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This is an announcement of Tushant Mittal's MS Presentation.<br class="">
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Candidate: Tushant Mittal<br class="">
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Date: Friday, November 12, 2021<br class="">
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Time: 2 pm CST
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<div class="">Remote Location: <span style="font-family: Arial, Helvetica, sans-serif; font-size: small;" class=""> </span><a href="https://urldefense.com/v3/__https://www.google.com/url?q=https:**Auchicago.zoom.us*j*96010336255*pwd*3DT0xCSzh1Y1RQZ1R4L1JEdzlWc21sQT09&sa=D&source=calendar&ust=1635885994819089&usg=AOvVaw35QXdU7zU3eS1mO6uPUxMN__;Ly8vLz8l!!BpyFHLRN4TMTrA!v4DcMXcR4Wg5n3Qn4ckGxtQttcEae-LEildPTvREczXdEcZUbhhgcAXwXuxnIyP_TaD3qx8z$" class="">https://uchicago.zoom.us/j/96010336255?pwd=T0xCSzh1Y1RQZ1R4L1JEdzlWc21sQT09</a></div>
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<div class=""><span class="gmail-JtukPc"><b class="">Title</b>: </span><span class="">Quantum LDPC codes: An exposition of recent product constructions</span></div>
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</span><span class=""><b class="">Abstract</b>: LDPC CSS codes is a class of quantum error correcting codes, and a highly sought-after goal is to construct such codes with distance as close to the number of qubits, N, as possible.<br class="">
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Until recently, the largest distance was slightly better than <img alt="\sqrt{N}" title="\sqrt{N}" class="va_li" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Csqrt{N}" id="l0.9288972880953006" height="16" width="27" style="font-family: Arial, Helvetica, sans-serif; display: inline; vertical-align: -2px;"> but
this has been improved significantly by many constructions based on tensor product and its modifications. In 2020, Evra, Kaufman and Zemor constructed codes of distance <img alt="\sqrt{N \log N}" title="\sqrt{N \log N}" class="va_li" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Csqrt{N%09%5Clog%09N}" id="l0.7432747509491562" height="16" width="68" style="font-family: Arial, Helvetica, sans-serif; display: inline; vertical-align: -3.667px;"> using
tensor products. This was improved by Kaufman and Tessler to <img alt="\sqrt{N} \log^k N" title="\sqrt{N} \log^k N" class="va_li" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Csqrt{N}%09%5Clog%5Ek%09N" id="l0.6325041504934885" height="18" width="75" style="font-family: Arial, Helvetica, sans-serif; display: inline; vertical-align: -3.667px;"> for
any <img alt="k" title="k" class="va_li" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=k" id="l0.14213830013494788" height="11" width="7" style="font-family: Arial, Helvetica, sans-serif; display: inline; vertical-align: -0.333px;">.
Hastings, Haah and O'Donnell gave a construction based on a "twisted tensor product" which achieved a distance <img alt="N^{3/5}/\mathrm{polylog}(N)" title="N^{3/5}/\mathrm{polylog}(N)" class="va_li" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=N%5E{3/5}/%5Cmathrm{polylog}(N)" id="l0.9951716519118885" height="18" width="118" style="font-family: Arial, Helvetica, sans-serif; display: inline; vertical-align: -4px;">.
Panteleev and Kalachev defined a "lifted product'' leading to an almost linear distance of <img alt="N/\log N" title="N/\log N" class="va_li" src="https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=N/%5Clog%09N" id="l0.3141080787349002" height="16" width="61" style="font-family: Arial, Helvetica, sans-serif; display: inline; vertical-align: -4.333px;">.
Breuckmann and Eberhardt unified and generalized these constructions by providing an abstract framework.<br class="">
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In this talk, we will survey these results focusing primarily on the property of distance. We will also briefly discuss connections to other areas and related open problems. The talk will be introductory and self-contained and no background in quantum computation
is assumed (or needed). <br class="">
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<div class=""><span class="gmail-JtukPc"><b class="">Advisors: </b>Janos Simon and Madhur Tulsiani</span></div>
<div class=""><span class="gmail-JtukPc"><b class="">Committee Members: </b><span class="">Janos Simon, Madhur Tulsiani, and Bill Fefferman</span></span></div>
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