Recently Updated Projects

This project investigates whether a simple quantum two-level system can provide an informative alternative to classical models of bull–bear regimes in financial markets. Standard regime-switching models treat the market as occupying one of two states, bull or bear, with fixed transition prob- abilities estimated from historical return data. Here, we instead model the market as an effective quantum two-state system with basis states Bull and Bear that evolve under a Hamiltonian gen- erating Rabi-like oscillations, supplemented by a tunable decoherence process that damps purely coherent behavior. Using daily price data from broad market indices, we will label returns as bull or bear using a transparent threshold rule, fit a classical two-state Markov chain as a baseline, and then construct and fit a quantum two-level model whose parameters are chosen to match empirical one-day and multi-day transition statistics.

External Mentor: Dr. Emil Polisensky, Naval Research Laboratory

The proposed research aims to detect a new class of astronomical objects known as Long Period Transients (LPT) using data collected by the Naval Research Laboratory’s Jansky Very Large Array (VLA) Low band Ionospheric and Transient Experiment (VLITE). VLITE receivers are currently installed on 18 of the 27 antennas on the VLA in New Mexico, detecting radio frequencies with a bandwidth of ~40 MHz centered at ~340 MHz while the VLA simultaneously collects data at higher wavelengths. As a result, VLITE gathers more than 6000 hours of imaging data each year, much of which remains relatively unprobed and in need of analysis. Because LPTs emit radio waves, VLITE is particularly well-suited for their detection. In fact, it has already found several of the 13 known LPTs, suggesting that further probing will yield additional candidates. Using VLITE source data, Bowen MacGillivray, Anavi Nellutla, Sarah Trainer, and Aarushi Kanigicherla under the direction of Dr. Emil Polisensky will filter images, clean up artifacts, and curate a list of potential LPT objects for manual review. Our hypothesis is that several LPTs will be found in the VLITE data, as well as other objects that may be serendipitously discovered.

EXTERNAL MENTOR: Hunter Nelson, Virginia Tech Center for Quantum Information Science and Engineering

A common tool for simplifying driven two-level systems is the rotating wave approximation (RWA). It applies when the driving pulse is weak compared to the transition energy difference and has a frequency near it.

However, in some instances, it would be interesting to go beyond this assumption and account for more general driving regimes.

Can we use the SCQC framework to account for noise that is induced under the violation of the RWA assumption?

EXTERNAL MENTOR: Dr. Atul Mantri, Virginia Tech Center for Quantum Information Science and Engineering

Introduction

The proposed research aims to simulate Grover’s search to “attack” toy ciphers. The efficacy of this approach will be demonstrated by comparing it to a classical brute force approach, which is significantly slower than quantum approaches. Grover’s algorithm provides a quadratic speedup compared to classical search algorithms. However, Simon’s algorithm offers an exponential speedup compared to classical algorithms, and its application can be used to further optimize encryption and decryption time efficiencies.

Intellectual Merit

The intellectual merit of this research is rooted in previous research surrounding the Grover and Simon search algorithms. In a previous paper (Kuwakado & Morii, 2013), classical and quantum cryptography algorithms are tested on the Even-Mansour Cipher (EM Cipher), a classical encryption cipher. This cipher is secure if n is large, as it requires O(2N/4) time to break. However, the quantum version is insecure because a key can be recovered in polynomial time of the key length.

This quantum version takes n qubits as plaintext and outputs n qubits as ciphertext. The cipher is represented by a unitary matrix, and using Grover’s algorithm, the cipher can be broken in O(2(N/2)) time, an improvement over the classical approach. However, the newly proposed algorithm in the paper, which is similar to Simon’s algorithm, is able to break the cipher in polynomial time (with the quantum time complexity being O(N) and the classical time complexity being O(N3)). This algorithm and paper demonstrates the advantage quantum cryptography approaches have over classical ones and provides an effective cryptography algorithm that is able to decrypt the EM Cipher exponentially faster than standard approaches.

