期刊
PHYSICAL REVIEW A
卷 96, 期 3, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.96.032321
关键词
-
资金
- EPSRC through Centre for Doctoral Training in Delivering Quantum Technologies [EP/L015242/1]
- Networked Quantum Information Technologies (NQIT) Hub [EP/M013243/1]
- Engineering and Physical Sciences Research Council [1382632, EP/M013243/1] Funding Source: researchfish
- EPSRC [EP/M013243/1] Funding Source: UKRI
A central result in the study of quantum Hamiltonian complexity is that the k-local Hamiltonian problem is quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据