空间量子计算中中间测量的消除
Eliminating Intermediate Measurements in Space-Bounded Quantum Computation
摘要：
量子计算理论中的一个基本结果被称为“安全存储原理”，它表明，总是有可能采取量子电路并产生一个等效电路，在计算结束时进行所有测量。虽然这个过程是时间有效的，这意味着它不会在门的数量上引入大量的开销，但它使用额外的辅助量子位，因此通常不是空间有效的。人们很自然地会问，是否有可能在不增加辅助量子比特数量的情况下，将测量推迟到量子计算的最后。我们给出了一个肯定的答案，这个问题展示了一个程序，以消除所有的中间测量，同时是空间效率和时间效率。我们的方法的一个关键组成部分，这可能是独立的利益，涉及到许多标准的线性代数问题的良好条件的版本可以解决量子计算机在更小的空间比经典计算机似乎可能。
英文摘要：
A foundational result in the theory of quantum computation known as the "principle of safe storage" shows that it is always possible to take a quantum circuit and produce an equivalent circuit that makes all measurements at the end of the computation. While this procedure is time efficient, meaning that it does not introduce a large overhead in the number of gates, it uses extra ancillary qubits and so is not generally space efficient. It is quite natural to ask whether it is possible to defer measurements to the end of a quantum computation without increasing the number of ancillary qubits. We give an affirmative answer to this question by exhibiting a procedure to eliminate all intermediate measurements that is simultaneously space-efficient and time-efficient. A key component of our approach, which may be of independent interest, involves showing that the well-conditioned versions of many standard linear-algebraic problems may be solved by a quantum computer in less space than seems possible by a classical computer.
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