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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal>Umesh Vazirani from UC Berkeley<o:p></o:p></p><p class=MsoNormal>Monday, April 23, 2018 - 12:30pm<o:p></o:p></p><p class=MsoNormal>Computer Science - Room 105<o:p></o:p></p><p class=MsoNormal>Host: Sanjeev Arora <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>“Quantum Supremacy” and the Complexity of Random Circuit Sampling<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>A critical goal for the field of quantum computation is quantum supremacy -- a demonstration of any quantum computation that is prohibitively hard for classical computers. Besides dispelling any skepticism about the viability of quantum computers, quantum supremacy also provides a test of quantum theory in the realm of high complexity. A leading near-term candidate, put forth by the Google/UCSB team, is sampling from the probability distributions of randomly chosen quantum circuits, called Random Circuit Sampling (RCS).<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>While RCS was defined with experimental realization in mind (the first results are expected later this year), we give the first complexity-theoretic evidence of classical hardness of RCS, placing it on par with the best theoretical proposals for supremacy. Specifically, we show that RCS satisfies an average-case hardness condition -- computing output probabilities of typical quantum circuits is as hard as computing them in the worst-case, and therefore #P-hard. Our reduction exploits the polynomial structure in the output amplitudes of random quantum circuits, enabled by the Feynman path integral. We also describe a new verification measure which in some formal sense maximizes the information gained from experimental samples.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Based on joint work with Adam Bouland, Bill Fefferman and Chinmay Nirkhe.<o:p></o:p></p></div></body></html>