Backtracking method applicable to optical quantum calculation
Kimihiro Saito
Optical quantum devices are promoting the development not only of communication but also of quantum computation using optical quantum gates. Here, we will explain how to replace circuits consisting of gates such as NOT, AND, etc. used in classical logic calculations with quantum calculation gates. These classical gates can be expressed as NOT and CNOT of quantum computing gates. We show how to express these quantum gates as optical devices using the behavior of the polarization of discrete photons. Next, we describe the backtracking method of quantum circuits utilizing the reversibility of quantum gates. Since classical gates are not unitary, we use probabilistic methods that rely on measurements. In a typical classical gate, there are multiple inputs corresponding to a certain output, so backtracking requires tracing multiple states. The quantum bit representation, which can represent superposition states, is suitable for this purpose. As an application example, we explain how to backtrack integer multipliers and perform factorization. In configuration using quantum gates, one measurement quantum bit is required for each element, resulting in a large number of state bits. However, by reusing bits that are no longer needed, it was possible to construct a circuit with a number of state bits proportional to the number of bits for the integer multiplicand. We simulated an integer multiplier circuit by combining classical gates, and backtrack the circuit to derive two factors from a composite number represented by quantum bits. We performed simulations on a PC and succeeded in factorizing a 100-bit composite number.
Industrial Optical Devices and Systems (ODS)•Oct 4, 2024•1 citation