Theory of solid state quantum information processing

Recent theoretical work on solid-state proposals for the implementation of quantum computation and quantum information processing is reviewed. The differences and similarities between microscopic and macroscopic qubits are highlighted and exemplified by the spin qubit proposal on one side and the superconducting qubits on the other. Before explaining the spin and supercondcuting qubits in detail, some general concepts that are relevant for both types of solid-state qubits are reviewed. The controlled production of entanglement in solid-state devices, the transport of carriers of entanglement, and entanglement detection will be discussed in the final part of this review.Comment: 57 pages, 33 figures, review article, prepared for Handbook of Theoretical and Computational Nanotechnology. v.2: minor revision; references adde

Non-Markovian qubit dynamics in the presence of 1/f noise

Within the lowest-order Born approximation, we calculate the exact dynamics of a single qubit in the presence of 1/f noise, without making any Markov approximation. We show that the non-Markovian qubit time-evolution exhibits asymmetries and beatings that cannot be explained within a Markovian theory. The present theory for 1/f noise is relevant for both spin- and superconducting qubit realizations in solid-state devices, where 1/f noise is ubiquitous.Comment: v2: 6.2 pages, 5 figures, published versio

Homo heidelbergensis: The Tool to Our Success

Homo heidelbergensis, a physiological variant of the species Homo sapien, is an extinct species that existed in both Europe and parts of Asia from 700,000 years ago to roughly 300,000 years ago (carbon dating). This “subspecies” of Homo sapiens, as it is formally classified, is a direct ancestor of anatomically modern humans, and is understood to have many of the same physiological characteristics as those of anatomically modern humans while still expressing many of the same physiological attributes of Homo erectus, an earlier human ancestor. Since Homo heidelbergensis represents attributes of both species, it has therefore earned the classification as a subspecies of Homo sapiens and Homo erectus. Homo heidelbergensis, like anatomically modern humans, is the byproduct of millions of years of natural selection and genetic variation. It is understood through current scientific theory that roughly 200,000 years ago (carbon dating), archaic Homo sapiens and Homo erectus left Africa in pursuit of the small and large animal game that were migrating north into Europe and Asia. As they migrated north with their food source, the climates that these individuals faced were completely opposite to the environment that they were subjected to in Africa

Lower bound for electron spin entanglement from beamsplitter current correlations

We determine a lower bound for the entanglement of pairs of electron spins injected into a mesoscopic conductor. The bound can be expressed in terms of experimentally accessible quantities, the zero-frequency current correlators (shot noise power or cross-correlators) after transmission through an electronic beam splitter. The effect of spin relaxation (T_1 processes) and decoherence (T_2 processes) during the ballistic coherent transmission of the carriers in the wires is taken into account within Bloch theory. The presence of a variable inhomogeneous magnetic field allows the determination of a useful lower bound for the entanglement of arbitrary entangled states. The decrease in entanglement due to thermally mixed states is studied. Both the entanglement of the output of a source (entangler) and the relaxation (T_1) and decoherence (T_2) times can be determined.Comment: 4 pages, 3 figure

Universal Quantum Computing with Spin and Valley

We investigate a two-electron double quantum dot with both spin and valley degrees of freedom as they occur in graphene, carbon nanotubes, or silicon, and regard the 16-dimensional space with one electron per dot as a four-qubit logic space. In the spin-only case, it is well known that the exchange coupling between the dots combined with arbitrary single-qubit operations is sufficient for universal quantum computation. The presence of the valley degeneracy in the electronic band structure alters the form of the exchange coupling and in general leads to spin-valley entanglement. Here, we show that universal quantum computation can still be performed by exchange interaction and single-qubit gates in the presence of the additional (valley) degree of freedom. We present an explicit pulse sequence for a spin-only controlled-NOT consisting of the generalized exchange coupling and single-electron spin and valley rotations. We also propose state preparations and projective measurements with the use of adiabatic transitions between states with (1,1) and (0,2) charge distributions similar to the spin-only case, but with the additional requirement of controlling the spin and the valley Zeeman energies by an external magnetic field. Finally, we demonstrate a universal two-qubit gate between a spin and a valley qubit, allowing universal gate operations on the combined spin and valley quantum register.Comment: 18 pages, 3 figures, 1 tabl