On the computational power of constant-depth quantum circuits with gates for addition
نویسندگان
چکیده
We investigate a class QNC(ADD) that is QNC with gates for addition of two binary numbers, where QNC is a class consisting of quantum operations computed by constant-depth quantum circuits. We show that QNC(ADD) = QAC(PAR) = QAC(MUL), where QAC(PAR) and QAC(MUL) are QAC with gates for parity and multiplication respectively, and where QAC is QNC with Toffoli gates of arbitrary fan-in. In the classical setting, similar relationships do not hold. These relationships suggest that QNC QNC(ADD); that is, the use of gates for addition increases the computational power of constant-depth quantum circuits. To prove QNC QNC(ADD), we characterize it by the one-wayness of a permutation that is constructed explicitly. We conjecture that the permutation is one-way, which implies QNC QNC(ADD).
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