Leveraging Machine Learning for Quantum Circuit Optimization

In the era of noisy, non-fault tolerant, quantum hardware, reducing the number of operations in quantum programs is essential to ensure computations produce meaningful results. Unitary synthesis is a particularly promising technique which uses non-linear numerical optimization tools paired with heuristic-guided tree search algorithms to produce resource efficient implementations of quantum algorithms. This report illustrates how unitary synthesis can be used to optimize quantum circuits with many qubits. The TopAS algorithm demonstrates how minimizing both operation count and interaction complexity before mapping can produce better circuit implementations than the state of the art. This report also presents several discoveries that enable the use of machine learning in accelerating unitary synthesis. Namely, a canonical representation of unitary matrices, and an argument for the learnability of mappings between a specific class of unitary matrices and parameterized quantum circuits are presented. The QSeed algorithm shows how machine learning can be leveraged to accelerate the optimization of wide quantum circuits without sacrificing solution quality.

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