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arXiv:1304.2954 · Physical Review B

Tomography scheme for two spin- 12 qubits in a double quantum dot

Niklas Rohling, Guido Burkard

Published Aug 2, 2013• 15 citations
arXivHTMLPDF

Abstract

We present a scheme for full quantum state tomography tailored for two spin qubits in a double quantum dot. A set of 15 quantum states allows to determine the density matrix in this two-qubit space by projective measurement. In this paper, we choose a set gained from mutually unbiased bases. We determine how those 15 projections can be represented by charge measurements after a spin-to-charge conversion and the application of quantum gates. The quantum gates include exchange-based gates as well as rotations by electron spin resonance (ESR). We assume the experimental realization of ESR operations to be more difficult than the exchange gate operation with respect to fidelity and speed. Therefore it is an important result that the ESR gates can be limited to a $\ensuremath{\pi}/2$ rotation for one of the electron spins per measurement.

DOI
10.1103/physrevb.88.085402

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We present a scheme for full quantum state tomography tailored for two spin qubits in a double quantum dot. A set of 15 quantum states allows to determine the density matrix in this two-qubit space by projective measurement. In this paper, we choose a set gained from mutually unbiased bases. We determine how those 15 projections can be represented by charge measurements after a spin-to-charge conversion and the application of quantum gates. The quantum gates include exchange-based gates as well as rotations by electron spin resonance (ESR). We assume the experimental realization of ESR operations to be more difficult than the exchange gate operation with respect to fidelity and speed. Therefore it is an important result that the ESR gates can be limited to a \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 rotation for one of the electron spins per measurement.
We propose a scheme for full Bell state measurement of spin qubits in a double quantum dot. Our scheme consists of Pauli spin-blockade measurements and biaxial electron-spin resonance. In order to eliminate the average of the Zeeman fields, the double quantum dot is designed so that the Land\'e ggg-factors of first and second dots satisfy ${g}_{1}=\ensuremath{-}{g}_{2}$ with the use of ggg-factor engineering. Thus, we can swap one of the three spin-triplet states for the spin-singlet state without disturbing the other states. Our study shows that the sequential spin-to-charge conversions enable us to implement the full Bell state measurement of electron-spin qubits.
We proposed a possible protocol for Bell state measurements of spin qubits in a double quantum dot (QD). Our scheme consists of Pauli spin blockade measurements and biaxial electron spin resonance. It is assumed that the two QDs here are designed so that the Land? g-factors satisfy g1 = ?g2 with the use of g-factor engineering. The opposite sign of the g-factors cancel the average of the Zeeman fields on the two QDs, and enable us to swap three spin-triplet states for a spin-singlet state sequentially. We showed that it is possible to implement the full Bell state measurement by the sequential spin-to-charge conversions in the QD-based spin qubits.
A crucial requirement for quantum-information processing is the realization of multiple-qubit quantum gates. Here, we demonstrate an electron spin-based all-electrical two-qubit gate consisting of single-spin rotations and interdot spin exchange in a double quantum dot. A partially entangled output state is obtained by the application of the two-qubit gate to an initial, uncorrelated state. We find that the degree of entanglement is controllable by the exchange operation time. The approach represents a key step towards the realization of universal multiple-qubit gates.
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.
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Exchange-coupled singlet-triplet spin qubits in two gate-defined double quantum dots are considered theoretically. Using charge density operators to describe the double-dot orbital states, we calculate the Coulomb couplings between the qubits and identify optimal bias points for single- and two-qubit operations, as well as convenient idle positions. The same intuitive formulation is used to derive dephasing rates of these qubits due to the fluctuating charge environment, thereby providing the main considerations for a quantum computation architecture that is within current experimental capabilities.