Fourier-based LCU decomposes diagonal and non-diagonal unitaries into hardware-friendly forms for QAOA-style optimization, trading circuit depth for sampling overhead with performance guarantees.
Chakraborty, Quantum8, 1496 (2024)
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A non-unitary extension of Grover's algorithm achieves O(sqrt(N)) query complexity matching the optimal bound by using a single large rotation via block encoding and Chebyshev approximation, at the cost of one additional qubit.
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Efficient Fourier-Based Linear Combination of Unitaries and Applications in Quantum Optimization
Fourier-based LCU decomposes diagonal and non-diagonal unitaries into hardware-friendly forms for QAOA-style optimization, trading circuit depth for sampling overhead with performance guarantees.
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Non-unitary extension of Grover's search algorithm
A non-unitary extension of Grover's algorithm achieves O(sqrt(N)) query complexity matching the optimal bound by using a single large rotation via block encoding and Chebyshev approximation, at the cost of one additional qubit.