We propose a variational quantum eigensolver (VQE) algorithm that uses a fault-tolerant (FT) gate-set, and is hence suitable for implementation on a future error-corrected quantum computer. VQE quantum circuits are typically designed for near-term, noisy quantum devices and have continuously parameterized rotation gates as the central building block. On the other hand, an FT quantum computer (FTQC) can only implement a discrete set of logical gates, such as the so-called Clifford+T gates. We show that the energy minimization of VQE can be performed with such an FT discrete gate-set, where we use the Ross–Selinger algorithm to transpile the continuous rotation gates to the error-correctable Clifford+T gate-set. We find that there is no loss of convergence when compared to the one of parameterized circuits if an adaptive accuracy of the transpilation is used in the VQE optimization. State preparation with VQE requires only a moderate number of T-gates, depending on the system size and transpilation accuracy. We demonstrate these properties on emulators for two prototypical spin models with up to 16 qubits. This is a promising result for the integration of VQE and more generally variational algorithms in the emerging FT setting, where they can form building blocks of the general quantum algorithms that will become accessible in an FTQC.

中文翻译：

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一种有限T深度的容错变分量子算法


我们提出了一种使用容错（FT）门集的变分量子本征求解器（VQE）算法，因此适合在未来的纠错量子计算机上实现。 VQE 量子电路通常是为近期、嘈杂的量子器件而设计的，并以连续参数化的旋转门作为中心构建块。另一方面，FT 量子计算机（FTQC）只能实现一组离散的逻辑门，例如所谓的 Clifford+T 门。我们证明了 VQE 的能量最小化可以用这样的 FT 离散门集来执行，其中我们使用 Ross-Selinger 算法将连续旋转门转换为可纠错的 Clifford+T 门集。我们发现，如果在 VQE 优化中使用转译的自适应精度，与参数化电路相比，不会出现收敛损失。使用 VQE 进行状态准备仅需要中等数量的 T 门，具体取决于系统大小和转译精度。我们在模拟器上展示了两个最多 16 个量子位的典型自旋模型的这些属性。对于在新兴 FT 设置中集成 VQE 和更普遍的变分算法来说，这是一个有前途的结果，它们可以形成通用量子算法的构建块，而这些算法将在 FTQC 中变得可用。