Abstract
Quantum annealing, which is particularly useful for combinatorial optimization, becomes more powerful by using excited states, in addition to ground states. However, such excited-state quantum annealing is prone to errors due to dissipation. Here we propose excited-state quantum annealing started with the most stable state, i.e., vacuum states. This counterintuitive approach becomes possible by using effective energy eigenstates of driven quantum systems. To demonstrate this concept, we use a network of Kerr-nonlinear parametric oscillators, where we can start excited-state quantum annealing with the vacuum state of the network by appropriately setting initial detuning frequencies for the oscillators. By numerical simulations of four oscillators, we show that the present approach can solve some hard instances whose optimal solutions cannot be obtained by standard ground-state quantum annealing because of energy-gap closing. In this approach, a nonadiabatic transition at an energy-gap closing point is rather utilized. We also show that this approach is robust against errors due to dissipation, as expected, compared to quantum annealing started with physical excited (i.e., nonvacuum) states. These results open new possibilities for quantum computation and driven quantum systems.
Highlights
Quantum annealing, which is useful for combinatorial optimization, becomes more powerful by using excited states, in addition to ground states
We have proposed an approach to excited-state Quantum annealing (QA), which is started with the most stable state, namely, vacuum states
This is based on the use of effective energy eigenstates of driven quantum systems
Summary
Quantum annealing, which is useful for combinatorial optimization, becomes more powerful by using excited states, in addition to ground states. Such excitedstate quantum annealing is prone to errors due to dissipation. We propose excited-state quantum annealing started with the most stable state, i.e., vacuum states This counterintuitive approach becomes possible by using effective energy eigenstates of driven quantum systems. By numerical simulations of four oscillators, we show that the present approach can solve some hard instances whose optimal solutions cannot be obtained by standard ground-state quantum annealing because of energy-gap closing. The thermal QA is quite different from the above method[23])
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