Reinforcement learning for semi-autonomous approximate quantum eigensolver

The characterization of an operator by its eigenvectors and eigenvalues allows us to know its action over any quantum state. Here, we propose a protocol to obtain an approximation of the eigenvectors of an arbitrary Hermitian quantum operator. This protocol is based on measurement and feedback processes, which characterize a reinforcement learning protocol. Our proposal is composed of two systems, a black box named environment and a quantum state named agent. The role of the environment is to change any quantum state by a unitary matrix $\hat{U}_E=e^{-i\tau\hat{\mathcal{O}}_E}$ where $\hat{\mathcal{O}}_E$ is a Hermitian operator, and $\tau$ is a real parameter. The agent is a quantum state which adapts to some eigenvector of $\hat{\mathcal{O}}_E$ by repeated interactions with the environment, feedback process, and semi-random rotations. With this proposal, we can obtain an approximation of the eigenvectors of a random qubit operator with average fidelity over 90\% in less than 10 iterations, and surpass 98\% in less than 300 iterations. Moreover, for the two-qubit cases, the four eigenvectors are obtained with fidelities above 89\% in 8000 iterations for a random operator, and fidelities of $99\%$ for an operator with the Bell states as eigenvectors. This protocol can be useful to implement semi-autonomous quantum devices which should be capable of extracting information and deciding with minimal resources and without human intervention.Comment: 15 pages, 6 figure

Quantum simulation of entanglement dynamics in a quantum processor

We implement a five-qubit protocol in IBM quantum processors to get entanglement dynamics in a two qubit system in the presence of an environment. Specifically, two qubits represent the main system, another two qubits the environment, and an additional qubit is used as an auxiliary qubit to perform the quantum entanglement estimation. We focus on measuring, in this superconducting quantum processor, the sudden death and sudden birth of entanglement. We obtain the quantum entanglement evolution of the main system qubits and the environment qubits as the average of $N=10$ independent experiments in the same quantum device, observing that the noisy nature of current quantum processors produce a shift on times signaling sudden death o sudden birth of entanglement. This work takes relevance showing the usefulness of current noisy quantum devices to test fundamental concepts in quantum information.Comment: 6 pages, and 12 figure

Embedded Quantum Correlations in thermalized quantum Rabi systems

We study the quantum correlations embedded in open quantum Rabi systems. Specifically, we study how the quantum correlation depends on the coupling strength, number of qubits, and reservoir temperatures. We numerically calculate the quantum correlations of up to three qubits interacting with a single field mode. We find that the embedded quantum correlations exhibit a maximum for a given coupling strength, which depends inversely on the number of subsystems and the reservoir temperature. We explore how this feature affects the performance of a many-qubit Otto heat engine, finding numerical evidence of a direct correspondence between the minimum of the extractable work and the maximum of the embedded quantum correlations in the qubit-cavity bi-partition. Furthermore, as we increase the number of qubits, the maximum extractable work is reached at smaller values of the coupling strength. This work could help design more sophisticated quantum heat engines that rely on many-body systems with embedded correlations as working substances.Comment: 12 pages and 12 figure