论文标题
在浅量子电路中欺骗线性跨透明基准测试
Spoofing Linear Cross-Entropy Benchmarking in Shallow Quantum Circuits
论文作者
论文摘要
线性跨熵基准（线性XEB）已被用作模拟量子电路的程序的测试。给定一个带有$ n $输入和输出的量子电路$ c $，并声称的模拟器，其输出是根据$ \ \ \ {0,1 \}^n $的分布分布的，模拟器的线性xeb xeb xeb xeb是$ \ \ \ m natercal {f} q_c（x）-1 $其中$ q_c（x）$是从分发$ c | 0^n \ rangle $输出$ x $的概率。一个琐碎的模拟器（例如，均匀分布）满足$ \ Mathcal {f} _C（p）= 0 $，而Google对53 Qubit Cource $ c $ noisy量子模拟$ C $实现了$（2.24 \ pm0.21）的保真度值， 在这项工作中，我们给出了一种经典的随机算法，该算法对于给定电路$ c $ depth $ d $，HAAR随机2 Qubit Gates可以实现$ω（\ tfrac {n} {n} {l} {l} {l} {l} \ cdot 15^{ - d}）$在运行时间$ \ textsf {n fextsf {n n of time $ \ cd {n}）$。这里$ l $是$ c $的\ emph {light锥}的大小：每个输出位取决于的最大输入位数。特别是，我们获得了一种多项式时间算法，该算法可实现深度$ o（\ sqrt {\ log n}）$二维电路的$ω（1）$。据我们所知，这是超恒定深度的两个维电路的第一个结果。我们的结果可以被视为证据表明，与实现量子电路的完整模拟相比，欺骗线性XEB测试可能更容易。
The linear cross-entropy benchmark (Linear XEB) has been used as a test for procedures simulating quantum circuits. Given a quantum circuit $C$ with $n$ inputs and outputs and purported simulator whose output is distributed according to a distribution $p$ over $\{0,1\}^n$, the linear XEB fidelity of the simulator is $\mathcal{F}_{C}(p) = 2^n \mathbb{E}_{x \sim p} q_C(x) -1$ where $q_C(x)$ is the probability that $x$ is output from the distribution $C|0^n\rangle$. A trivial simulator (e.g., the uniform distribution) satisfies $\mathcal{F}_C(p)=0$, while Google's noisy quantum simulation of a 53 qubit circuit $C$ achieved a fidelity value of $(2.24\pm0.21)\times10^{-3}$ (Arute et. al., Nature'19). In this work we give a classical randomized algorithm that for a given circuit $C$ of depth $d$ with Haar random 2-qubit gates achieves in expectation a fidelity value of $Ω(\tfrac{n}{L} \cdot 15^{-d})$ in running time $\textsf{poly}(n,2^L)$. Here $L$ is the size of the \emph{light cone} of $C$: the maximum number of input bits that each output bit depends on. In particular, we obtain a polynomial-time algorithm that achieves large fidelity of $ω(1)$ for depth $O(\sqrt{\log n})$ two-dimensional circuits. To our knowledge, this is the first such result for two dimensional circuits of super-constant depth. Our results can be considered as an evidence that fooling the linear XEB test might be easier than achieving a full simulation of the quantum circuit.
