A gate sequence of single qubit transformations may be condensed into a single microwave pulse that maps a qubit from an initialized state directly into the desired state of the composite transformation. Here, machine learning is used to learn the parameterized values for a single driving pulse associated with a  transformation of three sequential gate operations on a qubit. This implies that future quantum circuits may contain roughly a third of the number of single qubit operations performed, greatly reducing the problems of noise and decoherence. There is a potential for even greater condensation and efficiency using the methods of quantum machine learning.

Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work in a quantum context, and unwanted interactions with the environment can destroy coherence and thus the quantum nature of the computation. Because of the parallel and distributed nature of classical neural networks, they have long been successfully used to deal with incomplete or damaged data. In this work, we show that our model of a quantum neural network (QNN) is similarly robust to noise, and that, in addition, it is robust to decoherence. Moreover, robustness to noise and decoherence is not only maintained but improved as the size of the system is increased. Noise and decoherence may even be of advantage in training, as it helps correct for overfitting. We demonstrate the robustness using entanglement as a means for pattern storage in a qubit array. Our results provide evidence that machine learning approaches can obviate otherwise recalcitrant problems in quantum computing.

Designing and implementing algorithms for medium and large scale quantum computers is not easy. In previous work we have suggested, and developed, the idea of using machine learning techniques to train a quantum system such that the desired process is “learned,” thus obviating the algorithm design difficulty. This works quite well for small systems. But the goal is macroscopic physical computation. Here, we implement our learned pairwise entanglement witness on Microsoft’s Q\#, one of the commercially available gate model quantum computer simulators; we perform statistical analysis to determine reliability and reproducibility; and we show that after training the system in stages for an incrementing number of qubits (2, 3, 4, \ldots) we can infer the pattern for mesoscopic $N$ from simulation results for three-, four-, five-, six-, and seven-qubit systems. Our results suggest a fruitful pathway for general quantum computer algorithm design and for practical computation on noisy intermediate scale quantum devices.