Quantum Genetic Algorithms

Recent developments in quantum technology have shown that quantum computers can provide a dramatic advantage over classical computers for some algorithms. Since most problems of real interest for genetic algorithms (GAs) have a vast search space [Holland, 1975], it seems appropriate to consider how quantum parallelism can be applied to GAs. In this paper we present a simple quantum approach to genetic algorithms and analyze its benefits and drawbacks. This is significant because to date there are only a handful of quantum algorithms [Williams and Clearwater, 1997]. 1 QUANTUM GENETIC ALGORITHM There are two significant differences between a classical computer and a quantum computer. The first is in storing information, classical bits versus quantum q-bits. The second is the quantum mechanical feature known as entanglement, which allows a measurement on some qbits to effect the value of other q-bits. Figure 1 describes the generic quantum genetic algorithm (QGA). set Reg10 through Reg1n-1 into superpositions apply fitness function to Reg10,n-1 storing result in Reg20,n-1 (producing the entanglement) measure each of Reg20,n-1 (all Reg1i and Reg2i collapse) repeat crossover of Reg1i to generate new population (Reg2i is still entangled) apply fitness function as before measure Reg20,n-1 (producing collapse) until population converges or termination condition met Figure 1: QGA A q-bit differs from a bit in that it can either be a 1, 0 or a superposition of the two. In this example, Reg1and Reg2 are two registers of q-bits. Both registers are of length n. 2 ANALYSIS OF THE QGA One may ask, what is gained by the quantum genetic algorithm? Currently this answer cannot be quantified. The apparent advantage for a QGA is the increased diversity of a quantum population. A quantum population can be exponentially larger than a classical population of the same "size". However, it is unclear exactly how the additional diversity will influence the result.