Research

Graph-theoretic representations for quantum computing and machine learning.

The unifying object in my work is the representation: what information it preserves, what symmetries it respects, what resources are required to read it, and what computations become possible after changing the representation.

Quantum computing

Quantum representations of graph structure

I develop shallow quantum circuits that encode graph structure without requiring variational training, then study what graph information their measurement distributions retain.

Central question

Which graph properties are present in a quantum state, which are accessible through practical readout, and which remain recoverable under finite shots and hardware noise?

Contribution

QuIC uses phase-encoded quantum graph circuits and sorted measurement distributions to produce compact, permutation-invariant graph signatures from ideal simulation through hardware evaluation.

Evidence and outputs

Training-free quantum graph embedding for graph-invariant construction.
Structured readout designed for truncation and finite-shot measurement.
Accepted for oral presentation at IEEE Quantum Week 2026.

QuIC preprint

Computational graph theory

Structural accessibility under finite resources

My current theoretical work separates ideal structural signal from decoder conditioning, truncation loss, sampling error, and hardware effects.

Central question

When a circuit contains information about a graph invariant, what conditions make that information stably and efficiently recoverable?

Contribution

I analyze motif accessibility and structured readout as distinct layers: algebraic presence in the state, accessibility to a decoder, and recovery from finite measurements.

Evidence and outputs

Connects graph motifs to explicit circuit and readout behavior.
Treats finite-shot recovery as a resource question rather than an afterthought.
Provides a mathematical foundation for practical quantum graph representations.

Machine learning

Graph-minor representations for efficient learning

I replace large dense prediction domains with compact, topology-aware graph structures that preserve the support needed for downstream learning.

Central question

Can a representation discard most of a dense spatial domain while retaining the topology and geometry needed for accurate prediction?

Contribution

SEMIR constructs graph-minor representations for visual and medical segmentation, reducing the computational domain while preserving task-relevant structure.

Evidence and outputs

First-author work accepted at ICML 2026 and ECCV 2026.
Applied to volumetric and thin-structure segmentation.
Unifies graph construction, representation reduction, and downstream learning.

SEMIR preprint

Research practice

Theory, implementation, and evaluation belong in the same loop

The work is designed to move between mathematical characterization and computational evidence rather than treating either as an afterthought.

Characterize the representation

Identify which structural quantities are encoded, which symmetries are respected, and where information is lost.

Account for finite resources

Separate ideal-state properties from truncation, sampling, decoder conditioning, and hardware effects.

Build executable evidence

Pair analysis with reproducible implementations, simulations, hardware experiments, and task-level evaluation.

Technical capabilities

Methods and tools

The stack reflects the research program: quantum software, graph and machine learning, and systems-level implementation.

Quantum

Qiskit SDK
Qiskit Runtime
VQE
QAOA
QSVM

Machine learning

PyTorch
TensorFlow
scikit-learn
Computer vision

Software

Python
Rust
C++
Bash
Git
Linux

Discuss the work

Research collaborations and technical conversations

Email Luke Publications