量子加法的成本减半
Halving the cost of quantum addition
摘要：
我们将实现一个n位加法器所需的T门数从8n + O（1）提高到4n + O（1）。我们通过一个“临时逻辑与”结构来做到这一点，该结构使用四个T门来将两个量子位的逻辑与存储到一个辅助单元中，并使用零个T门来稍后擦除辅助单元。这种结构与琼斯的结构是等价的，只是我们的框架清楚地表明，这种技术比以前认识到的更广泛地适用。临时逻辑AND可以应用于整数运算、模运算、旋转合成、量子傅里叶变换、肖尔算法、格罗弗神谕和许多其他电路。由于T门在基于表面码的量子计算的成本中占主导地位，并且临时逻辑AND广泛适用，因此这代表了量子计算的预计成本的显著降低。除了我们的n位加法器，我们提出了一个n位控制加法器电路的T计数为8n + O（1），一个临时加法器，可以计算相同的成本作为正常的加法器，但其结果可以保持，直到它是以后不计算，而不使用T门，并讨论了一些其他的结构，其T计数的临时逻辑与改善。
英文摘要：
We improve the number of T gates needed to perform an n-bit adder from 8n + O(1) to 4n + O(1). We do so via a "temporary logical-AND" construction which uses four T gates to store the logical-AND of two qubits into an ancilla and zero T gates to later erase the ancilla. This construction is equivalent to one by Jones, except that our framing makes it clear that the technique is far more widely applicable than previously realized. Temporary logical-ANDs can be applied to integer arithmetic, modular arithmetic, rotation synthesis, the quantum Fourier transform, Shor's algorithm, Grover oracles, and many other circuits. Because T gates dominate the cost of quantum computation based on the surface code, and temporary logical-ANDs are widely applicable, this represents a significant reduction in projected costs of quantum computation. In addition to our n-bit adder, we present an n-bit controlled adder circuit with T-count of 8n + O(1), a temporary adder that can be computed for the same cost as the normal adder but whose result can be kept until it is later uncomputed without using T gates, and discuss some other constructions whose T-count is improved by the temporary logical-AND.
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