Suppressing noise in physical systems is of fundamental importance. As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level. However in the noisy, intermediate-scale quantum (NISQ) era, the complexity and scale required to adopt even the smallest QEC is prohibitive: a single logical qubit needs to be encoded into many thousands of physical qubits. Here we show that, for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms) one can indeed achieve an effective exponential suppression. We take $n$ independently prepared circuit outputs to create a state whose symmetries prevent errors from contributing bias to the expected value. The approach is very well suited for current and near-term quantum devices as it is modular in the main computation and requires only a shallow circuit that bridges the $n$ copies immediately prior to measurement. Using no more than four circuit copies, we confirm error suppression below ${10}^{-6}$ for circuits consisting of several hundred noisy gates (2-qubit gate error 0.5%) in numerical simulations validating our approach.

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近期量子器件的指数误差抑制

抑制物理系统中的噪声至关重要。随着量子计算机的成熟，将采用量子纠错码 (QEC) 以将错误抑制到任何所需的水平。然而，在嘈杂的中尺度量子 (NISQ) 时代，即使是最小的 QEC 所需的复杂性和规模也令人望而却步：单个逻辑量子位需要编码成数千个物理量子位。在这里，我们表明，对于估计可观测值的期望值（几乎所有 NISQ 算法的关键）的关键情况，确实可以实现有效的指数抑制。我们采取$n$独立准备的电路输出以创建一种状态，该状态的对称性可防止错误对预期值造成偏差。该方法非常适合当前和近期的量子设备，因为它在主计算中是模块化的，并且只需要一个浅层电路来桥接$n$测量前立即复印。使用不超过四个电路副本，我们在下面确认错误抑制${10}^{-6}$ 对于由数百个噪声门（2-qubit 门误差 0.5%）组成的电路，在验证我们的方法的数值模拟中。