<div dir="ltr"><div style="font-family:Calibri,Arial,Helvetica,sans-serif"><span style="font-family:Arial,Helvetica,sans-serif;font-size:large">******************************</span><span style="font-family:Arial,Helvetica,sans-serif;font-size:large">******************************</span><span style="font-family:Arial,Helvetica,sans-serif;font-size:large">**************************</span><b style="font-family:inherit;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;color:rgb(49,49,49);word-spacing:1px"><font size="4"><br></font></b></div><div style="font-family:Calibri,Arial,Helvetica,sans-serif"><b style="font-family:inherit;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;color:rgb(49,49,49);word-spacing:1px"><font size="4"><br></font></b></div><div style="font-family:Calibri,Arial,Helvetica,sans-serif"><b style="font-family:inherit;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;color:rgb(49,49,49);word-spacing:1px"><font size="4">Date</font></b><b style="font-family:inherit;font-style:inherit;font-variant-ligatures:inherit;font-variant-caps:inherit;font-size:1.13em;color:rgb(49,49,49);word-spacing:1px">:</b><span style="font-size:1.13em;color:rgb(49,49,49);word-spacing:1px"> </span><span style="color:rgb(49,49,49);word-spacing:1px"><font size="4">October 26, 2022</font></span><br></div><div><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="margin:0px"><div style="color:rgb(32,31,30);margin:0px"><div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;margin:0px;color:rgb(49,49,49);word-spacing:1px"><font style="font-size:1.13em"><b>Time: </b>12:30pm CT</font></div><div style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;margin:0px;color:rgb(49,49,49);word-spacing:1px"><font style="font-size:1.13em"><b>Location: </b>JCL 298</font></div><div dir="auto" style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;margin:0px;color:rgb(49,49,49);word-spacing:1px"><b><font style="font-size:1.13em"><br></font></b></div><div dir="auto" style="margin:0px;color:rgb(49,49,49);word-spacing:1px"><font size="4"><font face="Calibri, Arial, Helvetica, sans-serif" style="font-weight:bold">Speaker: </font><font style="" face="Arial"><a href="https://vishnuiyer.org/">Vishnu Iyer</a></font></font></div><div dir="auto" style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;margin:0px;color:rgb(49,49,49);word-spacing:1px"><font size="4"><br></font></div></div><div style="margin:0px"><span style="color:rgb(49,49,49);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:16px;word-spacing:1px"><font style="font-size:1.13em"><b>Title: </b></font></span><font size="4">Low-Stabilizer-Complexity Quantum States Are Not Pseudorandom</font></div><div style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:15px;margin:0px"><b style="color:rgb(49,49,49);font-size:16px;word-spacing:1px"><font style="font-size:1.13em"><br></font></b></div><div style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:15px;margin:0px"><span style="margin:0px;font-size:16px;color:rgb(49,49,49);word-spacing:1px"><font style="font-size:1.13em"><b>Zoom: </b>[<a href="https://uchicago.zoom.us/j/98326935804?pwd=ZFJGYUNXb2dkTFFQNWllM1JybUJwUT09">link</a>]</font></span></div><div style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:15px;margin:0px"><br></div><div style="margin:0px"><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="color:rgb(49,49,49);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:13pt;margin:0px"><b>Abstract:</b></span><span style="color:rgb(32,31,30);font-family:"trebuchet ms",sans-serif;font-size:12pt;margin:0px;word-spacing:0px"> </span></font><font size="4">We show that quantum states with "low stabilizer complexity" can be efficiently distinguished from Haar-random. Specifically, given an $n$-qubit pure state $\lvert \psi \rangle$, we give an efficient algorithm that distinguishes whether $\lvert \psi \rangle$ is (i) Haar-random or (ii) a state with stabilizer fidelity at least $\frac{1}{k}$ (i.e., has fidelity at least $\frac{1}{k}$ with some stabilizer state), promised that one of these is the case. With black-box access to $\lvert \psi \rangle$, our algorithm uses $O \big( k^{12} \cdot \log(1/\delta) \big)$ copies of $\lvert \psi \\rangle$ and $O\big( nk^{12} \cdot \log (1/\\delta) \big)$ time to succeed with probability at least $1 - \delta$, and, with access to a state preparation unitary for $\lvert \psi \rangle$ (and its inverse), $O\big( k^{3} \cdot \\log(1/\delta) \big)$ queries and $O(nk^{3} \cdot \log(1/ \delta) \big)$ time suffice.<br><br>As a corollary, we prove that $\omega\big( \log(n) \big)$ $T$-gates are necessary for any $\mathsf{Clifford} + T$ circuit to prepare computationally pseudorandom quantum states, a first-of-its-kind lower bound.<br><br>Based on <a href="https://arxiv.org/abs/2209.14530">https://arxiv.org/abs/2209.14530</a></font></div><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="margin:0px;word-spacing:0px"><font size="4"><br></font></span></font></div><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="margin:0px;word-spacing:0px"><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large">[</span><a href="https://urldefense.com/v3/__https://orecchia.net/event/theory-lunch/__;!!BpyFHLRN4TMTrA!pwdRh9yLA-IBD6NCNvREJGd9Nj5jtC6_N-AowF6HSwIQeb1FPAmu0L_tAswwp_F5nRs$" rel="noopener noreferrer" title="https://orecchia.net/event/theory-lunch/" target="_blank" style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large;margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px">Theory</span></span></span></span></span> <span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px">Lunch</span></span></span></span> Webpage</a><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large">]</span><br style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large"><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large">[</span><a href="https://urldefense.com/v3/__https://calendar.google.com/calendar/u/0/embed?src=c_osgf1c1qemdras8mu7l7pdhjrs@group.calendar.google.com&ctz=America*Chicago__;Lw!!BpyFHLRN4TMTrA!pwdRh9yLA-IBD6NCNvREJGd9Nj5jtC6_N-AowF6HSwIQeb1FPAmu0L_tAsww4XtIRnQ$" rel="noopener noreferrer" title="https://calendar.google.com/calendar/u/0/embed?src=c_osgf1c1qemdras8mu7l7pdhjrs@group.calendar.google.com&ctz=America/Chicago" target="_blank" style="font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large;margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px">Theory</span></span></span></span></span></span></span><span style="margin:0px"> </span><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px"><span style="margin:0px">Lunch</span></span></span></span></span><span style="margin:0px"> </span>Calendar</a><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large">]</span></span></font></div><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="margin:0px;word-spacing:0px"><span style="color:rgb(32,31,30);font-family:Calibri,Arial,Helvetica,sans-serif;font-size:large"><br></span></span></font></div><div dir="auto" style="margin:0px"><font style="word-spacing:1px"><span style="margin:0px;word-spacing:0px"><span style="font-size:large">******************************</span><span style="font-size:large">******************************</span><span style="font-size:large">**************************</span></span></font></div></div></div></div></div></div></div></div></div>