Abstract
Significant efforts are being directed towards developing a quantum annealer capable of solving combinatorial optimization problems. The challenges are Hamiltonian programming and large-scale implementations. Here we report quantum annealing demonstration of Ising Hamiltonians programmed with up to $N=22$ spins mapped on various Cayley tree graphs. Experiments are performed with a Rydberg-atom quantum simulator, in which rubidium single atoms are arranged in three dimensional space in such a way that their Rydberg atoms and blockaded strong couplings respectively represent the nodes and edges of each graph. Three different Cayley-tree graphs of $Z=3$ neighbors and of up to $S=4$ shells are constructed, and their ground-state phases and N\'{e}el's order formations are probed. In good agreement with model calculations, the anti-ferromagnetic phase in regular Cayley trees and frustrated competing ground-states in a dual-center Cayley tree are directly observed. This demonstrates the possibilities of high-dimensional qubit connection programming in quantum simulators.
Highlights
INTRODUCTIONQuantum simulations have received significant attention because quantum annealing in particular has the potential to solve complex computational problems which are often intractable with nonquantum computational methods [1,2,3,4]
In recent years, quantum simulations have received significant attention because quantum annealing in particular has the potential to solve complex computational problems which are often intractable with nonquantum computational methods [1,2,3,4]
While many efforts in quantum annealing are being focused on large-scale implementations [16,17,18,19,20] toward quantum speedup [21,22,23,24], here, we explore the possibility of high-dimensional qubit connectivities
Summary
Quantum simulations have received significant attention because quantum annealing in particular has the potential to solve complex computational problems which are often intractable with nonquantum computational methods [1,2,3,4]. In the context relevant to this paper, Rydberg-atom quantum simulators [28,29] draw attention because of their high tunability in qubit connectivities [30,31,32,33,34] as well as manybody controllability in adiabatic processes [35,36,37,38,39]. Cayley trees are homogeneous and isotropic tree graphs of a fixed number of edges and no loop [40,41] Their infinite version is a Bethe lattice, widely used in various physics areas as a fundamental theoretical platform, often providing exactly solvable models in classical and quantum problems [42].
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