Quantum Annealing with the Jarzynski Equality

We show a practical application of the Jarzynski equality in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many arguments. We consider to incorporate the Jarzynski equality into quantum annealing, which is one of the generic algorithms to solve the combinatorial optimization problem. The ordinary quantum annealing suffers from nonadiabatic transitions whose rate is characterized by the minimum energy gap ${\Delta }_{\min }$ of the quantum system under consideration. The quantum sweep speed is therefore restricted to be extremely slow for the achievement to obtain a solution without relevant errors. However, in our strategy shown in the present study, we find that such a difficulty would not matter.

Figure 1

Quantum Jarzynski annealing and quantum annealing for the one-dimensional random-potential problem. The probabilities for obtaining the ground state by both of the methods are plotted for $\tau =1$, 10, and 100 from top to bottom. The dashed curves denote the instantaneous Gibbs-Boltzmann factor for reference. The upper solid curves representing the results by QJA are fixed to these reference curves, while the lower ones express the time-dependent results by the ordinary QA.