Kivlichan Ian D, McClean Jarrod, Wiebe Nathan, Gidney Craig, Aspuru-Guzik Alán, Chan Garnet Kin-Lic, Babbush Ryan
Google Inc., Venice, California 90291, USA.
Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
Phys Rev Lett. 2018 Mar 16;120(11):110501. doi: 10.1103/PhysRevLett.120.110501.
As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the fermionic swap network, we can simulate a Trotter step of the electronic structure Hamiltonian in exactly N depth and with N^{2}/2 two-qubit entangling gates, and prepare arbitrary Slater determinants in at most N/2 depth, all assuming only a minimal, linearly connected architecture. We conjecture that no explicit Trotter step of the electronic structure Hamiltonian is possible with fewer entangling gates, even with arbitrary connectivities. These results represent significant practical improvements on the cost of most Trotter-based algorithms for both variational and phase-estimation-based simulation of quantum chemistry.
随着量子架构的物理实现不断涌现，考虑量子比特之间实际连接性的算法成本变得越来越重要。我们表明，通过使用一种我们称为费米子交换网络的门排列方式，我们可以在恰好为N的深度下，用N²/2个两比特纠缠门来模拟电子结构哈密顿量的一个特罗特步，并在最多N/2的深度下制备任意斯莱特行列式，所有这些都仅假设是一个最小的、线性连接的架构。我们推测，即使具有任意连接性，使用更少的纠缠门也不可能实现电子结构哈密顿量的显式特罗特步。这些结果在基于特罗特的算法成本方面，对于量子化学的变分模拟和基于相位估计的模拟而言，都代表了显著的实际改进。
