No abstract

Reinforcement learning has been widely used in many problems including quantum control of qubits. However, such problems can, at the same time, be solved by traditional, non-machinelearning based methods such as stochastic gradient descendent and Krotov algorithms, and it remains unclear which one is most suitable when the control has specific constraints. In this work we perform a comparative study on the efficacy of two reinforcement learning algorithms, Q-learning and deep Q-learning, as well as stochastic gradient descendent and Krotov algorithms, in the problem of preparing a desired quantum state. We found that overall, the deep Q-learning outperforms others when the problem is discretized, e.g. allowing discrete values of control. The Q-learning and deep Q-learning can also adaptively reduce the complexity of the control sequence, shortening the operation time and improving the fidelity. Our comparison provides insights on the suitability of reinforcement learning in quantum control problems.

Decoherence due to charge noise is one of the central challenges in using spin qubits in semiconductor quantum dots as a platform for quantum information processing. Recently, it has been experimentally demonstrated in both Si and GaAs singlet-triplet qubits that the effects of charge noise can be suppressed if qubit operations are implemented using symmetric barrier control instead of the standard tilt control. Here, we investigate the key issue of whether the benefits of barrier control persist over the entire set of single-qubit gates by performing randomized benchmarking simulations. We find the surprising result that the improvement afforded by barrier control depends sensitively on the amount of spin noise: for the minimal nuclear spin noise levels present in Si, the coherence time improves by more than 2 orders of magnitude whereas in GaAs, by contrast the coherence time is essentially the same for barrier and tilt control. However, we establish that barrier control becomes beneficial if qubit operations are performed using a new family of composite pulses that reduce gate times by up to 90%. With these optimized pulses, barrier control is the best way to achieve high-fidelity quantum gates in singlet-triplet qubits.

Composite pulses are essential for universal manipulation of singlet-triplet spin qubits. In the absence of noise, they are required to perform arbitrary single-qubit operations due to the special control constraint of a singlet-triplet qubits; while in a noisy environment, more complicated sequences have been developed to dynamically correct the error. Tailoring these sequences typically requires numerically solving a set of nonlinear equations. Here we demonstrate that these pulse sequences can be generated by a well-trained, double-layer neural network. For sequences designed for the noise-free case, the trained neural network is capable of producing almost exactly the same pulses known in the literature. For more complicated noise-correcting sequences, the neural network produces pulses with slightly different line-shapes, but the robustness against noises remains comparable. These results indicate that the neural network can be a judicious and powerful alternative to existing techniques, in developing pulse sequences for universal fault-tolerant quantum computation. arXiv:1708.00238v2 [quant-ph]