Renormalized Out of Time Order Correlator (2025)
This is work with Tianci Zhou and Brian Swingle, where we introduce the renormalized out‑of‑time‑order correlator (ROTOC) as a noise‑resilient probe of quantum scrambling. Working within an all‑to‑all Brownian‑circuit model of N qubits, we derive a closed set of N nonlinear rate equations that govern how operator weight flows when the “forward” and “backward” evolution branches are allowed to differ (correlation r < 1) and when depolarizing decoherence acts at rate κ. This weight‑space formulation collapses an intractable 4^N‑dimensional problem to O(N) variables and admits exact solutions in the thermodynamic “dilute” limit. For a single‑site probe (w₀ = 1), we obtain the compact analytic formula
showing that early‑time exponential growth retains the unperturbed Lyapunov rate while depolarization is only a well defined rescale in time.
Beyond the exact solution, we uncover metastable plateaus for initial operators of weight w₀ > 1, whose lifetimes scale logarithmically as ∼ ln(N/ w₀), and suggest that, in our model, the “localization‑delocalization” transitions reported in nuclear‑spin experiments are likely finite‑time crossovers rather than true phase transitions. Numerical integrations up to N ≈ 10³ validate the analytic predictions. The framework therefore supplies both a scalable diagnostic for imperfect quantum simulators and a benchmark for interpreting future scrambling measurements subjected to decoherence and control errors.
Beyond the exact solution, we uncover metastable plateaus for initial operators of weight w₀ > 1, whose lifetimes scale logarithmically as ∼ ln(N/ w₀), and suggest that, in our model, the “localization‑delocalization” transitions reported in nuclear‑spin experiments are likely finite‑time crossovers rather than true phase transitions. Numerical integrations up to N ≈ 10³ validate the analytic predictions. The framework therefore supplies both a scalable diagnostic for imperfect quantum simulators and a benchmark for interpreting future scrambling measurements subjected to decoherence and control errors.
- Paper: Scrambling Dynamics with Imperfections in a Solvable Model (2025), arxiv: 2505.00070
- Poster: as seen at QSim 2025
Past Research
Holographic Duality with Random Tensor Network (2022, Senior Thesis)
Under the supervision of Dr. Xi Dong, I offer a self‑contained tour of how Random Tensor Network (RTN) models capture holographic entanglement. After motivating the Ryu–Takayanagi prescription from AdS/CFT, the thesis walks through Hayden’s RTN construction, derives the mapping of the second Rényi entropy to a classical Ising partition function, and explains how the min‑cut in the network reproduces the RT area law. Detailed derivations highlight the role of large bond dimension D and replica‑trick techniques, providing readers with a step‑by‑step bridge from quantum information concepts to gravitational entanglement formulas.
Complementing the theory, the work implements numerical simulations—written in Mathematica—to compute Rényi entropies for single- and multi-interval boundary regions. The results verify the expected Page‑curve crossover and confirm the logD ∣γA∣ scaling in the large D limit, while also exploring how finite D corrections distort the area law. A final chapter surveys open problems such as bulk quantum corrections and time‑dependent generalizations, positioning the thesis as both a concise reference and a ready‑to‑run code base for students entering the field of holographic tensor networks.
Complementing the theory, the work implements numerical simulations—written in Mathematica—to compute Rényi entropies for single- and multi-interval boundary regions. The results verify the expected Page‑curve crossover and confirm the logD ∣γA∣ scaling in the large D limit, while also exploring how finite D corrections distort the area law. A final chapter surveys open problems such as bulk quantum corrections and time‑dependent generalizations, positioning the thesis as both a concise reference and a ready‑to‑run code base for students entering the field of holographic tensor networks.
Magnetic Field Insensitive Radio-Frequency Dressed Qubits (2019)
Under mentorship of Dr. Mingyu Fan and Dr. Andrew Jayich, we reproduced earlier demonstrations that radio‑frequency bichromatic dressing can render a qubit in 87Sr+ insensitive to first‑order magnetic‑field fluctuations. By applying counterrotating 1 MHz, 2 G RF fields and using the rotating‑wave approximation to analyze the Zeeman‑split ground state manifold, we verified the predicted “sweet‑spot” transition whose frequency stays nearly constant over a tens‑of‑gauss range, thereby suppressing dephasing and extending coherence without cryogenic shielding. The poster summarizes the replicated theoretical model, our measurement protocol, and planned steps toward high‑fidelity microwave gates on the dressed qubit, underscoring the technique’s practicality for robust trapped‑ion quantum processors.
Temperatures of the Galilean Satellites (2018)
Under mentorship of Dr. Samantha Trumbo and Dr. Michael E Brown, using Galileo’s long‑overlooked Photopolarimeter‑Radiometer data, this study reconstructs temperature maps for Europa, Ganymede, and Callisto to extract two key surface parameters: bolometric albedo and thermal inertia. A global thermal‑diffusion model—driven by Voyager‑derived albedo maps and spacecraft geometry—was iterated until steady state, then tuned locally by sweeping thermal‑inertia values to best match more than 20 000 individual PPR footprints. The approach resolves day‑night contrasts, eclipse cooling rates, and kilometer‑scale features with higher fidelity than earlier one‑ or two‑layer models.
The resulting thermal‑inertia map of Ganymede reveals crater‑centric “cold traps” and regolith clusters, while eclipse data isolate a low‑inertia belt that earlier models missed. Residual analyses also expose striping artefacts—warm bands aligned with Jupiter’s limb—attributed to Jovian infrared contamination, and refute two putative hotspots on Europa as processing artefacts rather than cryovolcanoes. These diagnostics refine landing‑site selection for missions such as Europa Clipper and provide a template for mining legacy spacecraft archives to identify thermophysical anomalies on other icy worlds.
