A CCCZ gate performed with 6 T gates
A CCCZ gate performed with 6 T gates
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由 6 个 T 门组成的 CCCZ 门
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
N. C. Jones
中科院分区：
文献类型：
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作者：
C. Gidney;N. C. Jones
这篇短文报告了我在与Cody讨论电路优化问题时的一个偶然发现。我用Quirk [2]来演示我的想法，Cody提出了一个解决这个问题的想法，即用两个Toffolis来瞄准一个辅助系统，这样一对T门就可以抵消Toffolis相遇的地方。我尝试过类似的想法之前，并通过演示它是如何不太工作的议案，当科迪指出，CCCZ回扣突然出现在电路，尽管只有6个T门。我隔离了CCCZ，清理了电路，并生成了图1。电路工作的原因是iab cd = ii（−1）。该电路使用两个Toffolis来准备在辅助器件上的ab_bcd，其中a，B，c，d是四个量子比特的计算基值。使用四个T门而不是七个T门来计算Toffolis，以获得控制上的相位反冲。Toffolis接触的方式，取消了两个T门。在计算辅助之后，它被定相，然后使用基于测量的非计算来移除。来自托佛利斯的反冲抵消了辅助相位产生的ii分量。这只留下了（-1）项，即CCCZ。具有n > 2个控制的泡利门可以通过使用n-2个临时AND门将控制减少到控制Toffoli的一对来用4 n-4个T门执行[3]。最后一个与门和Toffoli可以用6 T CCCZ代替，节省了2个T门，将T成本降低到4 n − 6。奇怪的是，我们还没有找到任何方法来以更低的T成本执行常见操作的方式对6 T CCCZ进行优化、嵌套或泛化。6 T CCCZ电路足够简单，因此本说明可能是重新发现，但我们不知道现有技术。我们确实发现Beverland等人的表I。2019 [1]声称，|CCCZ超导态可以用六个T门来制备，这表明他们知道这种结构。然而，该表引用了一篇论文[5]，其结构使用了8个T门，而不是6个。当我们联系Beverland等人时，他们猜测表中列出的T计数很可能是错别字。假设是这样的话，我们很高兴地报告说，错别字只是超前的时间。
This short note reports a small serendipitous discovery that occurred while I was discussing a circuit optimization problem [4] with Cody. I was using Quirk [2] to demonstrate ideas, and Cody suggested an idea for how to approach the problem based on targeting one ancilla with two Toffolis so that a pair of T gates would cancel where the Toffolis met. I’d tried a similar idea before, and was going through the motions of showing how it didn’t quite work, when Cody pointed out that a CCCZ kickback had suddenly appeared in the circuit despite there only being 6 T gates. I isolated the CCCZ, cleaned up the circuit, and produced Figure 1. The circuit works because iab⊕cd = ii(−1). The circuit uses two Toffolis to prepare ab⊕ cd onto an ancilla, where a, b, c, d are the computational basis values of four qubits. The Toffolis are computed using four T gates instead of seven, to get phase kickback onto the controls. The Toffolis touch in a way that cancels two more T gates. After the ancilla is computed, it is phased and then removed using measurement based uncomputation. The kickback from the Toffolis cancels the ii components that arise from phasing the ancilla. This leaves behind only the (−1) term, which is the CCCZ. A Pauli gate with n > 2 controls can be performed with 4n − 4 T gates by using n − 2 temporary AND gates to cut the controls down to a pair controlling a Toffoli [3]. The final AND gate and the Toffoli can be replaced by a 6T CCCZ, saving 2 T gates, reducing the T cost to 4n− 6. Oddly, we’ve otherwise not found any way to iterate or nest or generalize the 6T CCCZ in a way that performs common operations with lower T costs. The 6T CCCZ circuit is simple enough that this note is likely a rediscovery, but we aren’t aware of prior art. We did find that Table I of Beverland et al. 2019 [1] claims that a |CCCZ〉 state can be prepared using six T gates, suggesting they knew the construction. However, the table references a paper [5] with a construction that uses eight T gates, not six. When we contacted Beverland et al. they guessed that the T count listed in the table was most likely a typo. Assuming that’s the case, we’re happy to report that the typo was merely ahead of its time.
影响因子：
6.7
作者：
Beverland, Michael;Campbell, Earl;Kliuchnikov, Vadym
通讯作者：
Kliuchnikov, Vadym