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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

The interaction of matter and light is one of the fundamental processes occurring in nature, and its most elementary form is realized when a single atom interacts with a single photon. Reaching this regime has been a major focus of research in atomic physics and quantum optics1 for several decades and has generated the field of cavity quantum electrodynamics2,3. Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity consisting of a superconducting transmission line resonator. We show that the strong coupling regime can be attained in a solid-state system, and we experimentally observe the coherent interaction of a superconducting two-level system with a single microwave photon. The concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter. This system can also be exploited for quantum information processing and quantum communication and may lead to new approaches for single photon generation and detection.

https://arxiv.org/pdf/cond-mat/0407325.pdf

Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics

The semiconductor industry has seen a remarkable miniaturization trend, driven by many scientific and technological innovations. But if this trend is to continue, and provide ever faster and cheaper computers, the size of microelectronic circuit components will soon need to reach the scale of atoms or molecules—a goal that will require conceptually new device structures. The idea that a few molecules, or even a single molecule, could be embedded between electrodes and perform the basic functions of digital electronics—rectification, amplification and storage—was first put forward in the mid-1970s. The concept is now realized for individual components, but the economic fabrication of complete circuits at the molecular level remains challenging because of the difficulty of connecting molecules to one another. A possible solution to this problem is ‘mono-molecular’ electronics, in which a single molecule will integrate the elementary functions and interconnections required for computation.

Electronics using hybrid-molecular and mono-molecular devices

We propose a realizable architecture using one-dimensional transmission line resonators to reach the strong-coupling limit of cavity quantum electrodynamics in superconducting electrical circuits. The vacuum Rabi frequency for the coupling of cavity photons to quantized excitations of an adjacent electrical circuit (qubit) can easily exceed the damping rates of both the cavity and qubit. This architecture is attractive both as a macroscopic analog of atomic physics experiments and for quantum computing and control, since it provides strong inhibition of spontaneous emission, potentially leading to greatly enhanced qubit lifetimes, allows high-fidelity quantum nondemolition measurements of the state of multiple qubits, and has a natural mechanism for entanglement of qubits separated by centimeter distances. In addition it would allow production of microwave photon states of fundamental importance for quantum communication.

https://arxiv.org/pdf/cond-mat/0402216.pdf

Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation

5-7 as a candidate for a quantum bit or 'qubit'—the basic component of a quantum computer. Here we report the observation of quantum oscillations in a single- Cooper-pair box. By applying a short voltage pulse via a gate electrode, we can control the coherent quantum state evolution: the pulse modifies the energies of the two charge states non- adiabatically, bringing them into resonance. The resulting state— a superposition of the two charge states—is detected by a tunnelling current through a probe junction. Our results demon- strate electrical coherent control of a qubit in a solid-state

Coherent control of macroscopic quantum states in a single-Cooper-pair box

An atom in open space can be detected by means of resonant absorption and reemission of electromagnetic waves, known as resonance fluorescence, which is a fundamental phenomenon of quantum optics. We report on the observation of scattering of propagating waves by a single artificial atom. The behavior of the artificial atom, a superconducting macroscopic two-level system, is in a quantitative agreement with the predictions of quantum optics for a pointlike scatterer interacting with the electromagnetic field in one-dimensional open space. The strong atom-field interaction as revealed in a high degree of extinction of propagating waves will allow applications of controllable artificial atoms in quantum optics and photonics.

/pdf/resonance-fluorescence-of-a-single-artificial-atom-v3qlvwjd3t.pdf

Resonance Fluorescence of a Single Artificial Atom

We present experimental observation of electromagnetically induced transparency (EIT) on a single macroscopic artificial "atom" (superconducting quantum system) coupled to open 1D space of a transmission line. Unlike in an optical media with many atoms, the single-atom EIT in 1D space is revealed in suppression of reflection of electromagnetic waves, rather than absorption. The observed almost 100% modulation of the reflection and transmission of propagating microwaves demonstrates full controllability of individual artificial atoms and a possibility to manipulate the atomic states. The system can be used as a switchable mirror of microwaves and opens a good perspective for its applications in photonic quantum information processing and other fields.

Electromagnetically Induced Transparency on a Single Artificial Atom

The magnetic-flux analogue to coherent Josephson tunnelling of electric charge has been observed in a strongly disordered superconducting nanowire. Coherent quantum phase slip (CQPS) has not, until now, been observed experimentally. It is a phenomenon exactly dual to the Josephson effect, but whereas the latter is a coherent transfer of charges between superconducting contacts, CQPS is a coherent transfer of vortices or fluxes across a superconducting wire. This paper reports direct observation of CQPS in a strongly disordered indium oxide superconducting wire inserted in a loop; the effect manifests through the superposition of quantum states with different fluxes. The CQPS may — like the Josephson effect before it — lead to innovative applications in superconducting electronics and quantum metrology. A hundred years after the discovery of superconductivity, one fundamental prediction of the theory, coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual1 to the Josephson effect; whereas the latter is a coherent transfer of charges between superconducting leads2,3, the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations4,5,6,7,8 of incoherent phase slip, CQPS has been only a subject of theoretical study9,10,11,12. Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors near the superconductor–insulator transition. Here we report direct observation of CQPS in a narrow segment of a superconducting loop made of strongly disordered indium oxide; the effect is made manifest through the superposition of quantum states with different numbers of flux quanta13. As with the Josephson effect, our observation should lead to new applications in superconducting electronics and quantum metrology1,10,11.

/pdf/coherent-quantum-phase-slip-1cv1t9l6x1.pdf

Coherent quantum phase slip

We investigated temporal behavior of an artificial two-level system driven by a strong oscillating field; namely, quantum-state evolution between two charge states in a small Josephson-junction circuit irradiated with microwaves. Rabi oscillations corresponding to 0-, 1-, and 2-photon resonances were observed. As a function of microwave amplitude, the Rabi frequencies followed a first-kind Bessel function of the corresponding order to the number of photons.

Yu. A. Pashkin

Papers

Coherent control of macroscopic quantum states in a single-Cooper-pair box

Resonance Fluorescence of a Single Artificial Atom

Electromagnetically Induced Transparency on a Single Artificial Atom

Coherent quantum phase slip

Rabi Oscillations in a Josephson-Junction Charge Two-Level System