Marvian Iman, Lidar Daniel A
Center for Quantum Information Science and and Technology, University of Southern California, Los Angeles, California 90089, USA and Department of Physics, University of Southern California, Los Angeles, California 90089, USA.
Center for Quantum Information Science and and Technology, University of Southern California, Los Angeles, California 90089, USA and Department of Physics, University of Southern California, Los Angeles, California 90089, USA and Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA and Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA.
Phys Rev Lett. 2014 Dec 31;113(26):260504. doi: 10.1103/PhysRevLett.113.260504.
We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.
我们考虑了误差抑制方案，其中量子信息被编码到一个哈密顿量的基态子空间中，该哈密顿量由对易项之和组成。由于这样的哈密顿量存在能隙，它们被视为保护量子信息以及进行拓扑或绝热量子计算的自然候选者。然而，我们证明在双局域情形下它们不能用于此目的。通过做出能隙为无穷大这一有利假设，我们表明单格点微扰能够在这类哈密顿量的基态子空间中产生简并分裂，其与微扰大小具有相同量级，并且与相互作用格点的数量及其希尔伯特空间维度无关，就如同不存在保护哈密顿量时一样。这种分裂导致基态子空间的退相干，并且我们证明对于自然噪声模型，相干时间与简并分裂的倒数成正比。我们的证明涉及无隐藏定理的一个新版本，该版本表明量子信息不能近似隐藏在两个量子系统之间的关联中。双局域对易哈密顿量不能用于量子误差抑制的主要原因是它们的基态子空间仅具有短程（两体）纠缠。
