Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.
Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.
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DOI：
10.1103/physrevlett.114.140501
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发表时间：
2014-09
影响因子：
8.6
通讯作者：
David Gosset;B. Terhal;Anna Vershynina
中科院分区：
文献类型：
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作者：
David Gosset;B. Terhal;Anna Vershynina
我们展示了如何使用哈密顿量来进行通用绝热量子计算，该哈密顿量描述了一组在二维网格上具有局部相互作用的粒子。哈密顿量中的单个参数作为时间的函数被动态地改变以模拟量子电路。我们通过将我们的模型映射到具有扭结边界条件的铁磁XXZ链上，将本征值间隙束缚在唯一基态之上;该自旋链的差距由Koma和Nachtergaele使用其SU（2）对称性的q变形版本精确计算。我们还讨论了一个相关的时间无关的哈密顿量，这是由Janzing是能够通用的计算。我们观察到，在大系统尺寸的限制下，时间演化等价于杨氏晶格上精确可解的量子行走。
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.