Quantum Fan-out is Powerful

Peter Høyer, Robert Špalek · 2005 · Theory of Computing 1(1), 81-103

| 编号 QM007 | 主题 模运算与乘法 | 链接 DOI 10.4086/toc.2005.v001a005 |

摘要

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We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by ${\mathrm{QNC}}_{\mathrm{f}}^0$) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[t], and Counting. Classically, we need logarithmic depth even if we can use unbounded fan-in gates. If we allow arbitrary one-qubit gates instead of a fixed basis, then these circuits can also be made exact in log-star depth. Sorting, arithmetic operations, phase estimation, and the quantum Fourier transform with arbitrary moduli can also be approximated in constant depth.

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