Even with the recent rapid developments in quantum hardware, noise remains the biggest challenge for the practical applications of any near-term quantum devices. Full quantum error correction cannot be implemented in these devices due to their limited scale. Therefore instead of relying on engineered code symmetry, symmetry verification was developed which uses the inherent symmetry within the physical problem we try to solve. In this article, we develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes beyond symmetry verification, enabling us to achieve different balances between the estimation bias and the sampling cost of the scheme. We show that certain symmetry expansion schemes can achieve a smaller estimation bias than symmetry verification through cancellation between the biases due to the detectable and undetectable noise components. A practical way to search for such a small-bias scheme is introduced. By numerically simulating the Fermi-Hubbard model for energy estimation, the small-bias symmetry expansion we found can achieve an estimation bias 6 to 9 times below what is achievable by symmetry verification when the average number of circuit errors is between 1 to 2. The corresponding sampling cost for random shot noise reduction is just 2 to 6 times higher than symmetry verification. Beyond symmetries inherent to the physical problem, our formalism is also applicable to engineered symmetries. For example, the recent scheme for exponential error suppression using multiple noisy copies of the quantum device is just a special case of symmetry expansion using the permutation symmetry among the copies.

中文翻译：

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使用对称扩展的量子误差缓解

即使最近量子硬件发展迅速，噪声仍然是任何近期量子设备实际应用的最大挑战。由于规模有限，无法在这些设备中实现全量子纠错。因此，不是依赖于工程代码的对称性，而是开发了对称性验证，它使用我们试图解决的物理问题中的固有对称性。在本文中，我们开发了一个名为对称扩展的通用框架，它提供了除对称验证之外的广泛的基于对称的错误缓解方案，使我们能够在方案的估计偏差和采样成本之间实现不同的平衡。我们表明，由于可检测和不可检测的噪声分量，某些对称扩展方案可以通过消除偏差之间的偏差来实现比对称验证更小的估计偏差。介绍了一种搜索这种小偏置方案的实用方法。通过对 Fermi-Hubbard 能量估计模型进行数值模拟，我们发现的小偏置对称扩展可以实现比对称验证可实现的估计偏置低 6 到 9 倍，当电路错误的平均数量在 1 到 2 之间时。随机散粒噪声降低的相应采样成本仅比对称验证高 2 到 6 倍。除了物理问题固有的对称性之外，我们的形式主义也适用于工程对称性。例如，