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arXiv:1302.1933 · Nature Nanotechnology

Self-consistent measurement and state tomography of an exchange-only spin qubit

James Medford, J. Beil, Jacob M. Taylor, Stephen D. Bartlett, Andrew C. Doherty, Emmanuel I. RASHBA, David Peter Divincenzo, Hong Lü, Arthur C. Gossard, Charles M. Marcus

Published Aug 30, 2013• 245 citations
arXivHTMLPDF
DOI
10.1038/nnano.2013.168

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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 $\ensuremath{\pi}/2$ rotation for one of the electron spins per measurement.
As a possible physical realization of a quantum information processor, a system with stacked self-assembled InAs quantum dots buried in GaAs adjacent to the channel of a spin field-effect transistor has been proposed. In this system, only one of the stacked qubits, i.e., the edge qubit (the qubit closest to the channel), is measurable via ``spin-blockade measurement.'' It is shown that the state tomography of the whole chain of the qubits is still possible even under such a restricted accessibility. The idea is to make use of the entangling dynamics of the qubits. A recipe for the two-qubit system is explicitly constructed and the effect of an imperfect fidelity of the measurement is clarified. A general scheme for multiple qubits based on repeated measurements is also presented.