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There are two possible outcomes for the measurement of a qubit—usually taken to have the value "0" and "1", like a bit. However, whereas the state of a bit can only be binary (either 0 or 1), the general state of a qubit according to quantum mechanics can arbitrarily be a coherent superposition of all computable states simultaneously. [2]
The purpose of quantum computing focuses on building an information theory with the features of quantum mechanics: instead of encoding a binary unit of information (), which can be switched to 1 or 0, a quantum binary unit of information (qubit) can simultaneously turn to be 0 and 1 at the same time, thanks to the phenomenon called superposition.
Common quantum logic gates by name (including abbreviation), circuit form(s) and the corresponding unitary matrices. In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits.
[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]
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 density operator is a positive-semidefinite operator on the Hilbert space whose trace is equal to 1. [ 1 ] [ 2 ] For each measurement that can be defined, the probability distribution over the outcomes of that measurement can be computed from the density operator.
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 teleportion. While logically equivalent, deferring the measurement have physical implications.
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 ...