Quantum Matrices Using Quantum Gates

Hiu Yung Wong

Hiu Yung Wong

Hiu Yung Wong

Nikita Kolganov, AN. MOROZOV

Manu Mitra

Quantum mechanics explains the behavior of matter and its movement with energy in the scale of atoms and subatomic particles. In quantum circuits there are many gates such as Hadamard Gate, Pauli Gates, many more gates for half turns, quarter turns, eighth turns, sixteenth turns and so on, rest for spinning, parametrized etc. Linear operators in general and quantum mechanics can be represented in the form of vectors and in turn can be viewed as matrices format because linear operators are totally equivalent with the matrices view point. This paper discloses creation of various quantum matrices using Quantum bits. Square, Identity and Transposition of matrices are performed considering whole process in entanglement. Angle, phase, coordinates, magnitude, complex numbers and amplitude has been noted and documented in this paper for further research.

Pedro Juan Roig, Salvador Alcaraz, Katja Gilly +2 more

Quantum computing fundamentals are based on Hilbert spaces and linear algebra, which allows to describe quantum gates as matrix representations. In this paper, a matrix approach is taken in order to analyze basic quantum circuits, composed of basic quantum gates of 1, 2, and 3 qubits. The most common cases of all those gates are analyzed. One-qubit gates are expressed as 2x2 matrices, accounting for a rotation around a determined axis. Two-qubit gates are described as 4x4 matrices, standing for controlled gates. Three-quibit gates are defined as 8x8 matrices, extending the concept of controlled gates and rotations.