interactions we need to obtain a target code dim ension k and distance d. Focusing on 2 dimensions (and ignoring polylogart hmic corrections)\, we find that a code with distance d requires Ω(d) int eractions of length Ω(d/√n). Furthermore\, a constant-rate code distanc e d requires Ω(n) interactions of length Ω(√d).\n\nThis is joint work with Nouédyn Baspin. It is based on the papers arXiv: 2106.00765 (https:/ /arxiv.org/abs/2106.00765) and arXiv: 2109.10982 (https://arxiv.org/abs/21 09.10982)\n\nTo request the zoom link\, please send a message cqsiadmin@ut s.edu.au using your business/organisation/institution email address.\n LOCATION:https://researchseminars.org/talk/UTSQSI/36/ END:VEVENT END:VCALENDAR