Probing entanglement in adiabatic quantum optimization with trapped ions

Abstract

Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.

Trapped-ion quantum simulation of excitation transport: Disordered, noisy, and long-range connected quantum networks

“…In the trapped-ion quantum simulator, controlled noise can be induced by time-dependent laser fields to realize fluctuating on-site energies ω i (t) [52,53]. A strength of the proposed trapped-ion setup is that it can realize almost arbitrary power spectra, which will allow a quantitative modeling of the structured spectra characteristic of biomolecules [14][15][16][17][18]62].…”

“…In particular, the irregular networks found in biological molecules could be designed in special trap designs such as segmented Paul traps [48] or surface traps [49], as well as by engineering the interactions via timeperiodic driving [50] or additional laser frequencies [51]. Addressable AC-Stark shifts have been shown to enable the generation of programmable disorder [39] and have been proposed for the simulation of dephasing in adiabatic quantum optimization [52]. Amplitude and phase modulations have also been used to simulate a qubit in a dephasing environment [53].…”

Hybrid annealing: Coupling a quantum simulator to a classical computer

“…The mentioned requirements to the quantum simulator are already met, for instance, in existing trapped ion experiments [20,21]. There also exist proposals how to implement NP-complete problems in an ionic quantum simulator [22,23].…”

Quantum annealing with ultracold atoms in a multimode optical resonator

“…In the limit of strong on-site repulsion and low density one gets only zero or one atom per site mimicking a pseudo spin lattice. At least in principle any coupling matrix can be realized using order N 2 cavity modes [27]. In contrast to current implementations [28], which use minor embedding [29], and alternative architectures [30], our approach does not need auxiliary qubits to realize long-range coupling.…”