There exist several near-term quantum algorithms for approximately solving combinatorial optimization problems, however there is a need to develop fault-tolerant algorithms for solving combinatorial optimization problems. In this project, students will investigate how one can encoding generating functions, which are commonly used in combinatorics, into quantum circuits. Students will then determine if one can use these generating functions circuits in conjunction with other fault-tolerant algorithm primitives, such as quantum phase estimation or the quantum singular value transformation, to solve combinatorial optimization problems.

Students working on this project should be comfortable with mathematical proofs, particularly in graph theory or discrete mathematics. Previous Python experience is a bonus, but is not necessary.

The Quantum Informed Recursive Algorithm (QIRA) uses information from quantum circuits to inform a classical optimization routine. Qubit routing is a challenging problem on quantum computers. In qubit routing, the goal is to map qubits to physical hardware in a way that minimizes SWAP gates when implementing a quantum algorithm. In this work, students will use QIRA or develop new quantum-informed optimization approaches, for the qubit routing problem.

Students working on this project should be comfortable with discrete mathematics and Python. Experience in integer programming and mathematical optimization is preferred, but not necessary.

Inverse optimization seeks to determine the parameters of an optimization model from observed decisions or solutions. This project will investigate inverse optimization when the observed solutions are generated by quantum or hybrid quantum-classical optimization algorithms. The student will develop small combinatorial optimization test problems, such as MaxCut or knapsack, and study how accurately unknown objective parameters or constraints can be recovered from optimal and approximate solutions. Particular attention will be given to how sampling, approximation quality, and quantum algorithm parameters affect the ability to recover the underlying optimization model.

The project will involve mathematical modeling, Python programming, classical optimization, and simulation of quantum optimization algorithms.

Constrained optimization problems must typically be reformulated before they can be solved using quantum optimization algorithms. Constraints can be incorporated using penalty terms or represented more explicitly using gadgets and auxiliary variables, with important tradeoffs in qubit requirements, coefficient ranges, and solution quality. This project will investigate when different constraint representations are most effective. The student will compare penalty and gadget-based formulations for several common classes of optimization constraints and study how problem and constraint characteristics affect their performance. A longer-term goal is to develop rules or algorithms that automatically determine which constraints should be gadgetized and which should be penalized when compiling an optimization problem for a quantum computer.

The project will involve mathematical modeling, Python programming, combinatorial optimization, and quantum computing simulation.

Quantum computers represent and manipulate information in fundamentally different ways from conventional computers. An important question is how best to represent complex physical systems on emerging quantum hardware. While most quantum computers use two-level systems called qubits, some platforms also provide continuous-variable degrees of freedom, or qumodes, which behave mathematically like harmonic oscillators.

In this project, the student will use numerical methods to investigate simple quantum models and compare different ways of representing them. Possible systems include small lattice gauge theories, which provide simplified models of the interactions underlying particle physics. The student will construct finite-dimensional matrices, calculate eigenvalues and eigenvectors, study convergence as the representation is enlarged, and compare qubit and continuous-variable approaches. Depending on the student’s interests and progress, the project may extend to quantum circuits for state preparation or simulation of time evolution.

Many quantum-simulation algorithms formulate the determination of low-energy states as an optimization problem, for example by varying parameters in a trial quantum state to minimize its energy. This project therefore provides a natural setting for studying how representation, approximation, and optimization interact in quantum algorithms.

Prior coursework in quantum mechanics or quantum computing is not required. The necessary quantum concepts will be introduced during the project. Familiarity with linear algebra and some programming experience, preferably in Python, are helpful.

Quantum networks use photons to transmit quantum information between distant locations. Potential applications include secure communication, distributed quantum computing, and networks of extremely precise sensors and clocks. Building such networks requires understanding both quantum effects and very practical issues such as optical loss, timing uncertainty, detector noise, and synchronization.

This project will contribute to research using a long-distance optical-fiber quantum-network testbed. The student may analyze photon-detection data, identify correlations between events recorded at separated locations, characterize timing precision and noise, and develop numerical models of photon transmission and detection. Possible questions include how accurately two distant stations can synchronize their clocks using correlated photons and how fiber loss, detector timing jitter, and background counts affect the measurement. Students interested in experiment may also have opportunities to work with optical fibers, lasers, single-photon detectors, and timing electronics. Students with stronger computational interests can concentrate on data analysis, statistical inference, and simulation.

Operating a quantum network involves optimizing experimentally controllable parameters, such as timing offsets, detection windows, polarization settings, and synchronization protocols, to maximize performance in the presence of loss and noise. The project offers a concrete example of optimization driven by real quantum hardware data.

