Adiabatic quantum computation with trapped ions

Abstract: Quantum computers are expected to provide solutions to a variety of difficult problems that are intractable in classical computers. One challenging problem is to find ground states of a non-trivial Hamiltonian, which is classically demanding because of the exponentially increasing Hilbert-space of the Hamiltonian. Adiabatic method, which begins with a ground-state of a simple Hamiltonian and slowly evolves to the non-trivial Hamiltonian of interest, is one promising way to find the ground state. A few experimental demonstrations of the adiabatic preparation have been reported with a small number of effective spins, in particular, with trapped ions-qubits [1,2]. However, these realizations have not reached to the true ground-state due to couplings of spin-spin interactions to vibrational modes [3]. Also the interactions have been limited to near uniform regime [2]. Here, we report the adiabatic preparation of the true ground states of the transverse Ising models with programmable interactions with up to four spins. We adopt the digital realization of the adiabatic evolution to completely decouple the spin-spin interactions to phonons. We also apply the global gate-scheme [4] to generate arbitrary pre-programed interaction-geometry among spins. Our experimental demonstrations can be extended further to a larger number of spin-systems and applied to other computationally complex problems. [1] K. Kim, et al., “Quantum simulation of frustrated Ising spins with trapped ions,” Nature 465, 590 (2010) [2] C. Monroe, et al., “Programmable Quantum Simulations of Spin Systems with Trapped Ions,” arXiv:1921.07845 (2019). [3] C.-C. Joseph Wang, and J. K. Freericks, “Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions,” Phys. Rev. A 86, 032329 (2012). [4] Yao Lu, Shuaining Zhang, Kuan Zhang, et al., “Global