Matrix Quantum Computing and Matrix Quantum Information

David Peter Divincenzo

Wang Xiao-hong

We introduce some important matrices and their applications in quantum computation and quantum information,including density matrix,unitary matrix,etc.

康弘 都倉

Jincheng Zhang

Quantum hidden matrix computation (QHM) is a promising approach to quantum computing, offering the potential for solving complex problems beyond the reach of classical computers. This paper presents a theoretical framework for QHM, demonstrating a fundamental relationship between the computational complexity of quantum hidden matrices and the number of qubits employed. We propose a novel approach to representing quantum information as a quantum state, and subsequently, establish a linear relationship between the complexity of these states and the number of qubits. This relationship provides a basis for designing efficient quantum algorithms. The core mechanism centers on the concept of a 'quantum information representation' and its associated computational complexity. We offer a detailed analysis of this representation, demonstrating a significant reduction in computational complexity with increased qubit count, paving the way for practical implementations. This work represents a significant advancement in the field, offering a potential path towards significantly more efficient quantum computations.

Michael F. Insana

Quantum computing (QC) is an exciting new technology that completes the text with an application that relies heavily on the mathematics of linear algebra. There is more to explain than the conversion of common matrix notation into Dirac bra-ket notation. There is also the bizarre world of quantum physics that is inspiring a range of quantum information technologies. Qubits and their entangled superposition states are introduced to show that the “quantum advantage” stems from qubits storing exponentially more information that can be processed at exponentially faster rates. The process of preparing, modifying, and measuring qubit states is explained. Linear algebra skills are exercised by representing QC coding through the application of unitary operators to qubit states. QC algorithms are designed by diagramming quantum circuits, casting those circuits into sequences of operators applied to qubit states, and converting the operators into matrix forms. These are the tools of QC. Several algorithms that demonstrate a range of computational tasks from simple arithmetic through quantum Fourier analysis complete the chapter.

Chiara Macchiavello, G. Massimo Palma, Anton Zeilinger