Journal
PHYSICAL REVIEW A
Volume 90, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.90.032311
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Funding
- NSF [0844626, 1122374]
- NSF Waterman Award
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We present quantum observable Markov decision processes (QOMDPs), the quantum analogs of partially observable Markov decision processes (POMDPs). In a QOMDP, an agent is acting in a world where the state is represented as a quantum state and the agent can choose a superoperator to apply. This is similar to the POMDP belief state, which is a probability distribution over world states and evolves via a stochastic matrix. We show that the existence of a policy of at least a certain value has the same complexity for QOMDPs and POMDPs in the polynomial and infinite horizon cases. However, we also prove that the existence of a policy that can reach a goal state is decidable for goal POMDPs and undecidable for goal QOMDPs.
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