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arXiv:quant-ph/0503153

Quantum process tomography of a single solid state qubit

Mark Howard, Jason Twamley, Christoffer Wittmann, T. Gaebel, Fedor Jelezko, Jörg Wrachtrup

Published Mar 16, 2005• 3 citations
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Abstract

We present an example of quantum process tomography performed on a single solid state qubit. The qubit used is two energy levels of the triplet state in the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied to a qubit which has been allowed to decohere for three different time periods. In each case the process is found in terms of the $χ$ matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted.

DOI
10.48550/arxiv.quant-ph/0503153

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We present an example of quantum process tomography performed on a single solid state qubit. The qubit used is two energy levels of the triplet state in the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied to a qubit which has been allowed to decohere for three different time periods. In each case the process is found in terms of the χχχ matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted.
We present an example of quantum process tomography (QPT) performed on a single solid-state qubit. The qubit used is two energy levels of the triplet state in the nitrogen vacancy defect in diamond. QPT is applied to a qubit which has been allowed to decohere for three different time periods. In each case, the process is found in terms of the χ matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted. The results of QPT performed after three different decoherence times are used to find the error generators, or Lindblad operators, for the system, using the technique introduced by Boulant et al (2003 Phys. Rev. A 67 042322).
We present an example of quantum process tomography (QPT) performed on a single solid state qubit. The qubit used is two energy levels of the triplet state in the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied to a qubit which has been allowed to decohere for three different time periods. In each case the process is found in terms of the chi matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted. The results of QPT performed after three different decoherence times are used to find the error generators, or Lindblad operators, for the system, using the technique introduced by Boulant et al. [N. Boulant, T.F. Havel, M.A. Pravia and D.G. Cory, Phys. Rev. A 67, 042322 (2003)].
We present the experimental reconstruction of the Wigner function of an individual electronic spin qubit associated with a nitrogen-vacancy center in diamond at room temperature. This spherical Wigner function contains the same information as the density matrix for arbitrary spin systems. As an example, we exactly characterize the quantum state of a single qubit undergoing a nearly pure dephasing process by the Wigner function. The fidelities and purities during this process are extracted from the experimentally reconstructed Wigner functions, whose dynamics agree with the theoretical prediction.
We investigate a range of methods to perform tomography in a solid-state qubit device, for which a priori initialization and measurement of the qubit is restricted to a single basis of the Bloch sphere. We explore and compare several methods to acquire precise descriptions of additional states and measurements, quantifying both stochastic and systematic errors, ultimately leading to a tomographically complete set that can be subsequently used in process tomography. We focus in detail on the example of a spin qubit formed by the singlet-triplet subspace of two electron spins in a GaAs double quantum dot, although our approach is quite general.
A quantum logical NOT and a conditional two-qubit gate (CROT), are implemented with single spins in a solid. As quantum bits a single electron spin and a single 13C nuclear spin of a single nitrogen vacancy defect center in diamond are used. The quantum state of the electron spin can be read out optically. Owing to long decoherence and relaxation times the systems meets the requirements of hardware for quantum computation. Density matrix tomography of the CROT gate shows that the achieved performance of the two bit conditional quantum gate is promising. The gate fidelity achieved in our experiments is up to 0.9, good enough to be used in quantum algorithms. Further on, the system may allow for solid-state room temperature quantum computation