量子相位估计的精确误差界
A Precise Error Bound for Quantum Phase Estimation
摘要：
量子相位估计是量子计算领域的关键算法之一，但迄今为止，只得到了误差概率的近似表达式。我们重新审视了这些推导，发现通过保证误差定义的对称性，可以找到一个精确的公式。这种新的方法也可能对解决量子计算中的其他相关问题有价值，其中计算出预期的误差。还开发了公式的两种特殊情况的表达式，在量子计算机中的量子位数接近无穷大的极限中，以及在为了提高可靠性而额外添加的量子位数接近无穷大的极限中。它被发现，这个公式是有用的，在验证计算机模拟的相位估计过程中，并在避免高估所需的量子比特的数量，以达到一个给定的可靠性。因此，这个公式提高了量子计算机设计的精度。
英文摘要：
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.
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