Superfast encodings for fermionic quantum simulation
Superfast encodings for fermionic quantum simulation
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DOI：
10.1103/physrevresearch.1.033033
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发表时间：
2018-10
影响因子：
4.2
通讯作者：
Kanav Setia;S. Bravyi;Antonio Mezzacapo;J. Whitfield
中科院分区：
文献类型：
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作者：
Kanav Setia;S. Bravyi;Antonio Mezzacapo;J. Whitfield
在量子计算机上模拟费米子多体系统需要将费米子自由度适当编码为量子比特。在这里，我们重新审视Kitaev和作者之一介绍的超快编码。这种编码映射一个目标费米子哈密顿量与两体相互作用的度$d$的图到量子比特模拟器哈密顿量组成的泡利运营商的重量$O（d）$。$m$费米模式的系统被映射到$n=O（md）$量子位。我们提出了广义超快编码（GSE），它需要与原始编码相同数量的量子比特，但具有更有利的性质。首先，我们描述了一个GSE，使得相应的量子码纠正任何单量子比特错误，只要相互作用图的度为$d\ge 6$。相比之下，我们证明了原来的超快编码缺乏$d\le 6$的纠错属性。其次，我们描述了一个GSE，减少了泡利重量的模拟器哈密顿量从$O（d）$到$O（\log{d}）$。GSE提供的对误差的鲁棒性和简化的模拟器哈密顿量结构可以使费米系统的模拟在近期量子器件的范围内。作为一个例子，我们应用新的编码的费米子哈伯德模型的二维晶格。
Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the Superfast Encoding introduced by Kitaev and one of the authors. This encoding maps a target fermionic Hamiltonian with two-body interactions on a graph of degree $d$ to a qubit simulator Hamiltonian composed of Pauli operators of weight $O(d)$. A system of $m$ fermi modes gets mapped to $n=O(md)$ qubits. We propose Generalized Superfast Encodings (GSE) which require the same number of qubits as the original one but have more favorable properties. First, we describe a GSE such that the corresponding quantum code corrects any single-qubit error provided that the interaction graph has degree $d\ge 6$. In contrast, we prove that the original Superfast Encoding lacks the error correction property for $d\le 6$. Secondly, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from $O(d)$ to $O(\log{d})$. The robustness against errors and a simplified structure of the simulator Hamiltonian offered by GSEs can make simulation of fermionic systems within the reach of near-term quantum devices. As an example, we apply the new encoding to the fermionic Hubbard model on a 2D lattice.