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. Quantum Tensor-Bit extends this structure-first approach to collision-aware QNN encoding under limited input-qubit budgets.

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 finite-shot noise. AdaRO-Q adapts task-specific readout observables for task-incremental quantum continual learning and evaluates sequential performance, forgetting, ablations, and finite-shot robustness.

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 end-to-end execution cost and quality analyses, together with resource- and outcome-prediction models for quantum–classical workloads. This work compares complete CPU, GPU, simulator, and QPU workflows—including queueing, compilation, shots, mitigation, and classical processing.

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.
  • Adaptive readout observables (AdaRO-Q): task-specific measurements for task-incremental quantum continual learning.
  • Compact deep networks: depth- and rank-selective multilinear transformation layers for parameter-efficient CNNs.
  • Quantum tensor methods: tensor contraction layers, collision-aware Tensor-Bit encoding, quantum-assisted CP/PARAFAC decomposition, adaptive QUBO-based rank selection, and a review of foundations and open challenges.
  • Resource and outcome modeling: end-to-end cost, resource-demand, and output-quality prediction across CPU, GPU, simulator, and QPU workflows.

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.