arXiv quant-ph/01121792001-12quant-ph

保守量子计算

Conservative Quantum Computing

Masanao Ozawa

备注：: 5 pages, RevTex. Corrected to include a new statement that for bosonic ancillae the lower bound of the error probability is inversely proportional to the average number of photons, kindly suggested by Julio Gea-Banacloche
发表信息：: Phys. Rev. Lett. 89, 057902(1--4) (2002).
DOI：: 10.1103/PhysRevLett.89.057902

摘要：

守恒定律限制了基本量子逻辑门的物理实现的准确性。如果计算基由自旋分量表示，并且物理实现遵循角动量守恒定律，则任何物理上可实现的尺寸小于n量子位的酉算子都不能在错误概率1/（4n^2）内实现受控非门，其中尺寸被定义为计算量子位和辅助量子位的总数。一个类似的限制玻色子的附属也得到了显示的错误概率的下限是成反比的平均光子数。任何一组通用门都不可避免地服从一个相关的限制，错误概率为O（1/n^2）$。为了避免守恒律的上述或有关限制，建议计算基应选择与可加守恒量交换的基。

英文摘要：

Conservation laws limit the accuracy of physical implementations of elementary quantum logic gates. If the computational basis is represented by a component of spin and physical implementations obey the angular momentum conservation law, any physically realizable unitary operators with size less than n qubits cannot implement the controlled-NOT gate within the error probability 1/(4n^2), where the size is defined as the total number of the computational qubits and the ancilla qubits. An analogous limit for bosonic ancillae is also obtained to show that the lower bound of the error probability is inversely proportional to the average number of photons. Any set of universal gates inevitably obeys a related limitation with error probability O(1/n^2)$. To circumvent the above or related limitations yielded by conservation laws, it is recommended that the computational basis should be chosen as the one commuting with the additively conserved quantities.

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