There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

Quantum Computation and Quantum Information

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

/pdf/spintronics-fundamentals-and-applications-2dx38n6phu.pdf

Spintronics: Fundamentals and applications

All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized

Quantum entanglement

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Quantum computing for the very curious

Quantum computing and polynomial equations over Z_2

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes.

https://arxiv.org/pdf/quant-ph/0408129.pdf

Quantum computing and polynomial equations over the finite field Z_2

In a good physical theory dimensionless quantities, such as the ratio mp/me of the mass of the proton to the mass of the electron, do not depend on the system of units being used. This paper demonstrates that one widely used method for defining measures of entanglement violates this principle. Specifically, in this approach dimensionless ratios E(ρ)/E(σ) of entanglement measures may depend on what state is chosen as the basic unit of entanglement. This observation leads us to suggest three novel approaches to the quantification of entanglement. These approaches lead to unit-free definitions for the entanglement of formation and the distillable entanglement, and suggest natural measures of entanglement for multipartite systems. We also show that the behaviour of one of these novel measures, the entanglement of computation, is related to some open problems in computational complexity.

https://iopscience.iop.org/article/10.1088/0305-4470/34/35/324/pdf

On the units of bipartite entanglement: is sixteen ounces of entanglement always equal to one pound?

Computers in the future may weigh no more than 1.5 tons. – Popular Mechanics, forecasting the relentless march of science, 1949 I think there is a world market for maybe five computers. – Thomas Watson, chairman of IBM, 1943 Quantum computation and quantum information is a field of fundamental interest because we believe quantum information processing machines can actually be realized in Nature. Otherwise, the field would be just a mathematical curiosity! Nevertheless, experimental realization of quantum circuits, algorithms, and communication systems has proven extremely challenging. In this chapter we explore some of the guiding principles and model systems for physical implementation of quantum information processing devices and systems. We begin in Section 7.1 with an overview of the tradeoffs in selecting a physical realization of a quantum computer. This discussion provides perspective for an elaboration of a set of conditions sufficient for the experimental realization of quantum computation in Section 7.2. These conditions are illustrated in Sections 7.3 through 7.7, through a series of case studies, which consider five different model physical systems: the simple harmonic oscillator, photons and nonlinear optical media, cavity quantum electrodynamics devices, ion traps, and nuclear magnetic resonance with molecules. For each system, we briefly describe the physical apparatus, the Hamiltonian which governs its dynamics, means for controlling the system to perform quantum computation, and its principal drawbacks.

Michael A. Nielsen

Papers

Quantum computing for the very curious

Quantum computing and polynomial equations over Z_2

Quantum computing and polynomial equations over the finite field Z_2

On the units of bipartite entanglement: is sixteen ounces of entanglement always equal to one pound?

Quantum Computation and Quantum Information: Quantum computers: physical realization