C. H. W. Barnes

Haomu Yuan, Hanqing Wu, Kuan-Cheng Chen et al.

Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits the structure of the fixed-cardinality feasible subspace under a natural promise on solution existence. For quadratic objectives, our approach achieves ${O}\left(\sqrt{\frac{\binom{n}{k}}{M}}\right)$ Grover rotations for any fixed cardinality $k$ and degeneracy of the optima $M$, yielding an exponential reduction in the number of Grover iterations compared with unstructured search over $\{0,1\}^n$. Building on this result, we develop a hybrid classical--quantum framework based on the alternating direction method of multipliers (ADMM) algorithm. The proposed framework is guaranteed to output an $ε$-approximate solution with a consistency tolerance $ε+ δ$ using at most $ {O}\left(\sqrt{\binom{n}{k}}\frac{n^{6}k^{3/2} }{ \sqrt{M}ε^2 δ}\right)$ queries to a quadratic oracle, together with ${O}\left(\frac{n^{6}k^{3/2}}{ε^2δ}\right)$ classical overhead. Overall, our method suggests a practical use of quantum resources and demonstrates an exponential improvements over existing Grover-based approaches in certain parameter regimes, thereby paving the way toward quantum advantage in constrained binary optimization.

Haomu Yuan, Songqinghao Yang, Crispin H. W. Barnes

We provide a method to prepare a warm-started quantum state from measurements with an iterative framework to enhance the quantum approximate optimisation algorithm (QAOA). The numerical simulations show the method can effectively address the "stuck issue" of the standard QAOA using a single-string warm-started initial state described in [Cain et al., 2023]. When applied to the $3$-regular MaxCut problem, our approach achieves an improved approximation ratio, with a lower bound that iteratively converges toward the best classical algorithms for $p=1$ standard QAOA. Additionally, in the context of the discrete global minimal variance portfolio (DGMVP) model, simulations reveal a more favourable scaling of identifying the global minimal compared to the QAOA standalone, the single-string warm-started QAOA and a classical constrained sampling approach.

Noa Fish, Richard Zhang, Lilach Perry et al.

In image morphing, a sequence of plausible frames are synthesized and composited together to form a smooth transformation between given instances. Intermediates must remain faithful to the input, stand on their own as members of the set, and maintain a well-paced visual transition from one to the next. In this paper, we propose a conditional GAN morphing framework operating on a pair of input images. The network is trained to synthesize frames corresponding to temporal samples along the transformation, and learns a proper shape prior that enhances the plausibility of intermediate frames. While individual frame plausibility is boosted by the adversarial setup, a special training protocol producing sequences of frames, combined with a perceptual similarity loss, promote smooth transformation over time. Explicit stating of correspondences is replaced with a grid-based freeform deformation spatial transformer that predicts the geometric warp between the inputs, instituting the smooth geometric effect by bringing the shapes into an initial alignment. We provide comparisons to classic as well as latent space morphing techniques, and demonstrate that, given a set of images for self-supervision, our network learns to generate visually pleasing morphing effects featuring believable in-betweens, with robustness to changes in shape and texture, requiring no correspondence annotation.