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arXiv:0710.3572 · Physical Review B

Theory of semiconductor quantum-wire-based single- and two-qubit gates

Tobias Zibold, Peter Vogl, Andrea Bertoni

Published Nov 1, 2007• 21 citations
arXivHTMLPDF

Abstract

A $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ 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.

DOI
10.1103/physrevb.76.195301

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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.
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.
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.
A parity meter projects the state of two qubits onto two subspaces with different parities, the states in each parity class being indistinguishable. It has application in quantum information for its entanglement properties. In our work we consider the electronic Mach-Zehnder interferometer (MZI) coupled capacitively to two double quantum dots (DQDs), one on each arm of the MZI. These charge qubits couple linearly to the charge in the arms of the MZI. A key advantage of an MZI is that the qubits are well separated in distance so that mutual interaction between them is avoided. Assuming equal coupling between both DQDs and the arms and the same bias for each DQD, this setup usually detects three different currents, one for the odd states and two for each even state. Controlling the magnetic flux of the MZI, we can operate the MZI as a parity meter: only two currents are measured at the output, one for each parity class. In this configuration, the MZI acts as an ideal detector, its Heisenberg efficiency being maximal. Initially unentangled DQDs become entangled through the parity measurement process with probability one and for a class of initial states our parity meter deterministically generates Bell states.
We present a proposal for a qubit charge meter (detector) based on a linear wire of quantum dots placed between two electron reservoirs. A qubit formed by an excess electron in a double quantum dot is coupled electrostatically with a single wire site and the dynamics of this system is studied using the equation of motion for appropriate correlation functions and the evolution operator method. For the qubit-wire system, depending on the qubit position on the wire the readout current oscillates over a long time or the current oscillations decrease very rapidly. This effect cannot be explained in terms of different charges of the wire sites (the same occupancies of all sites are considered). We have found that the qubit's decoherence strongly depends on the structure of the local density of states of the site which is coupled with the qubit. Additionally, the period of the readout current oscillations changes with the wire-qubit electrostatic coupling.