In this paper, we study a shipment rerouting problem (SRP) which generalizes many NP-hard sequencing and packing problems. A SRP's solution has ample practical applications in vehicle scheduling and transportation logistics. Given a network of hubs, a set of goods must be delivered by trucks from their source-hubs to their respective destination-hubs. The objective is to select a set of trucks and to schedule these trucks' routes so that the total cost is minimized. The problem SRP is NP-hard; only classical approximation algorithms have been known for some of its NP-hard variants. In this work, we design classical algorithms and quantum annealing algorithms for this problem with various capacitated trucks. The algorithms that we design use novel mathematical programming formulations and new insights into solving sequencing and packing problems simultaneously. Such formulations take advantage of network infrastructure, shipments, and truck capacities. We conduct extensive experiments showing that in various scenarios, the quantum annealing solver generates near-optimal or optimal solutions much faster than the classical algorithm solver.
Several articles and books adequately cover quantum computing concepts, such as gate/circuit model (and Quantum Approximate Optimization Algorithm, QAOA), Adiabatic Quantum Computing (AQC), and Quantum Annealing (QA). However, they typically stop short of accessing quantum hardware and solve numerical problem instances. This tutorial offers a quick hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) problems on currently available quantum computers. We cover both IBM and D-Wave machines: IBM utilizes a gate/circuit architecture, and D-Wave is a quantum annealer. We provide examples of three canonical problems (Number Partitioning, Max-Cut, Minimum Vertex Cover), and two models from practical applications (from cancer genomics and a hedge fund portfolio manager, respectively). An associated GitHub repository provides the codes in five companion notebooks. Catering to undergraduate and graduate students in computationally intensive disciplines, this article also aims to reach working industry professionals seeking to explore the potential of near-term quantum applications.
The Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising Noisy Intermediate Quantum (NISQ) Algorithms in solving combinatorial optimizations and displays potential over classical heuristic techniques. Unfortunately, QAOA’s performance depends on the choice of parameters and standard optimizers often fail to identify key parameters due to the complexity and mystery of these optimization functions. In this paper, we benchmark QAOA circuits modified with metaheuristic optimizers against classical and quantum heuristics to identify QAOA parameters. The experimental results reveal insights into the strengths and limitations of both Quantum Annealing and metaheuristic-integrated QAOA across different problem domains. The findings suggest that the hybrid approach can leverage classical optimization strategies to enhance the solution quality and convergence speed of QAOA, particularly for problems with rugged landscapes and limited quantum resources. Furthermore, the study provides guidelines for selecting the most appropriate approach based on the specific characteristics of the optimization problem at hand.
Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in load forecasting. Transformer models have the potential to improve load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer-based Neural Network model integrated with different metaheuristic algorithms by their performance in load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in load forecasting accuracy and provide optimal hyperparameters for each model.
Weather forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of weather systems remains a challenge for traditional statistical models. Apart from Auto Regressive time forecasting models like ARIMA, deep learning techniques (Vanilla ANNs, LSTM and GRU networks), have shown promise in improving forecasting accuracy by capturing temporal dependencies. This paper explores the application of metaheuristic algorithms, namely Genetic Algorithm (GA), Differential Evolution (DE), and Particle Swarm Optimization (PSO), to automate the search for optimal hyperparameters in these model architectures. Metaheuristic algorithms excel in global optimization, offering robustness, versatility, and scalability in handling non-linear problems. We present a comparative analysis of different model architectures integrated with metaheuristic optimization, evaluating their performance in weather forecasting based on metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). The results demonstrate the potential of metaheuristic algorithms in enhancing weather forecasting accuracy and helps in determining the optimal set of hyper-parameters for each model. The paper underscores the importance of harnessing advanced optimization techniques to select the most suitable metaheuristic algorithm for the given weather forecasting task.
