**Akira Saitoh (Kinki University)**

**Title:** Progress in a quantum genetic algorithm

**Abstract:**
We have recently discussed that conventional quantum genetic algorithms
are not very useful in the sense that they do not surpass the standard
quantum search designed to find a maximum in the computational cost.
In particular, when the number of individuals in a generation is not
approximately equal to the total number of possible individuals, the
cost to translate nonconsecutive integers to consecutive ones is
similar to the cost of classical ordering. Furthermore, there has been
no known way to realize a crossover for a quantum register that is in a
superposition of individuals. We show a certain workaround for these
issues using a nonunitary linear map that is acceptable as a quantum
operation.