An Efficient Algorithm for Sparse Quantum State Preparation

Generating quantum circuits that prepare specific states is an essential part of quantum compilation. Algorithms that solve this problem for general states generate circuits that grow exponentially in the number of qubits. However, in contrast to general states, many practically relevant states are sparse in the standard basis. In this paper we show how sparsity can be used for efficient state preparation. We present a polynomial-time algorithm that generates polynomial-size quantum circuits (linear in the number of nonzero coefficients times number of qubits) that prepare given states, making computer-aided design of sparse state preparation scalable.