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Due to linearity, vectors can be defined in any number of dimensions, as each component of the vector acts on the function separately. One mathematical example is the del operator, which is itself a vector (useful in momentum-related quantum operators, in the table below). An operator in n-dimensional space can be written:
In quantum mechanics, a complete set of commuting observables (CSCO) is a set of commuting operators whose common eigenvectors can be used as a basis to express any quantum state. In the case of operators with discrete spectra, a CSCO is a set of commuting observables whose simultaneous eigenspaces span the Hilbert space and are linearly ...
Quantum Computation Language (QCL) is one of the first implemented quantum programming languages. [1] The most important feature of QCL is the support for user-defined operators and functions. Its syntax resembles the syntax of the C programming language and its classical data types are similar to primitive data types in C.
A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common abbreviation is ħ = h /2 π , also known as the reduced Planck constant or Dirac constant . Quantity (common name/s)
The rotation operator gates (), and () are the analog rotation matrices in three Cartesian axes of SO(3), [c] along the x, y or z-axes of the Bloch sphere projection. As Pauli matrices are related to the generator of rotations, these rotation operators can be written as matrix exponentials with Pauli matrices in the argument.
In quantum mechanics, an observable is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value.
Arbitrary Clifford group element can be generated as a circuit with no more than (/ ()) gates. [6] [7] Here, reference [6] reports an 11-stage decomposition -H-C-P-C-P-C-H-P-C-P-C-, where H, C, and P stand for computational stages using Hadamard, CNOT, and Phase gates, respectively, and reference [7] shows that the CNOT stage can be implemented using (/ ()) gates (stages -H- and -P ...
In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles. The following is in bra–ket notation : The number operator acts on Fock space .