No prior quantum mechanics or quantum-optics course is required. Useful preparation includes programming, statistics, and an interest in learning how experiments and quantitative data analysis work.

The harmonic oscillator is one of the simplest mathematical models in physics, appearing in systems ranging from vibrating molecules to electromagnetic fields and trapped ions. When treated quantum mechanically, however, it can display striking phenomena that have no classical analogue. These include squeezing, unusual photon statistics, and quantum states described by quasiprobability distributions that can take negative values.

In this project, the student will develop computational tools for exploring these states. Starting from basic linear algebra and the harmonic oscillator, the student will numerically construct quantum states, simulate transformations acting on them, and visualize quantities such as probability distributions and Wigner functions. The student will then investigate how nonlinear operations can generate increasingly nonclassical behavior. One possible direction is to study recently developed trigonometric quantum gates, whose action depends periodically on oscillator position, and which are relevant to emerging continuous-variable quantum processors.

The student can formulate questions such as which gate parameters produce a desired quantum state or maximize a chosen measure of nonclassicality, turning state preparation into a concrete optimization problem on a quantum system.

The project can be approached from either a physics or computational perspective and is well suited to students who enjoy mathematics, programming, and visualization. Previous quantum mechanics is not required. The project will introduce the necessary concepts as they arise. Familiarity with linear algebra and Python or another programming language would be useful.

Addressing Chaotic Signals, Data Imbalance, and Transferability: Clinical waveform data, such as electrocardiograms (ECGs), provide rich information for diagnosing cardiac arrhythmias and understanding abnormal heart function. Although normal ECG signals exhibit relatively regular and periodic patterns, arrhythmias such as atrial fibrillation (AF) can produce highly nonlinear, irregular, and complex electrical activity that is challenging to characterize using conventional data-driven methods. Classical machine learning has shown promise for ECG analysis, but important challenges remain, including capturing complex temporal dynamics, handling imbalanced clinical data, and developing models that generalize across diverse patients and recording conditions. Quantum computing offers a fundamentally different framework for representing and processing information through quantum states, superposition, and entanglement, creating new opportunities to investigate whether quantum-enhanced representations can capture patterns in complex biomedical signals that are difficult to learn with conventional approaches. This project will explore Quantum Machine Learning (QML) methods for ECG analysis, with a focus on understanding how quantum representations and hybrid quantum-classical algorithms can be used to characterize nonlinear temporal patterns and improve arrhythmia classification. Students will gain hands-on experience at the intersection of quantum computing, machine learning, signal processing, and biomedical engineering while investigating an emerging research question: Can quantum-enhanced learning provide new and effective ways to analyze complex clinical waveform data? The project will provide a systematic framework for evaluating QML approaches on real-world ECG data and identifying their potential, as well as their limitations, for future clinical applications.

Superconducting quantum processors require classical control hardware to generate, sequence, and manage operations on large numbers of qubits. Placing some of these control functions near the qubits can reduce wiring complexity, communication latency, and the thermal burden between room-temperature electronics and the cryogenic environment. However, conventional electronics face significant power and performance limitations at cryogenic temperatures.

In this project, the students will investigate the co-design of cryogenic memory and logic components for scalable superconducting-qubit controllers. The work may include modeling candidate cryogenic devices and circuits, designing a small control block that combines local instruction or calibration-data storage with digital logic, and evaluating tradeoffs in energy, latency, area, reliability, and cryogenic heat load. Depending on their backgrounds, the two students could pursue complementary tasks—one focusing on memory and device/circuit modeling and the other on logic and controller architecture—before integrating their results into a unified design.

The project will primarily involve simulation and computational analysis using tools such as Python, MATLAB, SPICE, or Verilog-A. Students will also gain exposure to superconducting electronics, cryogenic computing, quantum-control requirements, and device–circuit–system co-design. No previous experience in quantum computing or superconducting electronics is required.

Coursework or experience in digital logic, electronic circuits, computer architecture, semiconductor devices, or programming would be helpful. Students should be comfortable learning new technical concepts, working with simulation tools, analyzing data, and collaborating with others.

We are building an experiment on photonic quantum sensing and quantum network. Various undergraduate projects are available, including designing and building optical/fiber paths for quantum sensing; generating single photons from a fiber-coupled waveguide crystal; performing single photon detection and time-correlation measurements using superconducting nanowire detectors and a time tagger; supporting electronics/mechanical design and build with Python-based data acquisition/analysis.

Prior knowledge with quantum mechanics and optics is helpful but not required—students with interest in experimental physics, optics/photonics, electronics, coding are encouraged to apply.