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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]
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 ...
A reversible gate is a reversible function on n-bit data that returns n-bit data, where an n-bit data is a string of bits x 1,x 2, ...,x n of length n. The set of n-bit data is the space {0,1} n, which consists of 2 n strings of 0's and 1's. More precisely: an n-bit reversible gate is a bijective mapping f from the set {0,1} n of n-bit data ...
The classical bits control if the 1-qubit X and Z gates are executed, allowing teleportation. [ 1 ] By moving the measurement to the end, the 2-qubit controlled -X and -Z gates need to be applied, which requires both qubits to be near (i.e. at a distance where 2-qubit quantum effects can be controlled), and thus limits the distance of the ...
[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.