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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]
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 ...
[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]
A well known example of a two-state system is the spin of a spin-1/2 particle such as an electron, whose spin can have values +ħ/2 or −ħ/2, where ħ is the reduced Planck constant. The two-state system cannot be used as a description of absorption or decay, because such processes require coupling to a continuum.
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.
The purity of a normalized quantum state satisfies , [1] where is the dimension of the Hilbert space upon which the state is defined. The upper bound is obtained by tr ( ρ ) = 1 {\displaystyle \operatorname {tr} (\rho )=1\,} and tr ( ρ 2 ) ≤ tr ( ρ ) {\displaystyle \operatorname {tr} (\rho ^{2})\leq \operatorname {tr} (\rho ...
A qubit is a two-level system, and when we measure one qubit, we can have either 1 or 0 as a result. One corresponds to odd parity, and zero corresponds to even parity. This is what a parity check is. This idea can be generalized beyond single qubits. This can be generalized beyond a single qubit and it is useful in QEC.
The quantum volume of a quantum computer was originally defined in 2018 by Nikolaj Moll et al. [10] However, since around 2021 that definition has been supplanted by IBM's 2019 redefinition. [ 11 ] [ 12 ] The original definition depends on the number of qubits N as well as the number of steps that can be executed, the circuit depth d