For quantum search via the continuous-time quantum walk, the evolution of the whole system is usually limited in a small subspace. In this paper, we discuss how the symmetries of the graphs are related to the existence of such an invariant subspace,
which also suggests a dimensionality reduction method based on group representation theory. We observe that in the one-dimensional subspace spanned by each desired basis state which assembles the identically evolving original basis states, we always get a trivial representation of the symmetry group. So we could find the desired basis by exploiting the projection operator of the trivial representation. Besides being technical guidance in this type of problem, this discussion also suggests that all the symmetries are used up in the invariant subspace and the asymmetric part of the Hamiltonian is very important for the purpose of quantum search.
Recent studies on deep-learning-based small defection segmentation approaches are trained in specific settings and tend to be limited by fixed context. Throughout the training, the network inevitably learns the representation of the background of the
training data before figuring out the defection. They underperform in the inference stage once the context changed and can only be solved by training in every new setting. This eventually leads to the limitation in practical robotic applications where contexts keep varying. To cope with this, instead of training a network context by context and hoping it to generalize, why not stop misleading it with any limited context and start training it with pure simulation? In this paper, we propose the network SSDS that learns a way of distinguishing small defections between two images regardless of the context, so that the network can be trained once for all. A small defection detection layer utilizing the pose sensitivity of phase correlation between images is introduced and is followed by an outlier masking layer. The network is trained on randomly generated simulated data with simple shapes and is generalized across the real world. Finally, SSDS is validated on real-world collected data and demonstrates the ability that even when trained in cheap simulation, SSDS can still find small defections in the real world showing the effectiveness and its potential for practical applications.
Graph states are a unique resource for quantum information processing, such as measurement-based quantum computation. Here, we theoretically investigate using continuous-variable graph states for single-parameter quantum metrology, including both pha
se and displacement sensing. We identified the optimal graph states for the two sensing modalities and showed that Heisenberg scaling of the accuracy for both phase and displacement sensing can be achieved with local homodyne measurements.
Effective magnetic fields have enabled unprecedented manipulation of neutral particles including photons. In most studied cases, the effective gauge fields are defined through the phase of mode coupling between spatially discrete elements, such as op
tical resonators and waveguides in the case for photons. Here, in the paradigm of Bloch-wave modulated photonic crystals, we show creation of effective magnetic fields for photons in conventional dielectric continua for the first time, via Floquet band engineering. By controlling the phase and wavevector of Bloch waves, we demonstrated anomalous quantum Hall effect for light with distinct topological band features due to delocalized wave interference. Based on a cavity-free architecture, in which Bloch-wave modulations can be enhanced using guided-resonances in photonic crystals, the study here opens the door to the realization of effective magnetic fields at large scales for optical beam steering and topological light-matter phases with broken time-reversal symmetry.