The resulting thermal‑inertia map of Ganymede reveals crater‑centric “cold traps” and regolith clusters, while eclipse data isolate a low‑inertia belt that earlier models missed. Residual analyses also expose striping artefacts—warm bands aligned with Jupiter’s limb—attributed to Jovian infrared contamination, and refute two putative hotspots on Europa as processing artefacts rather than cryovolcanoes. These diagnostics refine landing‑site selection for missions such as Europa Clipper and provide a template for mining legacy spacecraft archives to identify thermophysical anomalies on other icy worlds.
Orbit Determination for Near-Earth Asteroid (2016)
Together with Elisa Zhao and Hernan Valles, under supervision of Dr. Cassandra Fallscheer and Dr. Michael Dubson, we determined the orbit of the potentially hazardous near‑Earth asteroid 40329 (1999 ML) during the 2016 Summer Science Program. Using a 16‑inch telescope at CU Boulder’s Sommers‑Bausch Observatory, we acquired time‑spaced CCD images, extracted precise centroids for the asteroid and six reference stars, and applied least‑squares plate reduction to obtain astrometric positions. Three‑epoch Gauss orbit determination—iterated with Gaussian‑day timing corrections—yielded heliocentric state vectors, from which we derived orbital elements (a = 2.28 AU, e = 0.456, i = 2.52°) that agree with JPL Horizons to <1 % across all elements.
Monte‑carlo propagation shows the asteroid’s path remains exterior to Earth’s orbit, intersecting Mars but posing negligible terrestrial impact probability for millennia. Our analysis also quantifies sources of observational error—CCD light‑leak artifacts and ephemeris frame mismatches—and demonstrates that evenly spaced observations are not strictly required for sub‑percent precision with Gauss’ method. The workflow and diagnostic checks presented here serve as a template for student‑led orbit‑determination campaigns on faint NEOs.
Besides the Gauss's method, which utilizes topocentric coordinates, there is also the Laplace's method, which utilizes the geocentric coordinate. Both are good in calculating the preliminary orbit. One good review for such method can be found in this note.
Monte‑carlo propagation shows the asteroid’s path remains exterior to Earth’s orbit, intersecting Mars but posing negligible terrestrial impact probability for millennia. Our analysis also quantifies sources of observational error—CCD light‑leak artifacts and ephemeris frame mismatches—and demonstrates that evenly spaced observations are not strictly required for sub‑percent precision with Gauss’ method. The workflow and diagnostic checks presented here serve as a template for student‑led orbit‑determination campaigns on faint NEOs.
Besides the Gauss's method, which utilizes topocentric coordinates, there is also the Laplace's method, which utilizes the geocentric coordinate. Both are good in calculating the preliminary orbit. One good review for such method can be found in this note.
Trajectory Optimization for Laser-Propelled Spacecraft (2015)
Under mentorship of Dr. Qicheng Zhang and Dr. Philip Lubin, I devised an optimizer that refines orbital trajectories for laser‑sail spacecraft driven by the DE‑STAR directed‑energy array. The algorithm continuously recalculates when to shut off the laser so that the sail and beam reconnect at their resonance point, maximizing net propulsion strength received by the sail and solving a timing mismatch that previously produced chaotic variations in trip duration. By rotating both the sail and laser orbits into a common reference plane, computing mean anomalies, and looping over integer beam‑lag periods n to satisfy a Gauss‑like timing equation, the optimizer selects the launch‑dependent laser‑off moment that minimizes transit time.
Simulations show that for gram‑ to kilogram‑class payloads the optimizer lowers Earth‑escape transit times by 30–60 %, smooths the sensitivity to the launch date perturbations, and yields near‑exponential gains when laser power scales. Example calculations show 4.84σ, 2.01σ, and 8.98σ of trajectories for laser power of 1.93MW, 2MW, and 3MW respectively receive improvements in trip duration from the Low Earth Orbit to the Geosynchronous Earth Orbit. These results demonstrate a practical pathway to stabilize directed‑energy missions across arbitrary launch windows and highlight residual regimes where further statistical tuning could still enhance performance.
Simulations show that for gram‑ to kilogram‑class payloads the optimizer lowers Earth‑escape transit times by 30–60 %, smooths the sensitivity to the launch date perturbations, and yields near‑exponential gains when laser power scales. Example calculations show 4.84σ, 2.01σ, and 8.98σ of trajectories for laser power of 1.93MW, 2MW, and 3MW respectively receive improvements in trip duration from the Low Earth Orbit to the Geosynchronous Earth Orbit. These results demonstrate a practical pathway to stabilize directed‑energy missions across arbitrary launch windows and highlight residual regimes where further statistical tuning could still enhance performance.
Journal Club Slides
- This is basic intro to CFT, followed by other talks in the high energy journal club at UCSB leading into more important concepts and models in 2D CFT
- (2021) What the heck is CFT, Part I
- This is an overview of recent breakthroughs in black hole info paradox for a Society of Physics Student (SPS) talk at UCSB, in undergrad friendly languages
- This is a talk extended from my term paper on entropy and computational power of universe
Term Papers
- In this term paper, I reviewed the path integral derivation for the Ryu-Takayanagi formula with gravity in a box setup.
- (2021) Paper
- My term paper on the canonical formulation of general relativity for a class on quantum gravity path integral and black hole information.
- (2021) Presentation slides
- (2021) Paper
- I wrote this short paper on black hole accretion disk for the fluid dynamics class
- A review I wrote to explain motivation of "entropy", which turns out to carry profound connections to black hole thermodynamics, and how black holes can be the ultimate quantum computer.
- Here is one for the group theory class