Notes
Equivalently, \({\mathbf {N}}{\mathbf {P}}\) is the class of the decision problems that can be verified in polynomial time, when a certificate is given. See Papadimitriou (1994) for details.
In fact, the computation tree in Fig. 5 shows that \(W^2\mid \! 0\rangle =\mid \! 0\rangle\), and it is equally easy to see that \(W^2\mid \! 1\rangle =\mid \! 1\rangle.\)
Characteristic functions \(f_g\) defined as \(f_g(g')=1\) if \(g=g'\) and 0 otherwise clearly form a basis (called the natural basis) for the function space \(G\rightarrow {\mathbb {C}}\).
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Hirvensalo, M. Interference as a computational resource: a tutorial. Nat Comput 17, 201–219 (2018). https://doi.org/10.1007/s11047-017-9654-x
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DOI: https://doi.org/10.1007/s11047-017-9654-x