In this paper, we design, analyze, and evaluate a hybrid quantum algorithm for the metric traveling salesman problem (TSP). TSP is a well-studied NP-complete problem that many algorithmic techniques have been developed for, on both classic computers and quantum computers. The existing literature of algorithms for TSP are neither adaptive to input data nor suitable for processing medium-size data on the modern classic and quantum machines. In this work, we leverage the classic computers’ power (large memory) and the quantum computers’ power (quantum parallelism), based on the input data, to fasten the hybrid algorithm’s overall running time. Our algorithmic ideas include trimming the input data efficiently using a classic algorithm, finding an optimal solution for the post-processed data using a quantum-only algorithm, and constructing an optimal solution for the untrimmed data input efficiently using a classic algorithm. We conduct experiments to compare our hybrid algorithm against the state-of-the-art classic and quantum algorithms on real data sets. The experimental results show that our solution truly outperforms the others and thus confirm our theoretical analysis. This work provides insightful quantitative tools for people and compilers to choose appropriate quantum or classical or hybrid algorithms, especially in the NISQ (noisy intermediate-scale quantum) era, for NP-complete problems such as TSP.
In this paper, we study the string matching problem. We design a quantum string-matching algorithm for noisy intermediate-scale quantum (NISQ) computers, given the current leading quantum processing units (QPUs) having no more than a few hundred qubits. We also compare the performance of classic algorithms and quantum algorithms under various combinations. Our study provides a comprehensive and quantitative guide for users to choose appropriate classic or quantum algorithms for their string matching problems.
Projects (Hackathons, Math Modeling, Data Science)
Alice and the Bobs (YQuantum 2025)
We address the challenge of reconstructing and denoising quantum states from Wigner functions using both optimization techniques and machine learning. First, we implemented a contour-based sampling algorithm to enhance density matrix reconstruction via least squares fitting, solving the resulting convex problem with SCS and CBC solvers. We demonstrated strong performance on simulated and real quantum states, including Fock, coherent, and cat states. Next, we analyzed superconducting noise models, constructing a large dataset of noisy Wigner functions with five distinct noise types. To denoise these, we employed a U-Net convolutional neural network, achieving high-fidelity reconstructions of heavily corrupted states. Our results highlight the effectiveness of combining physically informed sampling with deep learning for quantum state reconstruction.
Done in collaboration with Haadi Khan, Tanmay Neema, Ryan O'Farrell and Alice Wang.
This project won 1st in the Alice and Bob track at YQuantum 2025 and qualifed us for the The Yale Quantum Institute Grand Prize where we won 2nd place overall and were invited to present our work at our work at the QuantumCT Industry Collaboration Forum.
Fast Food, Fast Growth: The Health Implications of Processed Diets
(2024 Correlation One and Citadel Securities Summer Invitational Datathon)
Our project investigates the links between diet, health, and economics, focusing on the obesity epidemic in the US. With over 40% of adults affected by obesity, largely due to high consumption of processed foods, this issue not only impacts individual health but also imposes a significant financial burden on the healthcare system. We analyze how processed food consumption relates to obesity and financial markets using statistical tests and quantitative models.
A key feature of our study is an innovative pairs selection and trading algorithm, which reveals that stocks of companies producing or using processed foods show strong correlations with healthcare sector stocks. This pattern provides opportunities for financial gains, with our strategy yielding 7 profitable pairs and a Sharpe ratio of 1.58.
We propose further refining our approach with SARIMA forecasting models to enhance predictive accuracy and offer actionable insights for stakeholders in the food and healthcare sectors.
Done in collaboration with Pi Rey Low, Julia Huang, and Peter Zheng.
This project won 2nd place at the 2024 Correlation One and Citadel Securities Summer Invitational Datathon.
2Y2B (Tartanhacks 2024)
2Y2B simplifies the way users receive their news. Users enter their keywords of interest, and several news APIs fetch recent peer-reviewed articles related to those topics. OpenAI's GPT-3.5 Turbo-16 LLM then summarizes the news articles into concise 3-5 minute texts, which Google Text-To-Speech converts into MP3 audio files for easy listening. Our product is also integrated into an app/website that remembers user preferences for a personalized experience.
Done in collaboration with Michael Chen, Maximillian Chuang, and Praneel Varshney.
This project placed in the Top 15 at TartanHacks.
Eco Bin (HackCMU 2023)
Eco Bin aimed at enhancing environmental sustainability by automatically sorting waste into recycling, compost, and trash. It utilized two types of sensors: a camera for computer vision and a depth camera to detect the shape of objects. Leveraging this data along with a custom-built deep learning model, the robotic trash can accurately classified 80% of tested objects, achieving a 95% accuracy on the training dataset. This software was integrated with a hardware solution that would automatically process and sort the respective waste.
