Resonant Quantum Search with Monitor Qubits

We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary "monitor" qubits, can determine $k$ precisely, if it is unknown. The time complexity of our counting algorithm is $O(\sqrt{N})$, similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.Comment: 12 pages, 1 figur

Berry phase induced dimerization in one-dimensional quadrupolar systems

We investigate the effect of the Berry phase on quadrupoles that occur for example in the low-energy description of spin models. Specifically we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many years about this model is whether it has a non-dimerized fluctuating nematic phase. The dimerization has recently been proposed to be related to Berry phases of the quantum fluctuations. We use an effective low-energy description to calculate the scaling of the dimerization according to this theory, and then verify the predictions using large scale density-matrix renormalization group (DMRG) simulations, giving good evidence that the state is dimerized all the way up to its transition into the ferromagnetic phase. We furthermore discuss the multiplet structure found in the entanglement spectrum of the ground state wave functions.Comment: 4.5 pages + 4 pages supplementary material, 4 figure

Understanding Opportunities in Social Entrepreneurship: A Critical Realist Abstraction

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This paper extends social entrepreneurship (SE) research by drawing upon a critical realist perspective to analyse dynamic structure/agency relations in SE opportunity emergence, illustrated by empirical evidence. Our findings demonstrate an agential aspect (opportunity actualisation following a path-dependent seeding-growing-shaping process) and a structural aspect (institutional, cognitive and embedded structures necessary for SE opportunity emergence) related to SE opportunities. These structures provide three boundary conditions for SE agency: institutional discrimination, an SE belief system and social feasibility. Within this paper, we develop a novel theoretical framework to analyse SE opportunities plus, an applicable tool to advance related empirical research

Quantum Frenkel-Kontorova Model

This paper gives a review of our recent work on the quantum Frenkel-Kontorova model. Using the squeezed state theory and the quantum Monte Carlo method, we have studied the effects of quantum fluctuations on the Aubry transition and the behavior of the ground state wave function. We found that quantum fluctuations renormalize the sinusoidal standard map to a sawtooth map. Although quantum fluctuations have smeared the Aubry transition, the remnants of this transition are still discernible. The ground state wave function also changes from an extended state to a localized state. The squeezed state results agree very well with those from the Monte Carlo and mean field studies.Comment: 20 pages in elsart.sty, 11 eps figure

Meta-Learning For Vision-and-Language Cross-lingual Transfer

Current pre-trained vison-language models (PVLMs) achieve excellent performance on a range of multi-modal datasets. Recent work has aimed at building multilingual models, and a range of novel multilingual multi-modal datasets have been proposed. Current PVLMs typically perform poorly on these datasets when used for multi-modal zero-shot or few-shot cross-lingual transfer, especially for low-resource languages. To alleviate this problem, we propose a novel meta-learning fine-tuning framework. Our framework makes current PVLMs rapidly adaptive to new languages in vision-language scenarios by designing MAML in a cross-lingual multi-modal manner. Experiments show that our method boosts the performance of current state-of-the-art PVLMs in both zero-shot and few-shot cross-lingual transfer on a range of vision-language understanding tasks and datasets (XVNLI, xGQA, MaRVL, xFlicker&C