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量子アニーリングの基礎　西森 秀稔, 大関 真之, 共立出版, 2018
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T-QARDの日々 量子コンピュータへのお勧めの入口
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# 4
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The agreement of FERL using quantum annealer reads treated as classical Boltzmann samples, with that of FERL using SA and classical Boltzmann machines, suggests that, at least for this task, and this size of Boltzmann machine, the measurements provided by the D-Wave 2000Q can be considered good approximations of Boltzmann distribu- tion samples of classical Ising models.
VI. CONCLUSION
In this paper, we perform free energy-based reinforce- ment learning using existing quantum hardware, namely the D-Wave 2000Q. Our methods rely on Suzuki–Trotter decomposition and realization of the measured configu- rations by the quantum device as replicas of an effective classical Ising model of one dimension higher. Future research can employ these principles to solve larger-scale reinforcement learning tasks in the emerging field of quan- tum machine learning.
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􏰄 e−Ei
Z |i⟩⟨i|, (B1)
where Z = 􏶣i e−Ei is the normalization constant. Then, plug this expansion into the intractable expression and use Jensen’s inequality
ln⟨u|ρ|u⟩
ρ=
9
   i
􏰄 e−Ei = ln⟨u| Z
|i⟩⟨i|u⟩ = ln 􏰄 |⟨i|u⟩|2 e−Ei
 i
 Z
≥ 􏰄 |⟨i|u⟩|2 ln e−Ei (B2)
i
 i
Z
|i⟩⟨i|u⟩
􏰄 e−Ei = ⟨u| ln Z
i
 = ⟨u| ln ρ|u⟩,
where |⟨i|u⟩|2 are probabilities and sum up to 1.
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