通过使用核磁共振模拟配对哈密顿量来检查量子模拟的局限性
Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance
摘要：
量子模拟使用一个已知的量子系统来预测另一个量子系统的行为。在这种技术中出现的某些限制，但是，当应用到特定的问题，我们证明了一个算法的理论和实验研究，找到一个低的频谱的哈密顿。虽然基本量子门的数量确实与系统的大小成多项式比例，但它与期望的误差界$ε$成反比地增加。使用容错结构使这种模拟对去相干具有鲁棒性需要额外的$1/ ε$门因子。这些限制说明了使用三个量子位核磁共振系统来模拟配对哈密顿量，吴，伯德，和激光雷达提出的算法。
英文摘要：
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm to find the low-lying spectrum of a Hamiltonian. While the number of elementary quantum gates does scale polynomially with the size of the system, it increases inversely to the desired error bound $ε$. Making such simulations robust to decoherence using fault-tolerance constructs requires an additional factor of $1/ ε$ gates. These constraints are illustrated by using a three qubit nuclear magnetic resonance system to simulate a pairing Hamiltonian, following the algorithm proposed by Wu, Byrd, and Lidar.
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