We investigate the counterparts of random walks in universal quantum computing and their implementation using standard quantum circuits. Quantum walks have been recently well investigated for traversing graphs with certain oracles. We focus our study on traversing a 1D graph, namely a circle, and show how to implement a discrete-time quantum walk in quantum circuits built with universal CNOT and single qubit gates. We review elementary quantum gates and circuit decomposition techniques and propose a generalized version of all CNOT-based circuits of the quantum walk. We simulated these circuits on five different qubits IBM-Q quantum devices. This quantum computer has nonperfect gates based on superconducting qubits, and, therefore, we analyzed the impact of the CNOT errors and CNOT-depth on the fidelity of the circuit.

中文翻译：

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圆形图上的离散时间量子游走：门深度和误差的模拟和影响

我们研究了通用量子计算中随机游走的对应物及其使用标准量子电路的实现。最近已经很好地研究了量子游走以遍历具有某些预言的图。我们将研究重点放在遍历一维图（即圆）上，并展示如何在使用通用 CNOT 和单量子比特门构建的量子电路中实现离散时间量子游走。我们回顾了基本的量子门和电路分解技术，并提出了所有基于 CNOT 的量子行走电路的通用版本。我们在五个不同的量子位 IBM-Q 量子设备上模拟了这些电路。这台量子计算机具有基于超导量子位的非完美门，因此，我们分析了 CNOT 误差和 CNOT 深度对电路保真度的影响。