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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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

J. Appl. Cryst.の発刊に際して

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

Decoherence in quantum computers is formulated within the semigroup approach The error generators are identified with the generators of a Lie algebra This allows for a comprehensive description which includes as a special case the frequently assumed spin-boson model A generic condition is presented for errorless quantum computation: decoherence-free subspaces are spanned by those states which are annihilated by all the generators It is shown that these subspaces are stable to perturbations and, moreover, that universal quantum computation is possible within them

/pdf/decoherence-free-subspaces-for-quantum-computation-3cpk045d2s.pdf

Decoherence-Free Subspaces for Quantum Computation

Quantum annealing is expected to solve certain optimization problems more efficiently, but there are still open questions regarding the functioning of devices such as D-Wave One. A numerical and experimental investigation of its performance shows evidence for quantum annealing with 108 qubits.

/pdf/evidence-for-quantum-annealing-with-more-than-one-hundred-1i2tupxr4o.pdf

Evidence for quantum annealing with more than one hundred qubits

The simple act of slowly varying the parameters of a quantum system so that it remains always in its ground state is extremely rich from an information processing point of view. For an ideal, closed system, this adiabatic evolution is equivalent to full quantum computation, and it is convenient for establishing quantum algorithms for optimization. This review presents adiabatic quantum algorithms, proves the closed-system equivalence of the adiabatic and circuit models of quantum computation, reviews the placement of adiabatic quantum computation in the more general classification of computational complexity theory, and discusses the case of ``stoquastic'' quantum evolutions.

Adiabatic quantum computation

The development of small-scale quantum devices raises the question of how to fairly assess and detect quantum speedup. Here, we show how to define and measure quantum speedup and how to avoid pitfalls that might mask or fake such a speedup. We illustrate our discussion with data from tests run on a D-Wave Two device with up to 503 qubits. By using random spin glass instances as a benchmark, we found no evidence of quantum speedup when the entire data set is considered and obtained inconclusive results when comparing subsets of instances on an instance-by-instance basis. Our results do not rule out the possibility of speedup for other classes of problems and illustrate the subtle nature of the quantum speedup question.

/pdf/defining-and-detecting-quantum-speedup-5dsp6b6708.pdf

Defining and detecting quantum speedup

We review our work concerning a method of decoherence control via concatenated dynamical decoupling (DD) pulses. These recursively nested DD pulse sequences exhibit a fault-tolerance threshold similar to that of concatenated quantum error correcting codes. We briefly discuss how quantum logic gates can be incorporated into this framework.

/pdf/fault-tolerant-quantum-dynamical-decoupling-2j9g56phf3.pdf

Daniel A. Lidar

Papers

Decoherence-Free Subspaces for Quantum Computation

Evidence for quantum annealing with more than one hundred qubits

Adiabatic quantum computation

Defining and detecting quantum speedup

Fault-tolerant quantum dynamical decoupling