This chapter describes the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations. But the physical world is quantum mechanical, and therefore the proper problem is the simulation of quantum physics. A computer which will give the same probabilities as the quantum system does. The present theory of physics allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition is right, physical law is wrong. Quantum theory and quantizing is a very specific type of theory. The chapter talks about the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature. There are interesting philosophical questions about reasoning, and relationship, observation, and measurement and so on, which computers have stimulated people to think about anew, with new types of thinking.

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Simulating physics with computers

Although microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is this irreversibility that leads to intrinsic dissipations in electronic devices and limits the possibility of quantum computation. We theoretically predict that the electric field can induce a substantial amount of dissipationless quantum spin current at room temperature, in hole-doped semiconductors such as Si, Ge, and GaAs. On the basis of a generalization of the quantum Hall effect, the predicted effect leads to efficient spin injection without the need for metallic ferromagnets. Principles found here could enable quantum spintronic devices with integrated information processing and storage units, operating with low power consumption and performing reversible quantum computation.

https://arxiv.org/pdf/cond-mat/0308167.pdf

Dissipationless Quantum Spin Current at Room Temperature

Introduction: Science Hypotheses and Science Philosophy.- Data and Models.- Information Theory and Entropy.- Quantifying the Evidence About Science Hypotheses.- Multimodel Inference.- Advanced Topics.- Summary.

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Model Based Inference in the Life Sciences: A Primer on Evidence

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete-time quantum walks.

Quantum walks: a comprehensive review

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies.

/pdf/the-second-laws-of-quantum-thermodynamics-5gn40x68a0.pdf

The second laws of quantum thermodynamics

From the Publisher:
From 1983 to 1986, the legendary physicist and teacher Richard Feynman gave a course at Caltech called "Potentialities and Limitations of Computing Machines." Although the lectures are over ten years old, most of the material is timeless and presents a "Feynmanesque" overview of many standard and some not-so-standard topics in computer science. These include compatibility, Turing machines (or as Feynman said, "Mr. Turing's machines"), information theory, Shannon's Theorem, reversible computation, the thermodynamics of computation, the quantum limits to computation, and the physics of VLSI devices. Taken together, these lectures represent a unique exploration of the fundamental limitations of digital computers. Feynman's philosophy of learning and discovery comes through strongly in these lectures. He constantly points out the benefits of playing around with concepts and working out solutions to problems on your own - before looking at the back of the book for the answers. As Feynman says in the lectures: "If you keep proving stuff that others have done, getting confidence, increasing the complexities of your solutions - for the fun of it - then one day you'll turn around and discover that nobody actually did that one! And that's the way to become a computer scientist."

Robin W. Allen

Papers

Feynman Lectures on Computation

Coding and Information Theory