Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, the quantum error-correcting code achieving the best possible precision can be found by solving a semidefinite program. We also show that noiseless ancilla are not needed when the signal Hamiltonian and the error operators commute. Finally we provide two explicit, archetypal examples of quantum sensors: qubits undergoing dephasing and a lossy bosonic mode.
A feature extraction algorithm based on spectral clustering with adaptive multiparameters is proposed for synthetic aperture radar automatic target recognition (SAR-ATR). Spectral clustering has been widely applied in computer vision for its good performance. Meanwhile, the spectral mapping step in it has the property of feature space transformation. Spectral clustering based target feature extraction for SAR-ATR is constructed according to the framework of out-of-sample extensions in weighted kernel principal component analysis. To avoid the scaling parameter selection in spectral feature analysis (SFA) and eliminate the influence of scaling parameter on feature extraction performance as well, the multiple scaling parameters are calculated adaptively by local neighborhoods. Because the local statistics of the neighborhood of each point are taken into consideration, its performance is better than using only one fixed parameter. Based on the extracted features, target recognition is performed by the support vector machine for its good generalization capability. The experimental results show that the multiparameter SFA outperforms the principal component analysis, kernel principal component analysis and SFA with the selected scaling parameter for SAR target recognition in terms of recognition accuracy.
Graph cut criterion has been proven to be robust and applicable in clustering problems. In this paper the graph cut
criterion is applied to construct a supervised dimensionality reduction. A new graph cut, scaling cut, is proposed based on
the classical normalized cut. Scaling cut depicts the relationship between samples, which makes it can handle the
heteroscedastic and multimodel data in which LDA fails. Meanwhile, the solution to scaling cut is global optimal for it is
a generalized eigenvalue problem. To obtain a more reasonable projection matrix and reduce the computational
complexity as well, the localized k-nearest neighbor graph is introduced in, which leads to equivalent or better results
compared with scaling cut.