论文标题
算法阴影光谱
Algorithmic Shadow Spectroscopy
论文作者
论文摘要
我们将阴影光谱作为一种模拟器 - 敏锐的量子算法，用于使用很少的电路重复（镜头）估算能量差距，并且除了执行时间演变和测量值之外，没有额外的资源（Ancilla Qubits）。该方法建立在量子系统的每个可观察性属性必须根据相同的谐波组件演化的基本特征的基础上：我们可以通过对时间进化的量子状态进行经典的经典阴影来揭示它们，以提取大量时间周期性信号$ n_o \ propto \ propto 10^8 $，其频率对应于Hamiltonian Energion sansenniian Energion swimensensensensen heisensen nimensen insensen heisenner-inmenber insenber insenber insenber insen insen insen preisiss preisision-inmenber-inm-liminber-limiminber-l。 We provide strong analytical guarantees that (a) quantum resources scale as $O(\log N_o)$, while the classical computational complexity is linear $O(N_o)$, (b) the signal-to-noise ratio increases with the number of processed signals as $\propto \sqrt{N_o}$, and (c) spectral peak positions are immune to reasonable levels of noise.我们展示了我们在模型旋转系统和分子ch $ _2 $的激发状态圆锥形交集方面的方法，并验证我们的方法在实践中确实易于使用，在练习中易于使用，可与门噪声相配，可与新型的算法 - 误差技术相配，减轻算法的数量少于典型的量级量子，而不是典型的量子量的数量较少。最后，我们在易于获取的IBM量子计算机上测量了自旋链的高质量的，实验性的阴影光谱，在不使用任何高级误差的情况下达到了与无噪声模拟中相同的精度，并且在张量 - 最高100 Qubit Systems的Tensor-Network模拟中验证了可伸缩性。
We present shadow spectroscopy as a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) beyond performing time evolution and measurements. The approach builds on the fundamental feature that every observable property of a quantum system must evolve according to the same harmonic components: we can reveal them by post-processing classical shadows of time-evolved quantum states to extract a large number of time-periodic signals $N_o\propto 10^8$, whose frequencies correspond to Hamiltonian energy differences with Heisenberg-limited precision. We provide strong analytical guarantees that (a) quantum resources scale as $O(\log N_o)$, while the classical computational complexity is linear $O(N_o)$, (b) the signal-to-noise ratio increases with the number of processed signals as $\propto \sqrt{N_o}$, and (c) spectral peak positions are immune to reasonable levels of noise. We demonstrate our approach on model spin systems and the excited state conical intersection of molecular CH$_2$ and verify that our method is indeed intuitively easy to use in practice, robust against gate noise, amiable to a new type of algorithmic-error mitigation technique, and uses orders of magnitude fewer number of shots than typical near-term quantum algorithms -- as low as 10 shots per timestep is sufficient. Finally, we measured a high-quality, experimental shadow spectrum of a spin chain on readily-available IBM quantum computers, achieving the same precision as in noise-free simulations without using any advanced error mitigation, and verified scalability in tensor-network simulations of up to 100-qubit systems.
