My research interests can be broadly encapsulated in "How do we make quantum computers practically useful." To be more explicit, I am really interested in discovering the structures that prevent current quantum systems from being important/useful and attacking those bottlenecks. Naturally, the fields of Quantum error correction, systems for quantum computing, quantum algorithms, and dequantization are especially appealing to me. Below you can find some summaries on the research I have worked on so far.
2026
Coherent state preparation is necessary for learning various physical properties of a many-body ground state, including its correlation functions, dynamics and energy density. The quantum eigenvalue transformation of unitaries (QETU) algorithm targets this regime: through quantum signal processing (QSP), it prepares a ground state using only controlled time evolution and a single ancilla, leaving that state available for downstream observable measurement. However, the long shot experiments these measurements demand expose the computation to slow, time-dependent calibration drift, which perturbs the single-qubit rotations generated by the QSP phase factors.
Rather than interrupting the experiment for hardware recalibration, we correct this drift algorithmically and in flight with a feedforward estimator that exploits the structure of the QSP phase factors: it learns a sensor for the drift from cheap ancilla diagnostics, estimates the drift rate, and applies an open-loop phase correction whose overhead is small and amortizes away as the observable campaign lengthens. We derive a cost bound showing this overhead is independent of system size. Across the transverse-field Ising and critical XY models for upto 14 qubits, feedforward restores post-selected fidelity to drift-free ceiling across all system sizes, under a hardware-motivated coherent-drift benchmark.
This work is an ongoing collaborative research project in Prof. Murphy Niu's Lab and preliminary work was presented at the UCSB CS end-of-year research showcase.
2026
Quantum Signal Processing (QSP) is an algorithm that takes any target function f(x) and decomposes it into a quantum circuit that can exactly implement your desired f(x). In theory, QSP is an enormously useful framework with applications in quantum simulation or solving differential equations. But in practice, each element of your circuit is a physical operation on a quantum computer that is prone to all forms of error and hardware defects.
The basic premise of QSP is we can take any polynomial f(x) and decompose it as a series of unitary rotations controlled by a vector of phi angles that we colloquially call the phase factors. Interestingly, these phase factors are non-unique to a polynomial and recent years have introduced a plethora of methods on how to find these phase factors with various criterion on numerical stability or efficiency. Few studies have specifically analyzed these methods on their behavior under noise.
We develop a taxonomy on various methods for phase factor finding and their behavior under various noise models. We use perturbation theory and other techniques to present analytic models to predict the behavior of these phase factors.
This work was done as collaborative research project in Prof. Murphy Niu's Lab and was presented at the KITP conference on quantum advantage in the pre-fault-tolerant era.
2025
Simulating quantum circuits on classical computers is a game of what assumptions you hold. If you are interested in purely the theoretical ability of a quantum computer, then you simulate its behavior as though it were perfect. If you were interested in how a quantum computer would operate on near-term hardware, then you try to simulate some of the imperfections that a near-term device would face.
These imperfections are normally modeled as channels; CPTP maps that we can staple on each gate in the circuit, each acting independently of what came before. In this project, we go one step further and try simulating quantum circuits with memory, when those channels can no longer act independent of each other.
We introduce a framework for simulating these "non-Markovian" dynamics. The basic idea is to first compress our time-correlated dynamics into a matrix product operator, then inject each operation of our ideal quantum circuit into the evolution of those dynamics; effectively modeling a quantum circuit with non-markovian noise.
This work was done as a final project for a course on Tensor Computation
2025
One of the touted advantages of Quantum Computers is its ability to provide 'true randomness,' an output that is completely independent of what came before it. True randomness has a lot of real applications in cryptographic schemes. But if I were to give you a set of random numbers and claim that a quantum computer generated these, how would you know?
This requires the need for protocols that can verify the "quantumness" of a random output; a 'proof of quantumness.' Most protocols can be broken down as: I design a quantum circuit and send it to you to run on your supposed quantum device. You send me back the outputs, and if those outputs carry the expected statistical signature that my circuit produces AND no classical computer can fake that signature in reasonable time, I accept that you have a quantum device.
While the idea might seem simple enough, figuring what the expected statistical signature of a circuit can itself be a classically hard computation, and if not careful, the verification can cost as much as the thing being verified. With this premise, for my course project, I studied one family of quantum circuits that was designed to be both efficient and with a protocol for learning the signature; the Instantaneous Quantum Polynomial (IQP) circuit.
This project was done as a final report for a course on Post-Quantum Cryptography.