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

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

Long-range photon-mediated gate scheme between nuclear spin qubits in diamond

Defect centers in diamond are exceptional solid-state quantum systems that can have exceedingly long electron and nuclear spin coherence times. So far, single-qubit gates for the nitrogen nuclear spin, a two-qubit gate with a nitrogen-vacancy (NV) center electron spin, and entanglement between nearby nitrogen nuclear spins have been demonstrated. Here, we develop a scheme to implement a universal two-qubit gate between two distant nitrogen nuclear spins. Virtual excitation of an NV center that is embedded in an optical cavity can scatter a laser photon into the cavity mode; we show that this process depends on the nuclear spin state of the nitrogen atom. If two NV centers are simultaneously coupled to a common cavity mode and individually excited, virtual cavity photon exchange can mediate an effective interaction between the nuclear spin qubits, conditioned on the spin state of both nuclei, which implements a universal controlled-$\textit{Z}$ gate. We predict operation times below 100 nanoseconds, which is several orders of magnitude faster than the decoherence time of nuclear spin qubits in diamond.Comment: 6 pages (including 2 appendices), 3 figures, 1 tabl

Decoherence in Solid State Qubits

Interaction of solid state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review we discuss how decoherence affects two of the most successful realizations of solid state qubits, namely, spin-qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behavior at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin-orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux, and bias voltages, and via losses in the dissipative circuit elements.Comment: review article, 66 pages, 10 figure