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Semiconductor based quantum information devices

Tobias Zibold

Published Jan 1, 2007• 1 citation
OpenAlex

Abstract

The theory of semiconductor single- and two-qubit quantum logic gates based on quantum wires and quantum dots is studied. A concrete proposal for an all-electric Mach-Zehnder interferometer is worked out by numerical calculations of its electronic structure and ballistic quantum transport properties. We show that this interferometer acts as a single-qubit gate for electrons propagating in quantum wires. The proposal includes the three-dimensional device geometry, materials, doping profiles, and bias voltages. A novel quantum transport device is presented that acts as a two-qubit gate. It is based on the all-electric Mach-Zehnder interferometer and a double quantum dot. We show that this device allows for the controlled generation and detection of entanglement from DC I-V characteristics. To this end, a new quantum transport method has been developed that allows including the Coulomb interaction between two electrons non-perturbatively.

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The theory of semiconductor single- and two-qubit quantum logic gates based on quantum wires and quantum dots is studied. A concrete proposal for an all-electric Mach-Zehnder interferometer is worked out by numerical calculations of its electronic structure and ballistic quantum transport properties. We show that this interferometer acts as a single-qubit gate for electrons propagating in quantum wires. The proposal includes the three-dimensional device geometry, materials, doping profiles, and bias voltages. A novel quantum transport device is presented that acts as a two-qubit gate. It is based on the all-electric Mach-Zehnder interferometer and a double quantum dot. We show that this device allows for the controlled generation and detection of entanglement from DC I-V characteristics. To this end, a new quantum transport method has been developed that allows including the Coulomb interaction between two electrons non-perturbatively.
A GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs based two-qubit quantum device that allows the controlled generation and straightforward detection of entanglement by measuring a stationary current-voltage characteristics is proposed. We have developed a two-particle Green's function method of open systems and calculate the properties of three-dimensional interacting entangled systems nonperturbatively. We present concrete device designs and detailed charge-self-consistent predictions. One of the qubits is an all-electric Mach-Zehnder interferometer that consists of two electrostatically defined quantum wires with coupling windows, whereas the second qubit is an electrostatically defined double quantum dot located in a second two-dimensional electron gas beneath the quantum wires. We find that the entanglement of the device can be controlled externally by tuning the tunneling coupling between the two quantum dots.
We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates.
We study the two-qubit controlled-NOT gate operating on qubits encoded in the spin state of a pair of electrons in a double quantum dot. We assume that the electrons can tunnel between the two quantum dots encoding a single qubit, while tunneling between the quantum dots that belong to different qubits is forbidden. Therefore, the two qubits interact exclusively through the direct Coulomb repulsion of the electrons. We find that entangling two-qubit gates can be performed by the electrical biasing of quantum dots and/or tuning of the tunneling matrix elements between the quantum dots within the qubits. The entangling interaction can be controlled by tuning the bias through the resonance between the singly occupied and doubly occupied singlet ground states of a double quantum dot.
PACS. 73.23.-b – Electronic transport in mesoscopic systems. Abstract. – We study entanglement of charge qubits in a vertical tunnel-coupled double quantum dot containing two interacting electrons. Exact diagonalization is used to compute the negativity characterizing entanglement. We find that entanglement can be efficiently generated and controlled by sidegate voltages, and describe how it can be detected. For large enough tunnel coupling, the negativity shows a pronounced maximum at an intermediate interaction strength within the Wigner molecule regime. Semiconductor few-electron quantum dots (QDs) continue to attract a lot of interest, as it has now become possible to experimentally control both the electronic spin and charge in a condensed-phase environment in an unprecedented manner. In particular, double quantum dots (DQDs) can be fabricated in a well-controlled fashion in high-quality semiconductor devices, and are currently under intense study [1–9]. Vertical or lateral tunnel-coupled DQDs are among the most promising candidates for realizing spin or charge qubits in a quantum information processor [10–12]. Their main advantages are scalability, good control of physical properties via tunable external (sidegate-) voltages or magnetic fields, and spatial separation
We consider one- and two-qubit operations on charge qubits that represent double quantum dots with one electron in each of them. The dots are formed inside a high-Q semiconductor cavity (disk, toroidal, or spherical) in the antinodes of one of its optical eigenmodes; the frequencies of the transitions between the ground (logic) and excited (auxiliary) states of the discrete electron spectrum in quantum dots are close to the frequency of this mode. The precise tuning of the transition frequency is performed by applying an electric potential on the qubit control gate. Within the model of qubits coherently interacting with a cavity quantum field, a few methods for controlling their states are developed. In particular, we propose different variants for implementing two-qubit CNOT and CZ gates and generating qubit entangled states. By the example of a micro-disk cavity, we calculate the operating characteristics that ensure a high rate of quantum gate implementation.
A solid-state implementation of a universal set of gates for quantum computation is proposed and analysed using a time-dependent 2D Schrödinger solver. The qubit is defined as the state of an electron propagating along a couple of quantum wires. The wires are suitably coupled through a potential barrier with variable height and/or width. It is shown how a proper design of the system allows the implementation of any one-qubit transformation. The two-qubit gate is realized through a Coulomb coupler able to entangle the quantum states of two electrons running in two wires of two different qubits. The simulated devices are GaAs—AlGaAs heterostructures that should be on the borderline of present semiconductor technology. An estimate of decoherence effects due to phonon scattering is also presented.