Superposition as Memory: Unlocking Quantum Automatic Complexity
نویسنده
چکیده
We define the semi-classical quantum automatic complexity Qs(x) of a word x as the infimum in lexicographic order of those pairs of nonnegative integers (n, q) such that there is a subgroup G of the projective unitary group PU(n) with |G| ≤ q and with U0, U1 ∈ G such that, in terms of a standard basis {ek} and with Uz = ∏ k Uz(k), we have Uxe1 = e2 and Uye1 6= e2 for all y 6= x with |y| = |x|. We show that Qs is unbounded and not constant for strings of a given length. In particular, Qs(0 1) ≤ (2, 12) < (3, 1) ≤ Qs(0 1) and Qs(0 ) ≤ (2, 121).
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