This research investigates the possibility of using quantum optimal control techniques to co-optimize the energetic cost and the process fidelity of a quantum unitary gate. The energetic cost is theoretically defined, and thereby, the gradient of the energetic cost for pulse engineering is derived. The Pareto optimality is empirically demonstrated in the trade-off between process fidelity and energetic cost. Thereafter, two novel numerical quantum optimal control approaches are proposed: i) energy-optimized gradient ascent pulse engineering (EO-GRAPE) as an open-loop gradient-based method, and ii) energy-optimized deep reinforcement learning for pulse engineering (EO-DRLPE) as a closed-loop method. The performance of both methods is probed in the presence of increasing noise. It is found that the EO-GRAPE method performs better than the EO-DRLPE methods with and without a warm start for most experimental settings. Additionally, for one qubit unitary gate, the correlation between the Bloch sphere path length and the energetic cost is illustrated.

In this research, we extend the universal reinforcement learning agent models of artificial general intelligence to quantum environments. The utility function of a classical exploratory stochastic Knowledge Seeking Agent, KL-KSA, is generalized to distance measures from quantum information theory on density matrices. Quantum process tomography (QPT) algorithms form a tractable subset of programs for modeling environmental dynamics. The optimal QPT policy is selected based on a mutable cost function based on algorithmic complexity as well as computational resource complexity. The entire agent design is encapsulated in a self-replicating quine which mutates the cost function based on the predictive value of the optimal policy choosing scheme. Thus, multiple agents with pareto-optimal QPT policies evolve using genetic programming, mimicking the development of physical theories each with different resource trade-offs. This formal framework, termed Quantum Knowledge Seeking Agent (QKSA), is a resource-bounded participatory observer modification to the recently proposed algorithmic information-based reconstruction of quantum mechanics. A proof-of-concept is implemented and available as open-sourced software.