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arXiv:cond-mat/0405412 · Physical Review A

Double-dot chain as a macroscopic quantum bit

FERDINANDO DE PASQUALE, Gian Luca Giorgi, Simone Paganelli

Published Apr 4, 2005• 12 citations
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Abstract

We consider an array of $N$ quantum dot pairs interacting via Coulomb interaction between adjacent dots and hopping inside each pair. We show that at the first order in the ratio of hopping and interaction amplitudes, the array maps in an effective two-level system with energy separation becoming exponentially small in the macroscopic (large-$N$) limit. Decoherence at zero temperature is studied in the limit of weak coupling with phonons. In this case, the macroscopic limit is robust with respect to decoherence. Some possible applications in quantum information processing are discussed.

DOI
10.1103/physreva.71.042304

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We consider an array of NNN quantum dot pairs interacting via Coulomb interaction between adjacent dots and hopping inside each pair. We show that at the first order in the ratio of hopping and interaction amplitudes, the array maps in an effective two-level system with energy separation becoming exponentially small in the macroscopic (large-NNN) limit. Decoherence at zero temperature is studied in the limit of weak coupling with phonons. In this case, the macroscopic limit is robust with respect to decoherence. Some possible applications in quantum information processing are discussed.
Using exact diagonalization, we study double quantum dot system with one of the dots attached to the ideal leads acting as source and drain in T-shaped geometry. The leads are incorporated in zero-bandwidth limit by replacing their band structures with one level coinciding with Fermi levels in the respective leads. For the half-filled case, the spin-spin correlation for the dots are calculated numerically at zero as well as finite temperatures. At zero temperature, an antiferromagnetic correlation between the dots is observed for finite values of interdot tunneling matrix-element. The antiferromagnetic correlation between the dots changes remarkably for large values of ondot Coulomb interaction both at zero as well as finite temperatures. The spin-spin correlation between the dots is significantly reduced even for small values of the inderdot Coulomb interaction compared to the ondot Coulomb interaction. At a small value of temperature, the spin-spin correlation between the dots exhibits a (negative) maximum due to contributions coming from thermal excitations to low-lying states.
A potential implementation of quantum-information schemes in semiconductor nanostructures is studied. To this end, the formal theory of quantum encoding for avoiding errors is recalled and the existence of noiseless states for model systems is discussed. Based on this theoretical framework, we analyze the possibility of designing noiseless quantum codes in realistic semiconductor structures. In the specific implementation considered, information is encoded in the lowest energy sector of charge excitations of a linear array of quantum dots. The decoherence channel considered is electron-phonon coupling We show that besides the well-known phonon bottleneck, reducing single-qubit decoherence, suitable many-qubit initial preparation, as well as register design may enhance the decoherence time by several orders of magnitude. This behavior stems from the effective one-dimensional character of the phononic environment in the relevant region of physical parameters.
Coupled quantum dots are an example of the ubiquitous quantum double potential well. In a typical transport experiment, each quantum dot is also coupled to a continuum of states. Our approach takes this into account by using a Green’s function formalism to solve the full system. The time-dependent solution is then explored in different limiting cases. In general, a combination of coherent and incoherent behavior is observed. In the case that the coupling of each dot to the macroscopic world is equal, however, the time evolution is purely coherent. The double-well potential is one of the simplest and best understood problems in modern quantum mechanics. Its utility is likewise unparalleled. Potential applications of double-well devices have been noted in Refs. [1-5]. For such devices to be useful, an understanding of the processes which couple the microscopic device to the macroscopic environment is paramount. That is to say, the decoherence processes of such systems must be well understood. To this end, we consider a simple exactly solvable model of two coupled quantum dots. An excellent review of related systems and some approximate solutions are given in Ref. [6]. Each dot is coupled to an environment (a triple-barrier system) as in Fig. 1. The environment consists of a continuum of states, as would be appropriate for a macroscopic lead. Only one state in each quantum dot is considered, which amounts to the assumption that the tunneling parameters connecting our two states to any neglected state are much less than the energy differences with that state. The Hamiltonian of the system can be written as the sum of two terms, H = H0 + Hc. The first term, H0, represents the dynamics of the simple two-state system, H0 = ε1d † 1d1 + ε2d † 2 d2 + V (d† 1d2 + d†
We present a model of quantum teleportation protocol based on a double quantum dot array. The unknown qubit is encoded using a pair of quantum dots, with one excess electron, coupled by tunneling. It is shown how to create a maximally entangled state using an adiabatically increasing Coulomb repulsion between different dot pairs. This entangled state is exploited to perform teleportation again using an adiabatic coupling between itself and the incoming unknown state. Finally, a sudden separation of Bob's qubit allows a time evolution of Alice's, which amounts to a modified version of standard Bell measurement. A transmission over a long distance could be obtained by considering the entangled state of a chain of N coupled double quantum dots. The system is shown to be increasingly robust with N against decoherence due to phonons.
We present a model of quantum teleportation protocol based on a double quantum dot array. The unknown qubit is encoded using a pair of quantum dots, with one excess electron, coupled by tunneling. It is shown how to create a maximally entangled state using an adiabatically increasing Coulomb repulsion between different dot pairs. This entangled state is exploited to perform teleportation again using an adiabatic coupling between itself and the incoming unknown state. Finally, a sudden separation of Bob’s qubit allows a time evolution of Alice’s which amounts to a modified version of standard Bell measurement. A transmission over a long distance could be obtained by considering the entangled state of a chain of N coupled double quantum dots. The system is shown to be increasingly robust with N against decoherence due to phonons.
Recent experiments by [Hayashi et al., Phys. Rev. Lett. 91, 226804 (2003)] demonstrate coherent oscillations of a charge quantum bit in laterally defined quantum dots. We study the intrinsic electron-phonon decoherence and gate performance for the next step: a system of two coupled charge qubits. The effective decoherence model contains properties of local as well as collective decoherence. Decoherence channels can be classified by their multipole moments, which leads to different low-energy spectra. It is shown that due to the super-Ohmic spectrum, the gate quality is limited by the single-qubit Hadamard gates. It can be significantly improved, by using double dots with weak tunnel coupling.