基于浅层量子电路的共振隧穿和局域化现象的定性量子模拟
Qualitative quantum simulation of resonant tunneling and localization with the shallow quantum circuits
AI总结：
本文通过浅层量子电路研究了连续时间演化极限下的共振隧穿和局域化现象，展示了少量量子门即可实现显著量子现象的定性观察，为近期量子计算机的应用提供依据。
摘要：
在基于电路的量子计算机中，计算通过离散时间演化驱动量子门实现。精确模拟连续时间演化需要大量量子门，从而产生更多噪声。本文发现，浅层量子电路足以定性观察连续时间演化中的典型量子现象，如共振隧穿和局域化现象。我们研究了在Trotter电路中大步长下的自旋激发传播。电路由两种两量子比特门（即XY门和受控-Rx门）和单量子比特Rz门组成。Rz门的配置决定了演化结束时自旋激发的分布。我们展示了在Trotter电路中通过最多四步实现共振隧穿，通过数十步实现局域化现象。结果表明，实现某些显著量子现象的定性观察所需的电路深度远小于实现定量计算所需的深度，表明可以将定性观察应用于近期量子计算机。我们还提供了一种利用物理定律理解量子电路误差传播的方法。
英文摘要：
In a circuit-based quantum computer, the computing is performed via the discrete-time evolution driven by quantum gates. Accurate simulation of continuoustime evolution requires a large number of quantum gates and therefore suffers from more noise. In this paper, we find that shallow quantum circuits are sufficient to qualitatively observe some typical quantum phenomena in the continuous-time evolution limit, such as resonant tunneling and localization phenomena. We study the propagation of a spin excitation in Trotter circuits with a large step size. The circuits are formed of two types of two-qubit gates, i.e. XY gates and controlled- Rx gates, and single-qubit Rz gates. The configuration of the Rz gates determines the distribution of the spin excitation at the end of evolution. We demonstrate the resonant tunneling with up to four steps and the localization phenomenon with dozens of steps in Trotter circuits. Our results show that the circuit depth required for qualitative observation of some significant quantum phenomena is much smaller than that required for quantitative computation, suggesting that it is feasible to apply qualitative observations to near-term quantum computers. We also provide a way to use the physics laws to understand the error propagation in quantum circuits.
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