Gosset David, Terhal Barbara M, Vershynina Anna
Institute for Quantum Computing and Dept. of Combinatorics and Optimization, University of Waterloo, Ontario N2L 3G1, Canada.
JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, North Rhine-Westphalia, Germany.
Phys Rev Lett. 2015 Apr 10;114(14):140501. doi: 10.1103/PhysRevLett.114.140501. Epub 2015 Apr 6.
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.
我们展示了如何使用一个哈密顿量来执行通用绝热量子计算，该哈密顿量描述了二维网格上具有局部相互作用的一组粒子。哈密顿量中的单个参数作为时间的函数被绝热地改变，以模拟量子电路。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，我们界定了唯一基态之上的能隙；Koma和Nachtergaele利用其SU(2)对称性的q变形版本精确计算了这个自旋链的能隙。我们还讨论了一个相关的与时间无关的哈密顿量，Janzing已证明它能够进行通用计算。我们观察到，在大系统规模的极限情况下，时间演化等同于在杨格晶格上的精确可解量子游走。
