Cells are capable of maintaining a long-term memory in addition to genetic information, which is generally referred to as epigenetics. In the study of memory, digital memory has been often assumed, which is understood as multistability, whereas in the cell there is another form of memory – continuous (analog), kinetic memory. Referring to the kinetic constraints of the glass theory, it is shown that a kinetic memory with slow relaxation emerges as an alternative to the conventional memories of multiple stable states. It is characterized by a slow logarithmic change with several plateaus that can be occupied during the relaxation process. If the same enzyme catalyzes a stepwise reaction, as long as the amount of such enzyme is not sufficient, the reaction process can be hindered by enzyme-limited competition, resulting in kinetic memory. A combination of catalytic reactions can create a negative correlation between the amount of substrate and enzyme in it, thereby allowing a slow relaxation process with many plateaus, where multiple states can be maintained over a long period of time.

The appendix contains a detailed description of the sparse simulation infrastructure.

This chapter summarizes the concept and methodology of the present volume by emphasizing the relevance of macro-micro consistency. It also discusses current research topics on the origin of life, the relationship between developmental and evolutionary processes, the resilience of the ecosystem that maintains diversity, and dynamic memory in the brain, as well as possible future directions for establishing a theory of universal biology. All in all, fresh views of biology are presented with a physicist's perspective to reveal universality.

This chapter serves as a bridge from the introductory material to the sections on quantum algorithms. We start by implementing a classical circuit using quantum gates and show that quantum computers are at least as capable as classical computers. Then we discuss the term “beyond classical,” which is now the preferred term to describe computation that can be run efficiently on a quantum computer but would be intractable to run on a classical computer. For this, we discuss in detail Google’s seminal quantum supremacy paper.

The quantum Fourier transform is another fundamental quantum algorithm. The section begins with a simple phase-kick circuit and expands to quantum phase estimation before detailing the quantum Fourier transform itself. A short section on arithmetic in the quantum domain introduces techniques that are used in a final detailed section on Shor’s famous algorithm for number factorization.

This chapter presents the first real algorithm – a quantum "Hello World" program, which is just a simple random number generator. The chapter then details quantum teleportation, superdense coding, and entanglement swapping algorithms, as well as the CHSH game. This game is a simplified version of the Bell inequalities, which established that quantum entanglement cannot be explained by classical theories assuming hidden states

Quantum machine learning is an exciting field that explores the intersection of quantum computing and machine learning. It aims to leverage the principles of quantum computing to enhance machine learning algorithms and potentially revolutionize how we analyze data and solve complex problems. In this section, we begin with a simple algorithm for computing the Euclidean distance between vectors. Then we discuss the quantum principal component analysis. Finally, we explain the complex but beautiful HHL algorithm for solving systems of linear equations