Broader Impact

The broader impact of this research is preemptively discovering the power of quantum encryption and decryption algorithms, such as Grover’s algorithm and Simon’s algorithm. These algorithms can improve encryption and decryption efficiencies, offering quadratic and even exponential speedups compared to classical brute force algorithms. As a result, quantum algorithms make classical ciphers susceptible to attack and present a major threat to cybersecurity and communications. Demonstrating the computational speedup of Grover’s and Simon’s algorithms can encourage the development of new ciphers, perhaps quantum ciphers, that are more secure against quantum cryptography algorithms. Our research will validate existing research that demonstrates quantum algorithm speedups and creating more secure ciphers is necessary.

EXTERNAL MENTOR: Mafalda Ramôa, Virginia Tech Center for Quantum Information Science and Engineering

Magic and entanglement are both necessary for quantum advantage. These resources have been studied in the context of the QAOA algorithm (see arXiv:2205.12283, arXiv:2505.17185); the purpose of this project is to study their role in ADAPT-VQE.

Goal 1: Analyze the evolution of these resources along the ADAPT-VQE optimization and along the final optimized quantum circuit.

Goal 2: Understand the interplay between these resources and operator performance.

EXTERNAL MENTOR: Dr. Bharath Sambasivam, Virginia Tech Center for Quantum Information Science and Engineering

The proposed research aims to develop symmetry-preserving algorithms for simulating time-dependent quantum dynamics on quantum computers. Building on foundational work in quantum simulation and the use of product-formula (Trotterization) methods to approximate complex Hamiltonians, we will investigate new approximation strategies that respect conserved quantities inherent to the target system, such as particle number or total spin projection for symmetry-aware simulation frameworks. Conventional Trotterization decomposes the full interaction into a sequence of simpler unitary operations that can be implemented on quantum hardware, but this process can break the exact symmetries of the system, therefore allowing the quantum state to leak into other irrelevant subspaces.

The intellectual merit of this project lies in advancing the theoretical and algorithmic foundations of quantum simulation by directly addressing one of its central limitations: the breaking of phys- ical symmetries during time-evolution approximations. Conventional product-formula (Trotter) methods decompose complex interactions into implementable unitary steps but can also violate conserved quantities such as particle number or spin projection. Recent theoretical proposals have emphasized the importance of symmetry-adapted bases and constrained dynamics for improving quantum-simulation fidelity; however, a systematic framework for constructing such approximations has not yet been developed.

Beyond its immediate scientific contributions, this project will broaden the impact of quantum simulation by making it more resource-efficient and physically accurate. Additionally, this will accelerate its application to problems of chemical reactivity, materials discovery, and energy conversion.

External mentor: Tianci Zhou, Virginia Tech Center for Quantum Information Science and Engineering

The proposed research aims to explore the level statistics of quantum Hamiltonians. In this case, the energy levels are the eigenvalues of the Hamiltonian operators. Recently, we have seen such statistics applied to quantum circuits. We aim to study the properties of a quantum system using its eigenvalues via random matrix level statistics. In addition, we also aim to look at the entanglement of eigenstates in quantum scars. Eigenstates typically have volume-law entanglement to be consistent with thermalization. Quantum scars, however, are a special class of quantum systems, a subset of which can have area-law entanglement (entanglement scales with area, not volume; low entanglement), allowing them to periodically revive the wave function rather than trend towards thermal equilibrium.

The intellectual merit of this research lies in the potential of our work to develop our understanding of entanglement in many-body systems. For Project 1, we will build on the description of random matrix theory (RMT) of quantum chaos that predicts that the energy levels of chaotic Hamiltonians exhibit level repulsion and follow universal gap statistics. Project 2 will extend this to quantum circuits; we will explore whether the circuit spectra obey the same behavior to see if we can make a connection to quantum chaos. Conventional eigenstate thermalization predicts volume-law entanglement across the spectrum. Recent work has contradicted this by revealing quantum scar states with area-law (low) entanglement, causing dynamical revivals. By characterizing the entanglement structure of eigenstates in quantum scars, we aim to clarify when and how scars emerge.

Our results will guide us to design circuits that can emulate chaotic thermalization behavior or avoid it, based on use case. Our study of quantum scars may also lead us to develop protocols that exploit non-thermal states to enhance the lifetimes of quantum memory. Our work will generate datasets of spectra and gap ratios that can be utilized for machine learning approaches to state classification, or for educational purposes.