<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=Windows-1252">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:"Book Antiqua";
panose-1:2 4 6 2 5 3 5 3 3 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-ligatures:standardcontextual;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:#0563C1;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri",sans-serif;
color:windowtext;}
p.Default, li.Default, div.Default
{mso-style-name:Default;
margin:0in;
text-autospace:none;
font-size:12.0pt;
font-family:"Times New Roman",serif;
color:black;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri",sans-serif;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="EN-US" link="#0563C1" vlink="#954F72" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal" align="center" style="text-align:center"><a name="_Hlk78975152"><img width="624" height="189" style="width:6.5in;height:1.9687in" id="Picture_x0020_2" src="cid:image004.png@01D9DFE9.ED045B40"><o:p></o:p></a></p>
<p class="Default"><span style="mso-bookmark:_Hlk78975152"><o:p> </o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="mso-bookmark:_Hlk78975152"><b><span style="font-size:28.0pt;font-family:"Times New Roman",serif;color:#006FC0">Public Dissertation Defense</span></b></span><span style="mso-bookmark:_Hlk78975152"><b><span style="font-size:22.0pt;font-family:"Times New Roman",serif;color:#006FC0"><br>
</span></b></span><span style="mso-bookmark:_Hlk78975152"><i><span style="font-size:24.0pt;font-family:"Times New Roman",serif">Accelerating the Quantum Optimal Control
<o:p></o:p></span></i></span></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="mso-bookmark:_Hlk78975152"><i><span style="font-size:24.0pt;font-family:"Times New Roman",serif">of Multi-Qubit Systems With Symmetry-Based Hamiltonian Transformations<o:p></o:p></span></i></span></p>
<p class="MsoNormal" align="center" style="text-align:center"><span style="mso-bookmark:_Hlk78975152"><b><i><span style="font-size:26.0pt;font-family:"Times New Roman",serif"><br>
</span></i></b></span><span style="mso-bookmark:_Hlk78975152"><b><i><span style="font-size:28.0pt;font-family:"Times New Roman",serif">Xian Wang</span></i></b></span><span style="mso-bookmark:_Hlk78975152"><b><i><span style="font-size:26.0pt;font-family:"Times New Roman",serif"><br>
</span></i></b></span><span style="mso-bookmark:_Hlk78975152"><span style="font-size:16.0pt;font-family:"Times New Roman",serif">University of California, Riverside<o:p></o:p></span></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="mso-bookmark:_Hlk78975152"><b><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black;background:white">Abstract:
</span></b>I developed a computationally efficient framework for accelerating the quantum optimal control of various multi-qubit systems. This framework decomposes the Hilbert space of the multi-qubit system and enables unitary transformations of the Hamiltonians
based on the symmetry of finite groups. The Hamiltonians are block diagonalized after transformation, which features a natural structure for computing these blocks in parallel. Specifically, the size of the Hamiltonians of an
<i>n</i>-qubit system is reduced from 2^<i>n</i> × 2^<i>n</i> to <i>O</i>(<i>n</i> ×
<i>n</i>) or <i>O</i>(2^<i>n</i> / <i>n</i> × 2^<i>n</i> / <i>n</i>) under <i>S</i></span><span style="mso-bookmark:_Hlk78975152"><i><span style="font-size:7.5pt">n</span></i> symmetry or
<i>D</i></span><span style="mso-bookmark:_Hlk78975152"><i><span style="font-size:7.5pt">n</span></i> symmetry, respectively. This approach reduces the execution time of quantum optimal control by orders of magnitude while the accuracy of the output is not affected.
Lie-Trotter-Suzuki decomposition generalizes this symmetry-based approach to a more general variety of multi-qubit systems. Based on the symmetry-induced decomposition of the Hilbert space, I propose the concept of symmetry-protected subspaces, which are potential
platforms for preparing commonly used symmetric states, realizing simultaneous gate operations, quantum error suppression, and simulation of other quantum systems. A perspective on ladder operators and selection rules is provided to facilitate the understanding
of the transformation of the Hamiltonians. I provide the Python source code for the quantum optimal control framework and the symmetry-based methods.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-bookmark:_Hlk78975152"><b><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"><o:p> </o:p></span></b></span></p>
<p class="Default" align="center" style="text-align:center"><span style="mso-bookmark:_Hlk78975152"><b><span style="font-size:16.0pt;color:#2F5496">Wednesday, September 6, 2023
<o:p></o:p></span></b></span></p>
<p class="Default" align="center" style="text-align:center"><span style="mso-bookmark:_Hlk78975152"><b><span style="font-size:16.0pt;color:#2F5496">10:00am Via Zoom meeting<o:p></o:p></span></b></span></p>
<p class="MsoNormal" align="center" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-align:center">
<span style="mso-bookmark:_Hlk78975152"><span style="color:#500050">Join Zoom Meeting<br>
</span></span><a href="https://ucr.zoom.us/j/4840109559" target="_blank"><span style="mso-bookmark:_Hlk78975152">https://ucr.zoom.us/j/4840109559</span><span style="mso-bookmark:_Hlk78975152"></span></a><span style="mso-bookmark:_Hlk78975152"><span style="color:#500050"><br>
Meeting ID: 484 010 9559</span></span><span style="mso-bookmark:_Hlk78975152"></span><b><span style="font-size:16.0pt;color:#2F5496"><o:p></o:p></span></b></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Book Antiqua",serif;color:#2E74B5;mso-ligatures:none">Kind regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Book Antiqua",serif;color:#2E74B5;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Book Antiqua",serif;color:#2E74B5;mso-ligatures:none">Jennifer Reising</span><span style="mso-ligatures:none"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Book Antiqua",serif;color:#2E74B5;mso-ligatures:none">Financial Services Supervisor</span><span style="mso-ligatures:none"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black;mso-ligatures:none">UC Riverside<b> |</b> Physics & Astronomy
</span><span style="mso-ligatures:none"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black;mso-ligatures:none">3047 Physics Building
<b>|</b> Riverside, California 92521</span><span style="mso-ligatures:none"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black;mso-ligatures:none">Office: 951.827.5033
<b>|</b> </span><u><span style="color:#0563C1;mso-ligatures:none"><a href="mailto:jreising@ucr.edu"><span style="color:#0563C1">jreising@ucr.edu</span></a></span></u><span style="color:black;mso-ligatures:none">
</span><i><span style="font-size:10.0pt;font-family:"Arial",sans-serif;color:#1F3864;mso-ligatures:none"> </span></i><span style="font-size:10.0pt;font-family:"Arial",sans-serif;mso-ligatures:none"><o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:#4472C4;background:silver;mso-highlight:silver;mso-ligatures:none">In-person office hours: Monday, Wednesday & Thursday from 8:00 am – 5:00 pm</span></b><span style="font-size:10.0pt;color:#4472C4;background:silver;mso-highlight:silver;mso-ligatures:none"><o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="color:#4472C4;background:silver;mso-highlight:silver;mso-ligatures:none">Virtual office hours: Tuesday & Friday from 8:00 am – 5:00 pm</span></b><span style="font-size:10.0pt;color:#4472C4;mso-ligatures:none"><o:p></o:p></span></p>
<p class="MsoNormal"><img border="0" width="187" height="28" style="width:1.9479in;height:.2916in" id="Picture_x0020_1" src="cid:image003.png@01D9DFE9.B2C80FD0"><span style="mso-ligatures:none"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</body>
</html>