A linear-size quantum circuit for addition with no ancillary qubits
A linear-size quantum circuit for addition with no ancillary qubits
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发表时间：
2005-09
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通讯作者：
Y. Takahashi;N. Kunihiro
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作者：
Y. Takahashi;N. Kunihiro
我们构建了一个量子电路，用于添加两个n位二进制数，不使用辅助量子位。该电路基于纹波进位方法。算法的时间复杂度为O（n）。这是对Kyndham [1]关于是否可以使用纹波进位方法在没有辅助量子比特的情况下构造用于加法的线性深度量子电路的问题的肯定回答。我们还构造了量子电路，用于加法模2n，减法和比较，通过修改电路进行加法，不使用辅助量子位。
We construct a quantum circuit for addition of two n-bit binary numbers that uses no ancillary qubits. The circuit is based on the ripple-carry approach. The depth and size of the circuit are O(n). This is an affirmative answer to the question of Kutin [1] as to whether a linear-depth quantum circuit for addition can be constructed without ancillary qubits using the ripple-carry approach. We also construct quantum circuits for addition modulo 2n, subtraction, and comparison that use no ancillary qubits by modifying the circuit for addition.