Quantum state preparation for multivariate functions

Understand

A fundamental step of any quantum algorithm is the preparation of qubit registers in a suitable initial state.

• Often qubit registers represent a discretization of continuous variables and the initial state is defined by a multivariate function.
• We develop protocols for preparing quantum states whose amplitudes encode multivariate functions by linearly combining block-encodings of Fourier and Chebyshev basis functions.
• Without relying on arithmetic circuits, quantum Fourier transforms, or multivariate quantum signal processing, our algorithms are simpler and more effective than previous proposals.