Abstract: Systems and methods for transforming an initial quantum state to a target quantum state are disclosed. The initial quantum state is denoted by superposed initial quantum sample states and the target quantum state is denoted by superposed target quantum sample states. The initial quantum state is initialized with a set of primary registers for the initial quantum state and with at least one ancillary register. The initial quantum state is transformed such that the set of primary registers reflects the initial quantum sample states and the at least one ancillary register is varied to compose an intermediate quantum state. In addition, the intermediate quantum state is amplified by implementing quantum state rotations in accordance with a plurality of reflections on the intermediate quantum state such that the reflections result in the target quantum sample states of the target quantum state with a discarding of the at least one ancillary register.

Abstract: Systems and methods for transforming an initial quantum state to a target quantum state are disclosed. The initial quantum state is denoted by superposed initial quantum sample states and the target quantum state is denoted by superposed target quantum sample states. The initial quantum state is initialized with a set of primary registers for the initial quantum state and with at least one ancillary register. The initial quantum state is transformed such that the set of primary registers reflects the initial quantum sample states and the at least one ancillary register is varied to compose an intermediate quantum state. In addition, the intermediate quantum state is amplified by implementing quantum state rotations in accordance with a plurality of reflections on the intermediate quantum state such that the reflections result in the target quantum sample states of the target quantum state with a discarding of the at least one ancillary register.