A classification of the quantum mechanical measurements

Gerd Christian Krizek

Galina A. Nemova

Eiji Konishi

We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their nonunitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.

Qingshan Wu, Wenjie Liu, Xinran Li +2 more

With the increasing scale of data and complexity of problems, some researchers have explored the integration of parameterized quantum circuits (PQCs) within convolutional neural networks (CNNs) as a means to enhance algorithmic performance. However, in most current QCNN models, a single topological structure for quantum kernels (qkernels) is adopted and only one qubit of qkernels is measured, both of which may limit the model's performance. To solve these problems, a novel multi-topology quantum convolutional neural networks with qubit-measurement attention for image classification is proposed. In order to enhance the capability of feature extraction, a multi-topology PQCs strategy is proposed, i.e., we adopt the different topology PQCs to construct quantum convolutional layers. In addition, a qubit-measurement attention mechanism is designed to mitigate the significant loss of entanglement information during the measurement phase. Specifically, each qubit in the qkernel is measured to generate a local feature map, and the weight of each local feature map is then calculated, resulting in the final feature map. Nine image classification experiments conducted on CIFAR-10 demonstrate that our model outperforms the state-of-the-art QCNN model, achieving a improvement of 11.7% on ten categories classification. Our model not only introduces a new approach for constructing QCNNs but also provides valuable reference for designing attention mechanisms tailored to quantum computing.

Eugene Paul Wigner, Mutsuo M. Yanase

Gerd Christian Krizek

A physical theory consists of the mathematical formalism and an interpretation, which contains the definition of symbols, measurement assignments, concepts and principles, and an ontology. We present a scheme to classify these different levels of a physical theory and apply it to Newtonian Mechanics and the interpretations of Quantum Mechanics. We show that this classification scheme is embedded in the methodology of philosophy of science. With this scheme, different interpretations of Quantum Mechanics can be compared concerning the formalism and the used conceptions, and it serves as a guidance to identify ontological entities and reality conceptions in the different interpretations. Inspired by the commitments on the ontological level, we propose two heuristics concerning ontological statements.