Quantum computing potentially offers exponential speed-ups over classical computing for certain tasks. A central, outstanding challenge to making quantum computing practical is to achieve fault tolerance, meaning that computations of any length or size can be realized in the presence of noise. The Gottesman-Kitaev-Preskill code is a promising approach toward fault-tolerant quantum computing, encoding logical qubits into grid states of harmonic oscillators. However, for the code to be fault tolerant, the quality of the grid states has to be extremely high. Approximate grid states have recently been realized experimentally, but their quality is still insufficient for fault tolerance. Current implementable protocols for generating grid states rely on measurements of ancillary qubits combined with either postselection or feed forward. Implementing such measurements take up significant time during which the states decohere, thus limiting their quality. Here, we propose a measurement-free preparation protocol, which deterministically prepares arbitrary logical grid states with a rectangular or hexagonal lattice. The protocol can be readily implemented in trapped-ion or superconducting-circuit platforms to generate high-quality grid states using only a few interactions, even with the noise levels found in current systems.

对于某些任务，量子计算有可能比传统计算提供指数级的加速。使量子计算实用化的主要挑战是实现容错能力，这意味着可以在存在噪声的情况下实现任何长度或大小的计算。Gottesman-Kitaev-Preskill代码是一种有前途的容错量子计算方法，可以将逻辑量子比特编码为谐波振荡器的网格状态。但是，为了使代码具有容错性，网格状态的质量必须非常高。最近已经通过实验实现了近似网格状态，但是其质量仍然不足以实现容错功能。当前用于生成网格状态的可实现协议依赖于辅助量子位的测量以及后选择或前馈。进行此类测量会花费大量时间，在此期间状态会发生衰减，从而限制了它们的质量。在这里，我们提出了一种免测量的准备协议，该协议确定性地准备具有矩形或六边形格子的任意逻辑网格状态。该协议可以很容易地在陷离离子或超导电路平台中实施，以仅需很少的交互就可以生成高质量的网格状态，即使当前系统中的噪声水平也是如此。