Properties (57)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:physicist
|
| gptkbp:application |
Used in quantum mechanics.
Used in quantum computing. |
| gptkbp:characteristics |
They are used in the study of quantum phase transitions.
They are used in the formulation of quantum mechanics. They are used in the study of quantum entanglement measures. They are used in the implementation of quantum error correction. They are used in the analysis of quantum algorithms. They are used in the formulation of quantum thermodynamics. Eigenvalues are complex numbers with absolute value 1. They are used in the simulation of quantum systems. Their inverse is equal to their adjoint. They are closed under composition. They are continuous functions. They are essential for quantum state manipulation. They are invertible. They are norm-preserving. They are used in quantum cryptography. They are used in quantum measurement theory. They are used in quantum state discrimination. They are used in quantum teleportation. They are used in the analysis of quantum chaos. They are used in the analysis of quantum dynamics. They are used in the design of quantum circuits. They are used in the study of quantum control. They are used in the study of quantum information. They are used in the study of quantum networks. They are used in the study of quantum optics. They are used in the study of quantum simulations. They can be expressed as a product of rotations. They can be represented by unitary matrices. They can be represented in matrix form. They can be used to describe reversible processes. They can be used to describe symmetries. They can be used to represent quantum gates. They have a determinant of 1 or -1. They preserve the norm of vectors. They are related to the concept of quantum entanglement. They can be used to describe time evolution in quantum mechanics. They can be represented in terms of exponential functions. They are used in the formulation of quantum field theory. They are used in the study of quantum information theory. They are used in the study of quantum statistical mechanics. They are used in the analysis of quantum coherence. They are used in the analysis of quantum correlations. They are used in the formulation of quantum algorithms. |
| gptkbp:defines |
Operators_that_preserve_the_inner_product_in_a_Hilbert_space.
|
| gptkbp:examples |
The identity operator.
The rotation operator in quantum mechanics. The_Fourier_transform. The_Pauli_matrices. |
| https://www.w3.org/2000/01/rdf-schema#label |
Unitary Operators
|
| gptkbp:relationship |
Related to normal operators.
They form a group under multiplication. Related_to_Hermitian_operators. |
| gptkbp:result |
The spectral theorem applies to unitary operators.
They can be diagonalized by a unitary transformation. |