Satoshi Iriyama

Generalized Quantum Turing Machine and its Application to the SAT Chaos Algorithm

Ohya and Volovich have proposed a new quantum computation model with chaotic amplification to solve the SAT problem, which went beyond usual quantum algorithm. In this paper, we generalize quantum Turing machine, and we show in this general quantum Turing machine (GQTM) that we can treat the Ohya-Volovich (OV) SAT algorithm.

Mathematical description of drug movement into tumor with EPR effect and estimation of its configuration for DDS.

It is known that Drug Delivery System (DDS) is useful to remedy against tumors for the reduction of side effects and the effective dosage. However the shape, in particular, the size of drug (medicine) is empirically decided in the present stage, which will be related to a question how much medicine should be dosed. Taking a particular reaction of tumor tissues called the EPR effect into consideration, we try to mathematically describe the behavior (dynamics) of drug in blood vessel by applying several techniques used in mathematics and physics. In this paper, we estimate the configuration of drug which is most effective to remedy for tumors under various conditions. As a result, this model and its simulation will be useful to design the drug in nano-level.

Language Classes Defined by Generalized Quantum Turing Machine

Ohya and Volovich proposed a quantum algorithm with chaotic amplification to solve the SAT problem, which went beyond the notion of the usual quantum algorithm. In this paper, we generalize quantum Turing machines by rewriting the usual quantum Turing automaton in terms of a channel transformation. Moreover, we define some computational classes of generalized quantum Turing machines and show that we can describe the Ohya-Volovich (OV) SAT algorithm with completely positive channels.

On Quantum Algorithm for Binary Search and Its Computational Complexity

A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.

Rigorous Estimation of Computational Complexity for OMV SAT Algorithm

For SAT problem, which is known to be NP-complete, Ohya and Masuda found a quantum algorithm calculating a given boolean function for all truth assignments. They showed that we can decide whether this boolean function is satisfiable or not in polynomial time if a certain superposed state can be detected physically, which turns out to be related to an amplification process. Then Ohya and Volovich realized this amplification by means of chaos dynamics [4, 5]. In this paper, we study the complexity of the SAT algorithm by rigorously counting the steps of OMV algorithm discussed previously in [1, 2, 4, 5].

ON QUANTUM ALGORITHM FOR MULTIPLE ALIGNMENT OF AMINO ACID SEQUENCES

The alignment of genome sequences or amino acid sequences is one of fundamental operations for the study of life. Usual computational complexity for the multiple alignment of N sequences with common length L by dynamic programming is O(LN). This alignment is considered as one of the NP problems, so that it is desirable to find a nice algorithm of the multiple alignment. Thus in this paper we propose the quantum algorithm for the multiple alignment based on the works [7, 14] in which the NP complete problem was shown to be the P problem by means of quantum algorithm and chaos informarion dynamics.

Efficient Energy Transfer in Network Model of Photosynthesis

Recently, it has been shown that the mathematical model of photosynthetic process can be described by quantum network. The model is based on fully connected network, and the dynamics is written by the GKSL master equation. The system at room temperature is susceptible to a dissipative and dephasing noise from the environment. The previous research showed that the efficiency of energy transfer can be increased by dephasing noise in the case that there is no dissipative noise. In this study, we calculate the efficiency of energy transfer in the case of considering both noises rigorously and show that the transfer efficiency becomes better when the dephasing noise is stronger than the dissipative one.

Chaos Amplification Process Can Be Described by the GKSL Master Equation

In 2000, Ohya et al. proposed a quantum algorithm with the amplification process of success probability, so-called chaos amplifier. They defined the process based on the logistic map, and its chaos...

On efficien quantum algorithm using classical amplificatio process

Ohya and Volovich proposed the polynomial time quantum algorithm to solve SAT problem which is one of NP-complete problems. This algorithm contains effective amplification process, so called a Chaos Amplifie, based on classical Chaotic dynamics. Recently we described this process by the GKSL master equation on two qubits system. In this talk, we introduce an efficien quantum algorithm for searching problem using the Chaos Amplifie.

Polynomial Time Quantum Algorithm for Search Problem and Its Application

The well known quantum algorithm for search problem is Grovers one. However, its computational complexity is not a polynomial in the input. In this study, we propose a polynomial time quantum algorithm for it based on quantum binary search and an amplification process. This process can be written as a quantum Turing machine form, a so called generalized quantum Turing machine GQTM. We introduce the definition of GQTM and its language classes.