论文标题
使用Qubit重置的Qubit效率纠缠光谱
Qubit-efficient entanglement spectroscopy using qubit resets
论文作者
论文摘要
在NISQ设备上适合更大问题的一种策略是利用电路宽度和电路深度之间的权衡。不幸的是，这种折衷仍然限制了可拖动问题的大小，因为在噪声占主导地位之前，深度的增加通常无法实现。在这里，我们为避免这种权衡的纠缠光谱范围开发了Qubit效率的量子算法。特别是，我们开发了用于计算量子系统密度运算符的n次功率的轨迹，$ tr（ρ^n）$，（与n阶n订单n的rényi熵有关），这些量子使用量的Qubits少于任何以前的有效算法，而在噪声中实现了较大量子系统的情况下，在噪声中实现了相似的性能。我们的算法需要多个量子位独立于n，是先前算法的变体，其宽度与n成正比，渐近差。这些新算法中的关键要素是在计算过程中测量和重新初步量子集的能力，从而使我们能够重复使用量子位并增加电路深度而不会遭受通常的噪音后果。我们还将有效电路深度的概念作为标准电路深度的概括，适用于乘坐重置的电路。该工具有助于解释我们Qubit高效算法的噪声弹性，并有助于设计未来的算法。我们执行数值模拟，将我们的算法与原始变体进行比较，并表明它们在受到噪声时的性能类似。此外，我们在霍尼韦尔系统模型H0上实现了一种Qubit高效算法的实验，估计比以前的算法对N的$ tr（ρ^n）$。
One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop qubit-efficient quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the n-th power of the density operator of a quantum system, $Tr(ρ^n)$, (related to the Rényi entropy of order n) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of n, are variants of previous algorithms with width proportional to n, an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating $Tr(ρ^n)$ for larger n than possible with previous algorithms.
