Can I call $\{|0\rangle, |1\rangle\}$ the "standard computational basis" as it is done in linear algebra?

Question

$\newcommand{\ket}[1]{|#1\rangle}$Is there some standard computational basis defined in quantum computing? Can I just call $\{\ket{0}, \ket{1}\}$ the standard computational basis?

Answer 1

Yes, $|0\rangle$ and $|1\rangle$ is commonly called the computational basis. Some sources also call it the classical basis.

Answer 2

You can either call it the standard basis (as it can be mapped to the natural orthonormal basis of $\Bbb R^2$) or the computational basis, of the $2$-dimensional complex Hilbert space. The latter is more frequently used in the context of quantum computing, but you'll see mathematicians using the former more. Anyway, calling it the "standard computational" basis is simply redundant when you're dealing with $\Bbb C^2$, although I've seen some authors use it. For instance, check page 5 of From Qubits to Continuous-Variable Quantum Computation (Sanders et al., 2002).

Related: What is the Computational Basis?