A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
How to analyse evolutionary algorithms
Theoretical Computer Science - Natural computing
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Lower Bounds for Local Search by Quantum Arguments
SIAM Journal on Computing
Quantum Query Complexity of Some Graph Problems
SIAM Journal on Computing
New quantum algorithms and quantum lower bounds
New quantum algorithms and quantum lower bounds
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the hitting times of quantum versus random walks
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Quantum-inspired evolutionary algorithm for a class of combinatorial optimization
IEEE Transactions on Evolutionary Computation
An analysis on recombination in multi-objective evolutionary optimization
Artificial Intelligence
A quantum genetic algorithm with quantum crossover and mutation operations
Quantum Information Processing
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In this article, we formulate for the first time the notion of a quantum evolutionary algorithm. In fact we define a quantum analogue for any elitist (1+1) randomized search heuristic. The quantum evolutionary algorithm, which we call (1+1) quantum evolutionary algorithm (QEA), is the quantum version of the classical (1+1) evolutionary algorithm (EA), and runs only on a quantum computer. It uses Grover search [13] to accelerate the search for improved offsprings. To understand the speedup of the (1+1) QEA over the (1+1) EA, we study the three well known pseudo-Boolean optimization problems OneMax, LeadingOnes, and Discrepancy. We show that although there is a speedup in the case of OneMax and LeadingOnes in the quantum setting, the speedup is less than quadratic. For Discrepancy, we show that the speedup is at best constant. The reason for this inconsistency is due to the difference in the probability of making a successful mutation. On the one hand, if the probability of making a successful mutation is large then quantum acceleration does not help much. On the other hand, if the probabilities of making a successful mutation is small then quantum enhancement indeed helps.