Automatic spin-chain learning to explore the quantum speed limit

Abstract

One of the ambitious goals of artificial intelligence is to build a machine that outperforms human intelligence, even if limited knowledge and data are provided. Reinforcement Learning (RL) provides one such possibility to reach this goal. In this work, we consider a specific task from quantum physics, i.e. quantum state transfer in a one-dimensional spin chain. The mission for the machine is to find transfer schemes with fastest speeds while maintaining high transfer fidelities. The first scenario we consider is when the Hamiltonian is time-independent. We update the coupling strength by minimizing a loss function dependent on both the fidelity and the speed. Compared with a scheme proven to be at the quantum speed limit for the perfect state transfer, the scheme provided by RL is faster while maintaining the infidelity below 5 × 10 −4 . In the second scenario where a timedependent external field is introduced, we convert the state transfer process into a Markov decision process that can be understood by the machine. We solve it with the deep Q-learning algorithm. After training, the machine successfully finds transfer schemes with high fidelities and speeds, which are faster than previously known ones. These results show that Reinforcement Learning can be a powerful tool for quantum control problems.

A high-bias, low-variance introduction to Machine Learning for physicists

“…The long-term goal of the agent is to maximise the cumulative expected return, thus improving its performance in the longer run. Shadowed by more traditional optimal control algorithms, Reinforcement Learning has only recently taken off in physics (Albarran-Arriagada et al , 2018; August and Hernández-Lobato, 2018; Bukov, 2018; Bukov et al , 2018; Cárdenas-López et al , 2017; Chen et al , 2014; Chen and Xue, 2019; Dunjko et al , 2017; Fösel et al , 2018; Lamata, 2017; Melnikov et al , 2017; Neukart et al , 2017; Niu et al , 2018; Ramezanpour, 2017; Reddy et al , 2016b; Sriarunothai et al , 2017; Zhang et al , 2018). Of particular interest are biophysics inspired works that seek to use RL to understand navigation and sensing in turbulent environments (Colabrese et al , 2017; Masson et al , 2009; Reddy et al , 2016a; Vergassola et al , 2007).…”

Reinforcement Learning in Different Phases of Quantum Control

“…In this paper, we adopt a radically different approach to this problem based on machine learning (ML) [40][41][42][43][44][45][46]. ML has recently been applied successfully to several problems in equilibrium condensed matter physics [47,48], turbulent dynamics [49,50] and experimental design [51,52], and here we demonstrate that Reinforcement Learning (RL) provides deep insights into nonequilibrium quantum dynamics [53][54][55][56][57][58]. Specifically, we use a modified version of the Watkins Q-Learning algorithm [40] to teach a computer agent to find driving protocols which prepare a quantum system in a target state |ψ * starting from an initial state |ψ i by controlling a time-dependent field.…”

Deep reinforcement learning for universal quantum state preparation via dynamic pulse control

“…Except for these traditional routes, recently the deep reinforcement learning (RL) [37] shows a wide applicability in quantum control problems [38][39][40][41][42][43][44][45][46][47][48][49][50][51]. For example, how to drive a qubit from a fixed initial state to another fixed target state with discrete pulses by leveraging the deep RL [52] has been investigated [36].…”