Quantum mechanics provides the theoretical framework for the current understanding of the physical world. The differences between classical mechanics and quantum mechanics become especially notable in small scale systems. Current technology demands ever increasing computational power, which is achieved through a technological effort of miniaturization. This effort leads to smaller system scales, and eventually the technology will reach the quantum physics realm. Already, quantum effects are beginning to influence the design and operation of microprocessors and other devices.
This lends great motivation to investigating the question whether quantum mechanics provides enhanced computational power compared to classical computation. In fact, it is now proved that such an enhancement does exist, namely, that quantum computation offers higher computational power. Two of the most notable examples of this are Shor's algorithm and Grover's algorithm.
Shor's algorithm is a quantum algorithm, which finds the prime factors of any number. On a classical computer, such a task is considered unfeasible (if it is to be performed on an arbitrarily large number). However, on a quantum computer, the task is easy. This result is extremely significant, since most current encryption methods rely on the fact that finding prime factors of a number is hard.
Grover's algorithm is a quantum algorithm for finding an element in an unsorted list. Classically, the number of times the list would have to be checked would be roughly the size of the list. On a quantum computer (a quantum system capable of performing computations), the number of times the list would have to be checked would be reduced to the order of the square root of the size of the list.
Even though it is now known that quantum computers could provide more computational power than classical computers, the theoretical and logical reasons for this enhancement are lacking. A key aspect is believed to be a property of quantum systems, called quantum entanglement. Quantum entanglement can be simply (though not precisely) defined as correlations between parts of the quantum system, which cannot be explained classically. This entanglement seems to be what enables quantum computers to affect the whole system, while performing simple, local operations. Furthermore, it is proved that if a quantum algorithm runs without creating entanglement, then it can be efficiently simulated on a classical computer. Entanglement is also considered to be a resource in quantum communication, where the more entanglement there is, the more information can be transmitted. This leads to the understanding that entanglement is also related to the amount of information which resides in the quantum system.
In our research, we try to find a connection between the amount of entanglement which is created during the process of a quantum algorithm, and the efficiency enhancement it provides. In order to do that we develop both numerical and analytical tools to measure entanglement. This research aims at understanding which quantum algorithms are more efficient than is classically possible, and offer tools for developing more such algorithms. Furthermore, this research is likely to lead to new understandings of the roles of quantum entanglement in quantum systems and in quantum computation, and may also shed light on fundamental aspects of quantum physics.Every living cell performs a large number of computational tasks. These tasks are presented by the construction of the proteins needed for proper operation of the living cell or organism. These processes are computational ones, since at different times, and with different states of the environment (which we may consider as the input to the computation), the cell needs to construct different proteins, or change the construction rate of the proteins it constructs.
It is notable that all the information needed for the computation in a cell is somehow encoded in the DNA molecules which can be found within each cell. The interactions between the different genes in the DNA create an intricate network of control and regulation. Investigation of the complete network is a daunting task, and the only way seems to be to break the network into smaller parts or modules, each with a specific control or regulation function.
In recent years, experimental tools have been developed, which enable the mapping, the manipulation and even the construction of individual genes within a cell, or within a population of cells. Interactions between proteins and between genes are also experimentally investigated and manipulated with much success. Different models are being tested to understand how the computation process takes place within the cells.
In our research, we offer a novel approach to analyzing the dynamics of gene regulation networks of different modules. Our approach also deploys an arsenal of computational tools based on our experience in modeling complex systems and in complex systems simulations, such as master equation dynamics, monte-carlo simulations and more. Applying these methods to regulation networks, which are of interest to the scientific community networks has already yielded results, which seem to be more consistent with experimental results.
Further, in collaboration with Prof. Margalit's group, we analyze regulation networks which include not only regulation on the genes themselves, but in other level of protein construction, like protein-protein interaction, and micro-RNA inhibition. These regulation processes offer more models with which to explain experimental results, and understand the important aspect of gene regulation.
The main goals of this research are to understand the function of different modules in gene regulation networks, and to find the different models which explain different variants of regulations found in living systems. Eventually, it is our aim to be able to combine these modules together to run a simulation of complex processes that take place within living cells or organisms. We believe that computational modeling of genetic regulation may contribute to the understanding of diseases caused by gene regulation break-down.
