Research

My research asks a practical question: when does a quantum component genuinely earn its place in a learning system? I use tensor and multilinear structure to reduce the dominant costs of model representation, quantum measurement, optimization, and execution, then compare the result with strong classical alternatives.

Research Agenda

Structure-Aware Quantum–Classical Learning

I design hybrid architectures that preserve low-rank or tensor structure rather than flattening high-dimensional representations too early. In Quantum-Based Tensor Contraction Layers, for example, a small trainable quantum circuit operates inside a compressed tensor bottleneck, tying quantum cost to the bottleneck width rather than the raw input. Related work on multilinear transformation layers replaces late convolutions with compact mode-wise transformations and learns the effective rank rather than fixing it by hand.

Measurement-Aware Quantum Learning

Quantum measurement is often treated as a fixed final step. I instead study measurement and recovery as parts of the learning pipeline. My multilinear quantum-reservoir readout preserves time–qubit–observable structure and reduces trainable parameters by approximately 12.1× relative to an MLP readout. Variational Quantum Bayesian Regression separates a regression vector into a direction recovered by a shallow circuit and a scale solved for analytically, recovering the true MAP direction with 0.998 cosine similarity under realistic finite-shot noise.

Structured Optimization and Resource-Aware Execution

I formulate adaptive CP-rank selection as an interaction-aware QUBO, allowing a quantum solver to select tensor components based on their joint contribution rather than magnitude alone. I also investigate how quantum-encoded solutions can become explicit classical models through task-aligned recovery of missing sign and scale information.

A complementary line of work asks where these methods should run. I am developing a learning-aware execution policy, grounded in a systematic review of quantum-HPC integration, middleware, and workflow orchestration, that compares the complete cost of CPU, GPU, simulator, and QPU routes—including queueing, compilation, shots, and mitigation—and is explicitly allowed to reject the QPU route.

Current Research Portfolio

• Variational quantum Bayesian regression (VQBR): measurement-based MAP direction recovery and analytical scale estimation, evaluated on simulators and IBM Quantum hardware.
• Multilinear quantum reservoir computing (ML-QRC): Tucker-factored readouts that retain predictive quality while substantially reducing trainable parameters.
• Compact deep networks: depth- and rank-selective multilinear transformation layers for parameter-efficient CNNs.
• Quantum tensor methods: tensor contraction layers, quantum-assisted CP/PARAFAC decomposition, adaptive QUBO-based rank selection, and a review of foundations and open challenges.
• Resource-aware quantum-HPC execution: end-to-end policies for routing learning subtasks across classical, simulated, and quantum resources.

Evaluation Principles

I evaluate methods against strong classical baselines and report the assumptions that determine whether a quantum component is useful. Experiments combine mathematical analysis, reproducible simulation, GPU workflows, and real-hardware studies when hardware evidence answers a meaningful question. A negative or regime-dependent result is informative: the goal is not to make more things quantum, but to identify—with evidence—when doing so is worthwhile.

Selected outcomes are listed on the Publications page; fuller technical and professional details are available in my CV.

Collaboration

I welcome conversations about quantum machine learning, tensor methods, compact neural networks, measurement-efficient learning, quantum-HPC integration, and reproducible quantum experimentation. Please contact me at tien.nguyen@utsa.edu.