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Machine learning is seen as a promising application of quantum computation.For near-term noisy intermediate-scale quantum (NISQ) devices, parametrizedquantum circuits (PQCs) have been proposed as machine learning models due totheir robustness and ease of implementation. However, the cost function isnormally calculated classically from repeated measurement outcomes, such thatit is no longer encoded in a quantum state. This prevents the value from beingdirectly manipulated by a quantum computer. To solve this problem, we give aroutine to embed the cost function for machine learning into a quantum circuit,which accepts a training dataset encoded in superposition or an easilypreparable mixed state. We also demonstrate the ability to evaluate thegradient of the encoded cost function in a quantum state.

Cost function embedding and dataset encoding for machine learning with parameterized quantum circuits