论文标题
通过矩阵产品运营商缓解量子错误
Quantum error mitigation via matrix product operators
论文作者
论文摘要
在嘈杂的中间尺度量子（NISQ）设备的时代，可控硬件量子位的数量不足以实现量子误差校正（QEC）。作为替代方案，量子误差缓解（QEM）可以通过重复实验和数据后处理来抑制测量结果中的错误。误差缓解的典型技术，例如准概率分解方法，忽略了不同门之间的相关误差。在这里，我们基于量子电路的矩阵产品运算符（MPO）表示QEM方法，该量子电路可以用多项式复杂性来表征噪声通道。我们的技术在$ \ rm {depth} = 20 $完全平行的量子电路上，最多为$ n_q = 20 $ QUBITS进行本地和全局噪声。对于噪声通道，只有小债券尺寸$ d^{\ prime} = 1 $，电路误差减少了几次。 MPO表示会提高建模噪声的准确性而无需消耗更多的实验资源，从而提高了QEM性能并扩大其应用范围。我们的方法希望将其应用于更高量和更深深度的更高维度的电路。
In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors in measurement results via repeated experiments and postprocessing of data. Typical techniques for error mitigation, e.g., the quasi-probability decomposition method, ignore correlated errors between different gates. Here, we introduce a QEM method based on the matrix product operator (MPO) representation of a quantum circuit that can characterize the noise channel with polynomial complexity. Our technique is demonstrated on a $\rm{depth}=20$ fully parallel quantum circuit of up to $N_q=20$ qubits undergoing local and global noise. The circuit error is reduced by several times with only a small bond dimension $D^{\prime} = 1$ for the noise channel. The MPO representation increases the accuracy of modeling noise without consuming more experimental resources, which improves the QEM performance and broadens its scope of application. Our method is hopeful of being applied to circuits in higher dimensions with more qubits and deeper depth.
