Unified Information Dynamic Analysis of Quantum Decision-Making and Search Algorithms: Computational Intelligence Measure

There are important algorithms built upon a mixture of basic techniques described; for example, the Fast Fourier Transform (FFT) employs both Divide - and - Conquer and Transform - and - Conquer techniques. In this article, the evolution of a quantum algorithm (QA) is examined from a n information theory viewpoint. The complex vector entering the quantum algorithmic gate - QAG is considered as an information source both from the classical and the quantum level. The analysis of the classical and quantum information flow in Deutsch - Jozsa, Shor and Grover algorithm s is used. It is shown that QAG, based on superposition of states, quantum entanglement and interference, when acting on the input vector, stores information into the system state, minimizing the gap between classical Shannon ent ropy and quantum von Neumann entropy. Minimizing of the gap between Shannon and von Neumann entropies is considered as a termination criterion of QA computational intelligence measure. Let us discuss the main properties of classical and quantum information that in dynamic analysis of quantum algorithms are used. Additional necessary detail description of general properties of information amounts in Appendix 1 to this article is given. Any c omputation (both classical and quantum) is formally identical to a communication in time. By considering quantum computation as a communication process, it is possible to relate its efficiency to its classical communication capacity. At time, the programmer sets the computer to accomplish any one of several possible tasks. Each of these tasks can be regarded as embodying a different message. Another programmer can obtain this message by looking at the output of the computer when th e computation is finished at time . Computation based on quantum principles allows for more efficient algorithms for solving certain problems than algorithms based on pure classical principles [ 1 ]. The sender conveys the maximum information when all the message states have equal a priori probability (which also maximizes the channel capacity). In that case the mutual information (channel capacity) at the end of the computation is . Let us consider any peculiarities of information axioms and information capability of quantum computing as the dynamic evolution of QAs. If one breaks down the general unitary transformation of a QA into a number of successive unitary blocks, then the maximum capacity may be achieved only after the number of applications of the blocks. When its total value reaches the maximum possible value consistent with a given initial state o f the quantum computing, the computation is regarded as being complete (see, in details [ 2,3 ]). The classical capacity of a quantum communication channel is connected with the efficiency of quantum computing using entropic arguments [ 1 - 9 ]. This formalism allows us to derive lower bounds on the computational complexity of QA's in the most general context.