Resource-efficient quantum data representation based on Grover's algorithm

초록

The superposition state of qubits in quantum computers enables a more efficient data representation than conventional binary methods in classical computers. Grover's algorithm amplifies the amplitude of a target state within a superposed set of states having equal amplitudes. However, except for a 2-qubit system, the amplitudes of the nontarget states and left residual amplitudes induced by the algorithm do not reduce to zero. Therefore, a new method was devised to overcome this drawback. We select new target state among the nontarget states by applying Grover's algorithm and obtain two distinct states with different amplitudes. Consequently, by excluding duplicate cases, this method enables the representation of 22n data points. This technique is referred to as superdense data representation (SDR). Specifically, SDR is a new data representation method for quantum computers using superposition and entanglement. This offers several advantages for encoding data. For instance, 8-qubit data can be effectively represented in 4-qubit, thereby reducing the resources required to store the information. Additionally, SDR allows the representation of more complex data, such as Unicode, without increasing calculation or storage costs. UTF-8 encoding method can be implemented using only eight qubits. By extending SDR, Asian languages that require more than two bytes of data can also be expressed using eight qubits.

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