Quantum state preparation without coherent arithmetic

Abstract: We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum memory loads, to encode the function values. Instead, we use a template quantum eigenvalue transformation circuit to convert a low cost block encoding of the sine function into the desired function. Our method uses only 4 ancilla qubits (3 if the approximating polynomial has definite parity), providing order-of-magnitude qubit count reductions compared to state-of-the-art approaches, while using a similar number of Toffoli gates if the function can be well represented by a polynomial or Fourier approximation. Like black-box methods, the complexity of our approach depends on the 'L2-norm filling-fraction' of the function. We demonstrate the efficiency of our method for preparing states commonly used in quantum algorithms, such as Gaussian and Kaiser window states.