论文标题

固定QMA:在证明中固定一些量子的功能

Pinned QMA: The power of fixing a few qubits in proofs

论文作者

Nagaj, Daniel, Hangleiter, Dominik, Eisert, Jens, Schwarz, Martin

论文摘要

如果我们固定系统的单个量子并将其修复到特定状态,会发生什么?首先,我们表明,这可以大大增加静态问题的复杂性 - 术语类型有限类型的当地哈密顿问题的基础状态。特别是,我们表明,固定的通勤和固定的当地哈密顿问题是QMA完成的。其次,我们表明,通过经常重复测量来固定单个量子,还会导致通勤和停滞的汉密尔顿人的通用量子计算。最后,我们根据固定来讨论基态连接性(GSCON)问题的变体,并证明静态GSCON已完成QCMA。因此,我们确定了固定的计算能力的全面图片,让人联想到一个干净的量子模型的力量。

What could happen if we pinned a single qubit of a system and fixed it in a particular state? First, we show that this can greatly increase the complexity of static questions -- ground state properties of local Hamiltonian problems with restricted types of terms. In particular, we show that the Pinned commuting and Pinned Stoquastic Local Hamiltonian problems are QMA complete. Second, we show that pinning a single qubit via often repeated measurements also results in universal quantum computation already with commuting and stoquastic Hamiltonians. Finally, we discuss variants of the Ground State Connectivity (GSCON) problem in light of pinning, and show that Stoquastic GSCON is QCMA complete. We hence identify a comprehensive picture of the computational power of pinning, reminiscent of the power of the one clean qubit model.

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