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For the goal of strong artificial intelligence that can mimic human-levelintelligence, AI systems would have the ability to adapt to ever-changingscenarios and learn new knowledge continuously without forgetting previouslyacquired knowledge. When a machine learning model is consecutively trained onmultiple tasks that come in sequence, its performance on previously learnedtasks may drop dramatically during the learning process of the newly seen task.To avoid this phenomenon termed catastrophic forgetting, continual learning,also known as lifelong learning, has been proposed and become one of the mostup-to-date research areas of machine learning. As quantum machine learningblossoms in recent years, it is interesting to develop quantum continuallearning. This paper focuses on the case of quantum models for quantum datawhere the computation model and the data to be processed are both quantum. Thegradient episodic memory method is incorporated to design a quantum continuallearning scheme that overcomes catastrophic forgetting and realizes knowledgebackward transfer. Specifically, a sequence of quantum state classificationtasks is continually learned by a variational quantum classifier whoseparameters are optimized by a classical gradient-based optimizer. The gradientof the current task is projected to the closest gradient, avoiding the increaseof the loss at previous tasks, but allowing the decrease. Numerical simulationresults show that our scheme not only overcomes catastrophic forgetting, butalso realize knowledge backward transfer, which means the classifier'sperformance on previous tasks is enhanced rather than compromised whilelearning a new task.

Quantum continual learning of quantum data realizing knowledge backward transfer