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

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

▪ Abstract Solution phase syntheses and size-selective separation methods to prepare semiconductor and metal nanocrystals, tunable in size from ∼1 to 20 nm and monodisperse to ≤5%, are presented. Preparation of monodisperse samples enables systematic characterization of the structural, electronic, and optical properties of materials as they evolve from molecular to bulk in the nanometer size range. Sample uniformity makes it possible to manipulate nanocrystals into close-packed, glassy, and ordered nanocrystal assemblies (superlattices, colloidal crystals, supercrystals). Rigorous structural characterization is critical to understanding the electronic and optical properties of both nanocrystals and their assemblies. At inter-particle separations 5–100 A, dipole-dipole interactions lead to energy transfer between neighboring nanocrystals, and electronic tunneling between proximal nanocrystals gives rise to dark and photoconductivity. At separations <5 A, exchange interactions cause otherwise insulating ass...

Synthesis and Characterization of Monodisperse Nanocrystals and Close-Packed Nanocrystal Assemblies

as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

/pdf/decoherence-einselection-and-the-quantum-origins-of-the-5c70dshgfi.pdf

Decoherence, einselection, and the quantum origins of the classical

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansatze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry--calculating the ground-state molecular energy for He-H(+). The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future.

/pdf/a-variational-eigenvalue-solver-on-a-photonic-quantum-2nxrfjmr5w.pdf

A variational eigenvalue solver on a photonic quantum processor

In this paper we study a model quantum register $R$ made of $N$ replicas (cells) of a given finite-dimensional quantum system S. Assuming that all cells are coupled with a common environment with equal strength we show that, for $N$ large enough, in the Hilbert space of $R$ there exists a linear subspace ${C}_{N}$ which is dynamically decoupled from the environment. The states in ${C}_{N}$ evolve unitarily and are therefore decoherence-dissipation free. The space ${C}_{N}$ realizes a noiseless quantum code in which information can be stored, in principle, for an arbitrarily long time without being affected by errors.

Noiseless Quantum Codes

Holonomic quantum computation

We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and $XY$ models, we show that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it. Further, we discuss the connections between this approach and the Anderson orthogonality catastrophe as well as with the dynamical study of the Loschmidt echo for critical systems.

https://arxiv.org/pdf/quant-ph/0512249.pdf

Ground state overlap and quantum phase transitions.

We study the transition of a quantum system S from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system E coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of E modeled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of E strongly affects its capability of enhancing the decay of LE: near the critical value of the transverse field entailing the happening of quantum phase transition, the off-diagonal elements of the reduced density matrix describing S vanish sharply.

/pdf/decay-of-loschmidt-echo-enhanced-by-quantum-criticality-dwdpc4gqqr.pdf

Decay of Loschmidt echo enhanced by quantum criticality.

An all optical implementation of quantum information processing with semiconductor macroatoms is proposed. Our quantum hardware consists of an array of quantum dots and the computational degrees of freedom are energy-selected interband optical transitions. The quantum-computing strategy exploits exciton-exciton interactions driven by ultrafast multicolor laser pulses. Contrary to existing proposals based on charge excitations, our approach does not require time-dependent electric fields, thus allowing for a subpicosecond, decoherence-free, operation time scale in realistic semiconductor nanostructures.

/pdf/quantum-information-processing-with-semiconductor-macroatoms-54nmptzcgk.pdf

Paolo Zanardi

Papers

Noiseless Quantum Codes

Holonomic quantum computation

Ground state overlap and quantum phase transitions.

Decay of Loschmidt echo enhanced by quantum criticality.

Quantum information processing with semiconductor macroatoms.