The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan–Wigner transformation and the Bravyi–Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper, we discuss resource implications for the use of the Bravyi–Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems, which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi–Kitaev transformation is typically at least approximately as efficient as the canonical Jordan–Wigner transformation and results in substantially reduced gate count estimates when performing limited circuit optimizations.

中文翻译：

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量子化学量子模拟中 Bravyi–Kitaev 和 Jordan–Wigner 变换的比较

执行传统上难以处理的电子结构计算的能力通常被认为是量子计算的主要应用之一。为了支持这一目标，已经进行了大量的理论算法开发。大多数技术需要一种将电子状态和操作映射到量子位的状态和操作的方案。两种最常用的技术是 Jordan-Wigner 变换和 Bravyi-Kitaev 变换。然而，这些方案的比较以前仅限于单个小分子。在本文中，我们讨论了使用 Bravyi-Kitaev 映射方案的资源影响，特别是关于模拟所需的量子门的数量。我们认为小型系统可以在不久的将来的量子设备上进行模拟，而系统又足够大而使得经典模拟变得难以处理。我们使用 86 个分子系统来证明，使用 Bravyi-Kitaev 变换通常至少大约与规范的 Jordan-Wigner 变换一样有效，并且在执行有限的电路优化时会大大减少门数估计。