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This paper concerns optically driven quantum logic devices based on semiconductor quantum dots. It provides a brief review of recent theoretical and experimental progress towards building such devices and a description of a possible direction of further research. We consider both the exciton and the electron spin as a potential qubit. Quantum dot fabrication and single dot spectroscopy studies are briefly discussed followed by a description of experimental demonstrations of basic quantum logic operations. A scheme for a scalable quantum computer based on optical control of electron spins localized in quantum dots is described in detail. Important lessons as well as challenges for future research are summarized.

Superconducting qubits are solid state electrical circuits fabricated using techniques borrowed from conventional integrated circuits. They are based on the Josephson tunnel junction, the only non-dissipative, strongly non-linear circuit element available at low temperature. In contrast to microscopic entities such as spins or atoms, they tend to be well coupled to other circuits, which make them appealling from the point of view of readout and gate implementation. Very recently, new designs of superconducting qubits based on multi-junction circuits have solved the problem of isolation from unwanted extrinsic electromagnetic perturbations. We discuss in this review how qubit decoherence is affected by the intrinsic noise of the junction and what can be done to improve it.

Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite the ease of implementation of one-qubit gates. Two-qubit gates necessarily need a non-linear interaction between the two photons, and the efficiency of this non-linear interaction is typically very small in bulk materials. However, it has recently been shown that this barrier can be circumvented with effective non-linearities produced by projective measurements, and with this work linear-optical quantum computing becomes a new avenue towards scalable quantum computation. We review several issues concerning the principles and requirements of this scheme.

The last several years have seen tremendous progress toward practical optical quantum information processing, including the development of single- and entangled-photon sources and high-efficiency photon counting detectors, covering a range of wavelengths. We review some of the recent progress in the development of these photonic technologies.

Spins of single donor atoms are attractive candidates for large scale quantum information processing in silicon. Formation of devices with a few qubits is crucial for validation of basic ideas and development of a scalable architecture. We describe our development of a single ion implantation technique for placement of single atoms into device structures. Collimated highly charged ion beams are aligned with a scanning probe microscope. Enhanced secondary electron emission due to high ion charge states (e.g., P, or Te) allows efficient detection of single ion impacts. Studies of electrical activation of low dose, low energy implants of P in silicon show a drastic effect of dopant segregation to the SiO/Si interface, while SiN/Si retards P segregation. We discuss resolution limiting factors in ion placement, and process challenges for integration of single atom arrays with control gates and single electron transistors.

Solid state qubits promise the great advantage of being naturally scalable to large quantum computer architectures, but they also possess the significant disadvantage of being intrinsically exposed to many sources of noise in the macroscopic solid-state environment. With suitably chosen systems such as superconductors, many of sources of noise can be suppressed. However, imprecision in nanofabrication will inevitably induce defects and disorder, such as charged impurities in the device material or substrate. Such defects generically produce telegraph noise and can hence be modelled as bistable fluctuators. We demonstrate the possibility of the active suppression of such telegraph noise by bang-bang control through an exhaustive study of a qubit coupled to a single bistable fluctuator. We use a stochastic Schrödinger equation, which is solved both numerically and analytically. The resulting dynamics can be visualized as diffusion of a spin vector on the Bloch sphere. We find that bang-bang control suppresses the effect of a bistable fluctuator by a factor roughly equalling the ratio of the bang-bang period and the typical fluctuator period. Therefore, we show the bang-bang protocol works essentially as a high pass filter on the spectrum of such telegraph noise sources. This suggests how the influence of /f-noise ubiquitous to the solid state world could be reduced, as it is typically generated by an ensemble of bistable fluctuators. Finally, we develop random walk models that estimate the level of noise suppression resulting from imperfect bang-bang operations, such as those that cannot be treated as δ-function impulses and those that have phase and axis errors.

We discuss the simulation of complex dynamical systems on a quantum computer. We show that a quantum computer can be used to efficiently extract relevant physical information. It is possible to simulate the dynamical localization of classical chaos and extract the localization length with quadratic speed up with respect to any known classical computation. We can also compute with algebraic speed up the diffusion coefficient and the diffusion exponent, both in the regimes of Brownian and anomalous diffusion. Finally, we show that it is possible to extract the fidelity of the quantum motion, which measures the stability of the system under perturbations, with exponential speed up. The so-called quantum sawtooth map model is used as a test bench to illustrate these results.

We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of our expository article is on analyzing these processes using the Laplace transform on the stochastic recurrences. The resulting time evolution equations, classical vs. quantum, are strikingly similar in form, although dissimilar in behavior. We also provide comparisons with analyses performed using spectral methods.