Done in collaboration with Mehul Goel, Anirudh Mani, and Steven Yang.
This project earned the Graduate Student Association cash prize at HackCMU 2023.
Plane boarding and deplaning (IMMC 2023)
This project addresses the optimization of airline boarding and disembarking procedures. Our team has developed a series of robust models to simulate and analyze these processes from a comprehensive perspective. By identifying key factors such as passenger walking speed, sitting and standing speed, luggage amount, and customer satisfaction, we created a model that predicts individual passenger behavior during boarding and disembarking. We evaluated common boarding methods, including Random, By Seat, and By Section, to determine the most time-efficient and feasible procedures. Our simulations incorporated various passenger demographics and aircraft models, including Narrow Body, Flying Wing, and Two-Entrance, Two-Aisle configurations. The results indicate that the By Seat method was the fastest for the Narrow Body aircraft, with an average boarding time of 32.6 minutes. The enclosed paper provides a detailed analysis of the performance of other boarding methods.
Done in collaboration with Simon Beyzerov, Aaron Tian, and Gracie Sheng
This project earned finalist recognition at IMMC 2023.
Lake Mead Reservoir (HiMCM 2022)
Climate change and increased water demand have caused severe drought in Lake Mead, the largest U.S. reservoir, affecting 25 million people. This paper presents multiple predictive models for Lake Mead's water elevation, proposing a comprehensive model that accommodates complex volumetric relationships for advanced analyses. We analyze volumetric factors like inflow, outflow, and loss, guiding the creation of an adaptable model. Using a Seasonal Auto Regressive Integrated Moving Average (SARIMA) model on data from 2005-2020, we project future elevations and compare results to a linear regression model. Our enhanced approach integrates climate change impacts for more accurate predictions. We also propose a two-phase water reuse plan and recommend conservation practices, demonstrated through a case study highlighting effectiveness and metrics.
Done in collaboration with Simon Beyzerov, Aaron Tian, and Gracie Sheng
This project earned honorable mention recognition at HiMCM 2022.
Ongoing Work
A Comparative Analysis of Quantum Approaches for Solving the Electronic Structure Problem (2024)
In this project, we tackle the electronic structure problem, an NP-hard challenge in computational chemistry involving determining the distribution and energy of electrons a given molecular system. Solving this problem is essential for understanding material behavior at the atomic level and has far-reaching applications in material design, photovoltaics, nanotechnology, and drug discovery. Due to the high complexity of electronic structure calculations, classical methods face computational limitations, but recent quantum computing advances show promising potential for addressing this problem within quantum simulation. Our primary goal is to accurately and efficiently estimate a molecular system's ground state energy given its electronic Hamiltonian. The Variational Quantum Eigensolver (VQE) is the leading algorithm in this area, favored for its low circuit depth, variational guarantees, and hybrid quantum-classical approach, making it both practical for Noisy Intermediate-Scale Quantum (NISQ) devices and potentially capable of achieving quantum advantage. Alternatively, the Quantum Annealing Eigensolver (QAE), tailored for D-Wave’s adiabatic quantum computers, bypasses some of VQE’s challenges in ansatz construction and nonconvex optimization but grapples with limitations in QUBO scaling and accuracy. A further promising but less explored option, the Eigenvalue Estimation (EE) algorithm, combines Quantum Phase Estimation and Quantum Amplitude Estimation to provide a quadratic speedup over leading classical algorithms.
In our work, we implement VQE with various optimizers (including with a sequential triple-hybrid approach in which quantum annealing is used to optimize VQE’s ansatz parameters), along with QAE, EE, and the classical Hartree-Fock method as a baseline. Each algorithm's speed and accuracy are then tested on a diverse set of molecules, allowing us to analyze their performance in relation to molecular properties and algorithmic assumptions. Ultimately, our findings are summarized in a practical guide for industry users, such as those in pharmaceuticals and chemical manufacturing, to help them select the most suitable algorithm for determining a molecule’s electronic structure based on its properties.
