多寄存器Shor因子分解算法及量子计算机的认证问题
On Shor's Factoring Algorithm with More Registers and the Problem to Certify Quantum Computers
摘要：
Shor的因子分解算法使用两个量子寄存器。通过引入更多的寄存器，我们表明，在这些寄存器中的测量数是相同的预测量状态，应该是相等的，如果原来的Shor的复杂性参数是健全的。这与第二寄存器具有$r$可能的测量值的论点相矛盾。有一个匿名的评论认为，这些寄存器中的状态是纠缠在一起的。如果是这样的话，涉及多个量子寄存器的纠缠就不能用EPR对等机制来解释。鉴于这种特殊的纠缠尚未被提及和研究，我们认为Shor算法在多项式时间内运行的说法需要更多的物理验证。我们还讨论了量子计算机的认证问题。
英文摘要：
Shor's factoring algorithm uses two quantum registers. By introducing more registers we show that the measured numbers in these registers which are of the same pre-measurement state, should be equal if the original Shor's complexity argument is sound. This contradicts the argument that the second register has $r$ possible measured values. There is an anonymous comment which argues that the states in these registers are entangled. If so, the entanglement involving many quantum registers can not be interpreted by the mechanism of EPR pairs and the like. In view of this peculiar entanglement has not yet been mentioned and investigated, we think the claim that the Shor's algorithm runs in polynomial time needs more physical verifications. We also discuss the problem to certify quantum computers.
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