论文标题
逻辑阴影层析成像：有效估计错误减少的可观察结果
Logical shadow tomography: Efficient estimation of error-mitigated observables
论文作者
论文摘要
我们引入了一种技术，以估计噪声量子计算机上的错误减少期望值。我们的技术在逻辑状态下执行阴影层析成像，以产生嘈杂密度矩阵的记忆有效的经典重建。使用有效的经典后处理，可以通过将嘈杂密度矩阵的一般非线性功能投射到代码空间中来减轻错误。子空间的扩展和虚拟蒸馏可以看作是新Framekwork的特殊情况。我们表明我们的方法在量子和经典资源开销中有利。相对于需要$ o \ left（2^{n} \右）$样本的子空间扩展，以估算具有$ [[n，k]] $错误校正代码可观察到的逻辑Pauli，我们的技术仅需要$ o \左（4^{k} \ right）$。相对于虚拟蒸馏，我们的技术可以计算密度矩阵的功率，而无需其他量子状态或量子存储器。我们使用编码多达60个物理Qub的逻辑状态提出数值证据，并显示出仅$ 10^5 $样本在1％去极化噪声下的$ 10^5 $样本的快速收敛。
We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting a general nonlinear function of the noisy density matrix into the codespace. The subspace expansion and virtual distillation can be viewed as special cases of the new framekwork. We show our method is favorable in the quantum and classical resources overhead. Relative to subspace expansion which requires $O\left(2^{N} \right)$ samples to estimate a logical Pauli observable with $[[N, k]]$ error correction code, our technique requires only $O\left(4^{k} \right)$ samples. Relative to virtual distillation, our technique can compute powers of the density matrix without additional copies of quantum states or quantum memory. We present numerical evidence using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only $10^5$ samples under 1% depolarizing noise.
