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The so-called T 1 lifetime and T 2 dephasing time are a time to characterize the physical implementation and represent their sensitivity to noise. A higher time does not necessarily mean that one or the other qubit is better suited for quantum computing because gate times and fidelities need to be considered, too.
[1] [2] A logical qubit is a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit [3] subject to unitary transformations, has a long enough coherence time to be usable by quantum logic gates (c.f. propagation delay for classical logic gates). [1] [4] [5]
Example: The Hadamard transform on a 3-qubit register | . Here the amplitude for each measurable state is 1 ⁄ 2. The probability to observe any state is the square of the absolute value of the measurable states amplitude, which in the above example means that there is one in four that we observe any one of the individual four cases.
The qubit-qubit Ising coupling or Heisenberg interaction gates R xx, R yy and R zz are 2-qubit gates that are implemented natively in some trapped-ion quantum computers, using for example the Mølmer–Sørensen gate procedure. [17] [18]
A 5-qubit code is the smallest possible code that protects a single logical qubit against single-qubit errors. A generalisation of the technique used by Steane , to develop the 7-qubit code from the classical [7, 4] Hamming code , led to the construction of an important class of codes called the CSS codes , named for their inventors: Robert ...
For many years, the fields of quantum mechanics and computer science formed distinct academic communities. [1] Modern quantum theory developed in the 1920s to explain perplexing physical phenomena observed at atomic scales, [2] [3] and digital computers emerged in the following decades to replace human computers for tedious calculations. [4]
The gate is equal to the product of and gates. To show that a unitary U {\displaystyle U} is a member of the Clifford group, it suffices to show that for all P ∈ P n {\displaystyle P\in \mathbf {P} _{n}} that consist only of the tensor products of X {\displaystyle X} and Z {\displaystyle Z} , we have U P U † ∈ P n {\displaystyle UPU ...
[3] The number of dimensions of the Hilbert spaces depends on what kind of quantum systems the register is composed of. Qubits are 2-dimensional complex spaces ( C 2 {\displaystyle \mathbb {C} ^{2}} ), while qutrits are 3-dimensional complex spaces ( C 3 {\displaystyle \mathbb {C} ^{3}} ), etc.