J. C. Retamal

G. Alvarado Barrios, J. C. Retamal, E. Solano et al.

An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. To the best of our knowledge, this is the first time that circuits based on memristors are proposed for simulations. We study the performance of these analog computers by simulating integro-differential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to $13\%$ relative error for relevant timescales.

F. Albarrán-Arriagada, J. C. Retamal, E. Solano et al.

Machine learning employs dynamical algorithms that mimic the human capacity to learn, where the reinforcement learning ones are among the most similar to humans in this respect. On the other hand, adaptability is an essential aspect to perform any task efficiently in a changing environment, and it is fundamental for many purposes, such as natural selection. Here, we propose an algorithm based on successive measurements to adapt one quantum state to a reference unknown state, in the sense of achieving maximum overlap. The protocol naturally provides many identical copies of the reference state, such that in each measurement iteration more information about it is obtained. In our protocol, we consider a system composed of three parts, the "environment" system, which provides the reference state copies; the register, which is an auxiliary subsystem that interacts with the environment to acquire information from it; and the agent, which corresponds to the quantum state that is adapted by digital feedback with input corresponding to the outcome of the measurements on the register. With this proposal we can achieve an average fidelity between the environment and the agent of more than $90\% $ with less than $30$ iterations of the protocol. In addition, we extend the formalism to $ d $-dimensional states, reaching an average fidelity of around $80\% $ in less than $400$ iterations for $d=$ 11, for a variety of genuinely quantum and semiclassical states. This work paves the way for the development of quantum reinforcement learning protocols using quantum data and for the future deployment of semi-autonomous quantum systems.

F. A. Cárdenas-López, M. Sanz, J. C. Retamal et al.

We study the quantum synchronization between a pair of two-level systems inside two coupled cavities. By using a digital-analog decomposition of the master equation that rules the system dynamics, we show that this approach leads to quantum synchronization between both two-level systems. Moreover, we can identify in this digital-analog block decomposition the fundamental elements of a quantum machine learning protocol, in which the agent and the environment (learning units) interact through a mediating system, namely, the register. If we can additionally equip this algorithm with a classical feedback mechanism, which consists of projective measurements in the register, reinitialization of the register state and local conditional operations on the agent and environment subspace, a powerful and flexible quantum machine learning protocol emerges. Indeed, numerical simulations show that this protocol enhances the synchronization process, even when every subsystem experience different loss/decoherence mechanisms, and give us the flexibility to choose the synchronization state. Finally, we propose an implementation based on current technologies in superconducting circuits.

F. A. Cárdenas-López, L. Lamata, J. C. Retamal et al.

We propose a protocol to perform quantum reinforcement learning with quantum technologies. At variance with recent results on quantum reinforcement learning with superconducting circuits, in our current protocol coherent feedback during the learning process is not required, enabling its implementation in a wide variety of quantum systems. We consider diverse possible scenarios for an agent, an environment, and a register that connects them, involving multiqubit and multilevel systems, as well as open-system dynamics. We finally propose possible implementations of this protocol in trapped ions and superconducting circuits. The field of quantum reinforcement learning with quantum technologies will enable enhanced quantum control, as well as more efficient machine learning calculations.