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clarified language on math thesis post
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@@ -221,7 +221,7 @@ <h2>Projects</h2>
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<img src="images/hologram.png" alt="Project 2 Image" class="project-image">
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<figcaption class="project-figcaption">a) and b) demonstrate the AdS/CFT correspondence: a) shows a system of two clouds of quantum particles, which are made to interact as a another particle (pink arrow) is injected into the system (conformal field theory); b) shows a system holographically dual system in a gravitation setting (AdS), in which the event horizons of two black holes are connected by an Einstein-Rosen bridge, which a particle traverses.</figcaption>
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<p class="project-description">For my math senior thesis with Professor Ami Radunskaya of Pomona College, we are working on a method to decompose unitaries as quantum circuits, via a combination of variation autoencoder (VAE), transformer, and custom gradient descent. As an application, we are simulating Sachdev-Ye-Kitaev Hamiltonians, which describe how a cloud of Majorana fermions. Inspired by Jafferis et al. 2022's simulation of quantum teleportation in this system of two of these clouds (which are dual in a gravitational system by the AdS-CFT correspondence to wormhole teleportation) but eager to address Kobrin et al. (2023)'s concerns over operator overfitting, we are developing a new training procedure and ML architecture in order to preserve scrambling dynamics while sparsifying the SYK Hamiltonians that describe the evolution of the system. I am pursuing a generalized algorithm to approximate unitaries with 2-qubit gates.</p>
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<p class="project-description">For my math senior thesis with Professor Ami Radunskaya of Pomona College, we are working on a method to decompose unitaries as quantum circuits using the fundamental gate set {Rx, Ry, Rz, P, CNOT}, via a combination of variation autoencoder (VAE), transformer, and custom gradient descent. As an application, we are simulating Sachdev-Ye-Kitaev Hamiltonians, which describe how a cloud of Majorana fermions. Inspired by Jafferis et al. 2022's simulation of quantum teleportation in this system of two of these clouds (which are dual in a gravitational system by the AdS-CFT correspondence to wormhole teleportation) but eager to address Kobrin et al. (2023)'s concerns over operator overfitting, we are developing a new training procedure and ML architecture in order to preserve scrambling dynamics while sparsifying the SYK Hamiltonians that describe the evolution of the system.</p>
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