Limitations of probabilistic error cancellation for open dynamics beyond sampling overhead
Limitations of probabilistic error cancellation for open dynamics beyond sampling overhead
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DOI：
10.1103/physreva.109.012431
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发表时间：
2023-08
影响因子：
2.9
通讯作者：
Yue-Chi Ma;M. Kim
中科院分区：
文献类型：
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作者：
Yue-Chi Ma;M. Kim
动力学的量子模拟是NISQ时代的一个重要目标，其中量子误差缓解可能是修正或消除噪声影响的可行途径。由于量子误差在电路深度上呈指数级变化，因此对量子误差抑制的研究主要集中在资源开销上。概率误差抵消等方法依赖于将演化离散成有限时间步长，并在每个时间步长之后应用缓解层，仅修改噪声部分，而不依赖于任何哈密顿。即使实现了理想的误差抑制，这也可能会在仿真结果中导致类似Trotter的误差，这意味着样本数量被视为无穷大。在这里，我们分析前面提到的错误，这些错误以前在很大程度上被忽视了。我们表明，它们是由要模拟的开放动力学的么正部分、装置噪声部分和噪声部分的超算符间的对易关系决定的。我们包括数字量子模拟和模拟量子模拟设置，并考虑通过精确地反转噪声通道并通过在时间步长中将其近似到一阶来定义理想的误差抑制图。我们以单量子比特玩具模型为例对我们的发现进行了数值验证。我们的结果说明了以逐步方式将概率误差抵消应用于连续动力学的基本局限性，从而激励了对真正的时间连续误差抵消方法的研究。
Quantum simulation of dynamics is an important goal in the NISQ era, within which quantum error mitigation may be a viable path towards modifying or eliminating the effects of noise. Most studies on quantum error mitigation have been focused on the resource cost due to its exponential scaling in the circuit depth. Methods such as probabilistic error cancellation rely on discretizing the evolution into finite time steps and applying the mitigation layer after each time step, modifying only the noise part without any Hamiltonian-dependence. This may lead to Trotter-like errors in the simulation results even if the error mitigation is implemented ideally, which means that the number of samples is taken as infinite. Here we analyze the aforementioned errors which have been largely neglected before. We show that, they are determined by the commutating relations between the superoperators of the unitary part, the device noise part and the noise part of the open dynamics to be simulated. We include both digital quantum simulation and analog quantum simulation setups, and consider defining the ideal error mitigation map both by exactly inverting the noise channel and by approximating it to the first order in the time step. We take single-qubit toy models to numerically demonstrate our findings. Our results illustrate fundamental limitations of applying probabilistic error cancellation in a stepwise manner to continuous dynamics, thus motivating the investigations of truly time-continuous error cancellation methods.