Ground State and Resonances in the Standard Model of Non-relativistic QED

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change

Topologically protected quantum bits from Josephson junction arrays

All physical implementations of quantum bits (qubits), carrying the information and computation in a putative quantum computer, have to meet the conflicting requirements of environmental decoupling while remaining manipulable through designed external signals. Proposals based on quantum optics naturally emphasize the aspect of optimal isolation, while those following the solid state route exploit the variability and scalability of modern nanoscale fabrication techniques. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation, however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task. Protecting qubits from decoherence by exploiting topological stability, a qualitatively new proposal due to Kitaev, holds the promise for long decoherence times, but its practical physical implementation has remained unclear so far. Here, we show how strongly correlated systems developing an isolated two-fold degenerate quantum dimer liquid groundstate can be used in the construction of topologically stable qubits and discuss their implementation using Josephson junction arrays.Comment: 6 pages, 4 figure

An addressable quantum dot qubit with fault-tolerant control fidelity

Exciting progress towards spin-based quantum computing has recently been made with qubits realized using nitrogen-vacancy (N-V) centers in diamond and phosphorus atoms in silicon, including the demonstration of long coherence times made possible by the presence of spin-free isotopes of carbon and silicon. However, despite promising single-atom nanotechnologies, there remain substantial challenges in coupling such qubits and addressing them individually. Conversely, lithographically defined quantum dots have an exchange coupling that can be precisely engineered, but strong coupling to noise has severely limited their dephasing times and control fidelities. Here we combine the best aspects of both spin qubit schemes and demonstrate a gate-addressable quantum dot qubit in isotopically engineered silicon with a control fidelity of 99.6%, obtained via Clifford based randomized benchmarking and consistent with that required for fault-tolerant quantum computing. This qubit has orders of magnitude improved coherence times compared with other quantum dot qubits, with T_2* = 120 mus and T_2 = 28 ms. By gate-voltage tuning of the electron g*-factor, we can Stark shift the electron spin resonance (ESR) frequency by more than 3000 times the 2.4 kHz ESR linewidth, providing a direct path to large-scale arrays of addressable high-fidelity qubits that are compatible with existing manufacturing technologies

Quantum computation with two-level trapped cold ions beyond Lamb-Dicke limit

We propose a simple scheme for implementing quantum logic gates with a string of two-level trapped cold ions outside the Lamb-Dicke limit. Two internal states of each ion are used as one computational qubit (CQ) and the collective vibration of ions acts as the information bus, i.e., bus qubit (BQ). Using the quantum dynamics for the laser-ion interaction as described by a generalized Jaynes-Cummings model, we show that quantum entanglement between any one CQ and the BQ can be coherently manipulated by applying classical laser beams. As a result, universal quantum gates, i.e. the one-qubit rotation and two-qubit controlled gates, can be implemented exactly. The required experimental parameters for the implementation, including the Lamb-Dicke (LD) parameter and the durations of the applied laser pulses, are derived. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.Comment: 12 pages, no figures, to appear in Phys. Rev.

Towards Quantum Repeaters with Solid-State Qubits: Spin-Photon Entanglement Generation using Self-Assembled Quantum Dots

In this chapter we review the use of spins in optically-active InAs quantum dots as the key physical building block for constructing a quantum repeater, with a particular focus on recent results demonstrating entanglement between a quantum memory (electron spin qubit) and a flying qubit (polarization- or frequency-encoded photonic qubit). This is a first step towards demonstrating entanglement between distant quantum memories (realized with quantum dots), which in turn is a milestone in the roadmap for building a functional quantum repeater. We also place this experimental work in context by providing an overview of quantum repeaters, their potential uses, and the challenges in implementing them.Comment: 51 pages. Expanded version of a chapter to appear in "Engineering the Atom-Photon Interaction" (Springer-Verlag, 2015; eds. A. Predojevic and M. W. Mitchell

Silicon-based spin and charge quantum computation

Silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals due to the relatively long spin coherence times. For these spin qubits, donor electron charge manipulation by external gates is a key ingredient for control and read-out of single-qubit operations, while shallow donor exchange gates are frequently invoked to perform two-qubit operations. More recently, charge qubits based on tunnel coupling in P$_2^+$ substitutional molecular ions in Si have also been proposed. We discuss the feasibility of the building blocks involved in shallow donor quantum computation in silicon, taking into account the peculiarities of silicon electronic structure, in particular the six degenerate states at the conduction band edge. We show that quantum interference among these states does not significantly affect operations involving a single donor, but leads to fast oscillations in electron exchange coupling and on tunnel-coupling strength when the donor pair relative position is changed on a lattice-parameter scale. These studies illustrate the considerable potential as well as the tremendous challenges posed by donor spin and charge as candidates for qubits in silicon.Comment: Review paper (invited) - to appear in Annals of the Brazilian Academy of Science

Control and manipulation of entanglement between two coupled qubits by fast pulses

We have investigated the analytical and numerical dynamics of entanglement for two qubits that interact with each other via Heisenberg XXX-type interaction and subject to local time-specific external kick and Gaussian pulse-type magnetic fields in x-y plane. The qubits have been assumed to be initially prepared in different pure separable and maximally entangled states and the effect of the strength and the direction of external fast pulses on concurrence has been investigated. The carefully designed kick or pulse sequences are found to enable one to obtain constant long-lasting entanglement with desired magnitude. Moreover, the time ordering effects are found to be important in the creation and manipulation of entanglement by external fields.Comment: 18 pages, 6 figure

Phase-locked indistinguishable photons with synthesized waveforms from a solid-state source

Resonance fluorescence in the Heitler regime provides access to single photons with coherence well beyond the Fourier transform limit of the transition, and holds the promise to circumvent environment-induced dephasing common to all solid-state systems. Here we demonstrate that the coherently generated single photons from a single self-assembled InAs quantum dot display mutual coherence with the excitation laser on a timescale exceeding 3 seconds. Exploiting this degree of mutual coherence we synthesize near-arbitrary coherent photon waveforms by shaping the excitation laser field. In contrast to post-emission filtering, our technique avoids both photon loss and degradation of the single photon nature for all synthesized waveforms. By engineering pulsed waveforms of single photons, we further demonstrate that separate photons generated coherently by the same laser field are fundamentally indistinguishable, lending themselves to creation of distant entanglement through quantum interference.Comment: Additional data and analysis in PDF format is available for download at the publications section of our website: http://www.amop.phy.cam.ac.uk/amop-ma