Educational Outreach
NousQuest (2023 - 2024)
Mathematics is often seen by students as unintuitive and tedious, which can hinder their academic and career prospects. NousQuest was created to address this issue by leveraging a unique problem bank architecture and machine learning to offer interactive and personalized gamification features, making math learning engaging and enjoyable for students.
MathEx (2019 - 2024)
MathEx is a 501(c)(3) non-profit organization dedicated to fostering interest in competitive mathematics and related fields. Our YouTube channel features over 160 videos, with more than 75,000 views and 1,200 subscribers. Additionally, we conduct in-person courses and training camps throughout the eastern Massachusetts region.
We address the challenge of reconstructing and denoising quantum states from Wigner functions using both optimization techniques and machine learning. First, we implemented a contour-based sampling algorithm to enhance density matrix reconstruction via least squares fitting, solving the resulting convex problem with SCS and CBC solvers. We demonstrated strong performance on simulated and real quantum states, including Fock, coherent, and cat states. Next, we analyzed superconducting noise models, constructing a large dataset of noisy Wigner functions with five distinct noise types. To denoise these, we employed a U-Net convolutional neural network, achieving high-fidelity reconstructions of heavily corrupted states. Our results highlight the effectiveness of combining physically informed sampling with deep learning for quantum state reconstruction.
Done in collaboration with Haadi Khan, Tanmay Neema, Ryan O'Farrell and Alice Wang.
This project won 1st in the Alice and Bob track at YQuantum 2025 and qualifed us for the The Yale Quantum Institute Grand Prize where we won 2nd place overall and were invited to present our work at our work at the QuantumCT Industry Collaboration Forum.
(2024 Correlation One and Citadel Securities Summer Invitational Datathon)
Our project investigates the links between diet, health, and economics, focusing on the obesity epidemic in the US. With over 40% of adults affected by obesity, largely due to high consumption of processed foods, this issue not only impacts individual health but also imposes a significant financial burden on the healthcare system. We analyze how processed food consumption relates to obesity and financial markets using statistical tests and quantitative models. A key feature of our study is an innovative pairs selection and trading algorithm, which reveals that stocks of companies producing or using processed foods show strong correlations with healthcare sector stocks. This pattern provides opportunities for financial gains, with our strategy yielding 7 profitable pairs and a Sharpe ratio of 1.58. We propose further refining our approach with SARIMA forecasting models to enhance predictive accuracy and offer actionable insights for stakeholders in the food and healthcare sectors.
Done in collaboration with Pi Rey Low, Julia Huang, and Peter Zheng.
This project won 2nd place at the 2024 Correlation One and Citadel Securities Summer Invitational Datathon.
2Y2B simplifies the way users receive their news. Users enter their keywords of interest, and several news APIs fetch recent peer-reviewed articles related to those topics. OpenAI's GPT-3.5 Turbo-16 LLM then summarizes the news articles into concise 3-5 minute texts, which Google Text-To-Speech converts into MP3 audio files for easy listening. Our product is also integrated into an app/website that remembers user preferences for a personalized experience.
Done in collaboration with Michael Chen, Maximillian Chuang, and Praneel Varshney.
This project placed in the Top 15 at TartanHacks.
Eco Bin aimed at enhancing environmental sustainability by automatically sorting waste into recycling, compost, and trash. It utilized two types of sensors: a camera for computer vision and a depth camera to detect the shape of objects. Leveraging this data along with a custom-built deep learning model, the robotic trash can accurately classified 80% of tested objects, achieving a 95% accuracy on the training dataset. This software was integrated with a hardware solution that would automatically process and sort the respective waste.
Done in collaboration with Mehul Goel, Anirudh Mani, and Steven Yang.
This project earned the Graduate Student Association cash prize at HackCMU 2023.
This project addresses the optimization of airline boarding and disembarking procedures. Our team has developed a series of robust models to simulate and analyze these processes from a comprehensive perspective. By identifying key factors such as passenger walking speed, sitting and standing speed, luggage amount, and customer satisfaction, we created a model that predicts individual passenger behavior during boarding and disembarking. We evaluated common boarding methods, including Random, By Seat, and By Section, to determine the most time-efficient and feasible procedures. Our simulations incorporated various passenger demographics and aircraft models, including Narrow Body, Flying Wing, and Two-Entrance, Two-Aisle configurations. The results indicate that the By Seat method was the fastest for the Narrow Body aircraft, with an average boarding time of 32.6 minutes. The enclosed paper provides a detailed analysis of the performance of other boarding methods.
