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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">This is an announcement of Danylo Lykov's Candidacy Exam.</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">===============================================</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Candidate: Danylo Lykov</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Date: Tuesday, May 28, 2024</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Time: 2 pm CT</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Location: JCL 298</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Title: Large-scale Tensor Network contractions for quantum algorithms</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Abstract: "Tensor networks allow to model probabilistic processes over many variables. Quantum computing is built on using complex numbers in place of conventional
probability, which is an easy change to add to tensor networks. Despite the availability of efficient tools for physics simulations, simulating quantum circuits presents unique challenges, which I address in this work, specifically using the Quantum Approximate
Optimization Algorithm (QAOA) as an example.</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">In this work I start by delving into two basic steps of using TNs for quantum simulation: creating a TN from quantum circuit and efficiently computing inference
from (contracting) a TN. Both steps have interesting optimizations that allow for orders of magnitude cost reduction. This also includes discussion on how to contract TNs on GPUs.</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Tensor networks give a particular advantage for some special cases of quantum simulations, which involve calculating expectation values for shallow circuits.
This allowed me to use TN simulations to study performance of QAOA and compare it against classical counterparts.</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Finally, I examine various methods to reduce the memory footprint of simulations at the expense of simulation quality. These methods can simulate larger circuits
but depend not only on the circuit connectivity, but on the gate parameters. As quantum circuit complexity increases, continued simulation efforts will inevitably require some compromise in quality."</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Advisors: Fred Chong, Yuri Alexeev</span><br style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">
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<span style="font-family: Calibri, Helvetica, sans-serif; font-size: 14.666666984558105px;" class="">Committee Members: Fred Chong, Yuri Alexeev, and Robert Rand</span><br class="">
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