Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
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DOI：
10.1103/physreva.98.052319
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发表时间：
2018-11-15
影响因子：
2.9
通讯作者：
Barkeshli, Maissam
中科院分区：
文献类型：
--
作者：
Lavasani, Ali;Barkeshli, Maissam
容错量子计算最有前途的途径之一是利用拓扑量子纠错码，如Z（2）表面码。逻辑量子位可以在表面代码中以各种方式编码，基于边界缺陷，空穴或体扭曲缺陷。然而，提出的容错实现的Clifford组在这些计划是有限的，往往需要不必要的开销。例如，在某些平面和空穴编码中的Clifford相位门已经被提出使用昂贵的状态注入和蒸馏协议来实现。在本文中，我们表明，在任何编码方案的逻辑量子位，我们可以容错实现完整的克利福德组使用联合测量涉及一个适当的编码逻辑辅助。这使我们能够在表面和颜色代码中提供完整Clifford群的低开销实现。它还提供了第一个提出的实现全Clifford群的双曲码。我们进一步使用我们的方法为少量的逻辑量子位提出最先进的编码方案;例如，对于代码距离d = 3，5，7，我们提出了一个使用60，160，308（分别）物理数据量子位的方案，这允许在两个逻辑量子位上实现完整的逻辑Clifford群。据我们所知，这是迄今为止的最佳方案，因此可能有助于在小型近期量子计算机中演示容错逻辑门。
One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the Z(2) surface code. Logical qubits can be encoded in a variety of ways in the surface code, based on either boundary defects, holes, or bulk twist defects. However, proposed fault-tolerant implementations of the Clifford group in these schemes are limited and often require unnecessary overhead. For example, the Clifford phase gate in certain planar and hole encodings has been proposed to be implemented using costly state injection and distillation protocols. In this paper, we show that within any encoding scheme for the logical qubits, we can fault tolerantly implement the full Clifford group by using joint measurements involving a single appropriately encoded logical ancilla. This allows us to provide low overhead implementations of the full Clifford group in surface and color codes. It also provides the first proposed implementations of the full Clifford group in hyperbolic codes. We further use our methods to propose state-of-the art encoding schemes for small numbers of logical qubits; for example, for code distances d = 3, 5, 7, we propose a scheme using 60, 160, 308 (respectively) physical data qubits, which allow for the full logical Clifford group to be implemented on two logical qubits. To our knowledge, this is the optimal proposal to date, and thus may be useful for demonstration of fault-tolerant logical gates in small near-term quantum computers.