Done in collaboration with Simon Beyzerov, Aaron Tian, and Gracie Sheng
This project earned finalist recognition at IMMC 2023.
Climate change and increased water demand have caused severe drought in Lake Mead, the largest U.S. reservoir, affecting 25 million people. This paper presents multiple predictive models for Lake Mead's water elevation, proposing a comprehensive model that accommodates complex volumetric relationships for advanced analyses. We analyze volumetric factors like inflow, outflow, and loss, guiding the creation of an adaptable model. Using a Seasonal Auto Regressive Integrated Moving Average (SARIMA) model on data from 2005-2020, we project future elevations and compare results to a linear regression model. Our enhanced approach integrates climate change impacts for more accurate predictions. We also propose a two-phase water reuse plan and recommend conservation practices, demonstrated through a case study highlighting effectiveness and metrics.
Done in collaboration with Simon Beyzerov, Aaron Tian, and Gracie Sheng
This project earned honorable mention recognition at HiMCM 2022.
In this project, we tackle the electronic structure problem, an NP-hard challenge in computational chemistry involving determining the distribution and energy of electrons a given molecular system. Solving this problem is essential for understanding material behavior at the atomic level and has far-reaching applications in material design, photovoltaics, nanotechnology, and drug discovery. Due to the high complexity of electronic structure calculations, classical methods face computational limitations, but recent quantum computing advances show promising potential for addressing this problem within quantum simulation. Our primary goal is to accurately and efficiently estimate a molecular system's ground state energy given its electronic Hamiltonian. The Variational Quantum Eigensolver (VQE) is the leading algorithm in this area, favored for its low circuit depth, variational guarantees, and hybrid quantum-classical approach, making it both practical for Noisy Intermediate-Scale Quantum (NISQ) devices and potentially capable of achieving quantum advantage. Alternatively, the Quantum Annealing Eigensolver (QAE), tailored for D-Wave’s adiabatic quantum computers, bypasses some of VQE’s challenges in ansatz construction and nonconvex optimization but grapples with limitations in QUBO scaling and accuracy. A further promising but less explored option, the Eigenvalue Estimation (EE) algorithm, combines Quantum Phase Estimation and Quantum Amplitude Estimation to provide a quadratic speedup over leading classical algorithms. In our work, we implement VQE with various optimizers (including with a sequential triple-hybrid approach in which quantum annealing is used to optimize VQE’s ansatz parameters), along with QAE, EE, and the classical Hartree-Fock method as a baseline. Each algorithm's speed and accuracy are then tested on a diverse set of molecules, allowing us to analyze their performance in relation to molecular properties and algorithmic assumptions. Ultimately, our findings are summarized in a practical guide for industry users, such as those in pharmaceuticals and chemical manufacturing, to help them select the most suitable algorithm for determining a molecule’s electronic structure based on its properties.
Educational Outreach
NousQuest (2023 - 2024)
Mathematics is often seen by students as unintuitive and tedious, which can hinder their academic and career prospects. NousQuest was created to address this issue by leveraging a unique problem bank architecture and machine learning to offer interactive and personalized gamification features, making math learning engaging and enjoyable for students.
MathEx (2019 - 2024)
MathEx is a 501(c)(3) non-profit organization dedicated to fostering interest in competitive mathematics and related fields. Our YouTube channel features over 160 videos, with more than 75,000 views and 1,200 subscribers. Additionally, we conduct in-person courses and training camps throughout the eastern Massachusetts region.
Mathematics is often seen by students as unintuitive and tedious, which can hinder their academic and career prospects. NousQuest was created to address this issue by leveraging a unique problem bank architecture and machine learning to offer interactive and personalized gamification features, making math learning engaging and enjoyable for students.
MathEx is a 501(c)(3) non-profit organization dedicated to fostering interest in competitive mathematics and related fields. Our YouTube channel features over 160 videos, with more than 75,000 views and 1,200 subscribers. Additionally, we conduct in-person courses and training camps throughout the eastern Massachusetts region.