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“Quantum-Inspired Trainable and Parameter-Efficient Tensor Networks for Image Inpainting” (with Konstantinos Slavakis) is now on arXiv: arXiv:2609.17298. It has been submitted to ICASSP 2027.
This is the follow-up to Fast Trainable Multilinear Bases for Image Compression: the same quantum Fourier transform circuits, trained this time for image inpainting rather than compression. Inpainting recovers an image from a subset of its pixels, and there the coherence of the transform with the pixel basis matters as much as its sparsity. The diagonal QFT relaxation keeps one fixed Hadamard per wire and frees only the controlled-phase gates, so its coherence is pinned at the minimum for every parameter value, by circuit topology alone. That removes the need for a coherence penalty and for Riemannian optimization: the phases are trained with plain Adam through an unrolled hard-thresholding recovery, and the transform stays exactly invertible with O(N2 log N) cost.
On DIV2K at 10% observed pixels, the diagonal model with 288 trainable parameters outperforms the DFT by 2.0 dB and the best fixed transform by 1.6 dB in PSNR, and comes within 0.2 dB of a learned butterfly factorization that carries 64 times as many parameters.
“Fast Trainable Multilinear Bases for Image Compression” (with Zhongyi Ni, Huanhai Zhou, and Jin-Guo Liu) is now on arXiv: arXiv:2608.00053.
We generalize the DFT, the DCT, and their block-wise variants to isometric multilinear bases that keep near-linear transform cost, exact invertibility, and a parameter count polylogarithmic in the image size. The basis is parameterized as an isometric tensor network inspired by quantum many-body theory and trained per dataset with Riemannian optimization on the manifold of unitary matrices. On Quick Draw line drawings, the trained basis stores images in roughly 20% fewer bytes than JPEG’s 8×8 block cosine transform at the same reconstruction quality.
The implementation ships as the JAX-based Python library zazabap/pdft, with the benchmark suite and reproduction scripts at zazabap/pdft-benchmarks.
“Riemannian Gauss–Newton Method for Open-System Projected Variational Quantum Dynamics” (with Konstantinos Slavakis) is accepted to the poster track of IEEE Quantum Week 2026 (QCE 2026), held in Toronto, Canada, on 13–18 September 2026. The two-page proceedings paper is available here.
Projected variational quantum dynamics (p-VQD) refits a fixed-depth circuit to each Trotter step by maximizing a pure-state fidelity. For an open system the target is a mixed reduced state, so that objective is undefined, and the obvious repair, fitting the reduced trace overlap, is provably capped below unity: its maximizer is the dominant eigenvector rather than the target. We purify the thermal bath with a thermofield ancilla so that the joint system–bath–ancilla state stays pure. The fidelity then applies exactly on the joint state, and tracing out the bath and the ancilla afterwards returns the physical reduced dynamics.
Each projection becomes a pure-state least-squares fit. A Riemannian Gauss–Newton inner loop with trust-region damping, whose normal matrix is the Fubini–Study metric, drives it to the ansatz ceiling in two or three iterations where first-order p-VQD stalls orders of magnitude short. On finite-temperature spin–boson and central-spin benchmarks, validated against an independent TDVP baseline, the ansatz sets the attainable fidelity and the optimizer sets the convergence rate. Where the ansatz is under-resourced, the second-order step attains the best tested fidelities.
The JAX reference implementation is at zazabap/RiemannianPVQD.
“Problem Reductions at Scale: Agentic Integration of Computationally Hard Problems” (with Xi-Wei Pan and Jin-Guo Liu) is now on arXiv: arXiv:2604.11535.
The companion Rust library and CLI (pred) is open-sourced at CodingThrust/problem-reductions, implementing 100+ NP-hard problem types and 200+ reduction rules, with automatic reduction-path search that lets a single registered solver be reused across the whole connected problem graph.
I will be exchanged at HKUST guangzhou campus from Jan.-Mar. 2026. Please check the work at Prof. Jinguo Liu’s group for Tensor Network related topics and research.
The official paper on LogosQ is published on the arXiv: arXiv:2512.23183. Please check it if you are interested in the implementation details.
The paper on graph encoding with variational quantum circuits, Tensor-Based Binary Graph Encoding for Variational Quantum Classifiers, is accepted by IEEE QCNC 2025 in Nara, Japan. The details are on the conference page.
Last updated September 22, 2026.