Prepare Linear Distributions with Quantum Arithmetic Units.

Area of Science:

• Quantum Computing
• Quantum Information Science

Background:

• Quantum arithmetic logic units (QALUs) are fundamental for quantum computations.
• Developing efficient methods for generating specific quantum states is crucial for advancing quantum algorithms.

Purpose of the Study:

• To present a novel approach for preparing linear probability distributions using quantum full adders.
• To demonstrate the utility of QALUs in constructing complex quantum states.

Main Methods:

• Utilizing Hadamard gates to prepare input qubits in uniform superposition states.
• Implementing a quantum full adder to sum the input states, representing the output as a two's complement signed integer.
• Applying a phase shift of -1 to negative components and employing the Repeat-Until-Success process to selectively discard components.

Main Results:

• Successfully prepared linear probability distributions using quantum full adders.
• Demonstrated the ability to manipulate quantum states to represent signed integers and control probability distributions.
• Showcased the flexibility of the method by enabling the discarding of positive or negative components.

Conclusions:

• The proposed method offers a viable pathway for generating linear probability distributions with quantum adders.
• The resulting quantum state serves as a valuable intermediate step for subsequent quantum operations.
• This work contributes to the development of essential building blocks for advanced quantum computing applications.