【講題】From Schrödinger’s Cat to Quantum Channels: How Mathematics Shapes Quantum Reality

【演講時間】11月14日(星期五)下午1點30分  

【演講地點】清華大學校本部第二綜合大樓B側8樓A813室

【摘要】

The rise of quantum technology has redefined the very notion of computation, extending it beyond the traditional Turing framework. The principles of superposition and entanglement enable quantum algorithms to operate within exponentially large Hilbert spaces. To truly understand the nature and limitations of quantum computation, however, one must return to its mathematical foundations. This talk presents quantum computation from a mathematical perspective, starting with the core model of qubits and quantum gates as composable linear mappings. Simple circuit examples will illustrate how the linear algebraic structure underlies quantum algorithms. The discussion then extends to the concept of quantum channels—completely positive and trace-preserving (CPTP) maps—which describe the dynamics of open quantum systems under noise. Through the Choi–Jamiołkowski isomorphism and the diamond-norm distance, we will examine the mathematical conditions for reversibility and error correction in quantum processes. Finally, I will introduce recent research on the quantum channels and the quasi-inverse recovery mapping.