Configurable sublinear circuits for quantum state preparation

The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A prerequisite for applying quantum algorithms to a wide range of real-world problems is loading classical data to a quantum state. Several circuit-based methods have been proposed for encoding classical data as probability amplitudes of a quantum state. However, in these methods, either quantum circuit depth or width must grow linearly with the data size, nullifying the advantage of representing exponentially many classical data in a quantum state. In this paper, we present a configurable bidirectional procedure that addresses this problem by tailoring the resource trade-off between quantum circuit width and depth. In particular, we show a configuration that encodes an N-dimensional classical data using a quantum circuit whose width and depth both grow sublinearly with N. We demonstrate proof-of-principle implementations on five quantum computers accessed through the IBM and IonQ quantum cloud services.