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Acta Physica Polonica A

Collective Encoding of Quantum Information in a Quantum Dot Register

Anna Grodecka, Paweł Machnikowski

Published Aug 1, 2006• 1 citation
Publisher

Abstract

We define the collective logical quantum bit as a state on an array of 2, 4, and 8 quantum dots.We show that such an array can be controlled with less phonon-induced pure dephasing than a single dot.We calculate the dephasing accompanying a single-qubit operation on the collective logical qubit by means of perturbative method describing the open system evolution under arbitrary driving.

DOI
10.12693/aphyspola.110.195

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We define the collective logical quantum bit as a state on an array of 2, 4, and 8 quantum dots.We show that such an array can be controlled with less phonon-induced pure dephasing than a single dot.We calculate the dephasing accompanying a single-qubit operation on the collective logical qubit by means of perturbative method describing the open system evolution under arbitrary driving.
We show that phonon-induced pure dephasing of an excitonic (charge) quantum bit in a quantum dot (QD) may be reduced by collective encoding of logical qubits in QD arrays. We define the logical qubit on an array of 2, 4 and 8 QDs, connecting the logical |0⟩ state with the presence of excitons in the appropriately chosen half of dots and the logical |1⟩ state with the other half of the dots occupied. We give quantitative estimates of the resulting total error of a single qubit operation for an InAs/GaAs system.
We designed an encoding scheme, using quantum dots (QDs), for single logical qubit information by encoding quantum information onto four-photon decoherence-free states to acquire immunity against collective decoherence. The designed scheme comprised of QDs, confined in single-sided cavities (QD-cavity systems), used for arbitrary quantum information, encoded onto four-photon decoherence-free states (logical qubits). For our scheme, which can generate the four-photon decoherence-free states, and can encode quantum information onto logical qubits, high efficiency and reliable performance of the interaction between the photons and QD-cavity systems is essential. Thus, through our analysis of the performance of QD-cavity systems under vacuum noise and sideband leakage, we demonstrate that the encoding scheme for single logical qubit information could be feasibly implemented.
A potential implementation of quantum-computation schemes in semiconductor-based structures is proposed. In particular, an array of quantum dots is shown to be an ideal quantum register for a noiseless information encoding. In addition to the suppression of phase-breaking processes in quantum dots due to the well-known phonon bottleneck, we show that a proper quantum encoding allows one to realize a decoherence-free evolution on a time scale long compared to the femtosecond scale of modern ultrafast laser technology. This result might open the way to the realization of semiconductor-based quantum processors.
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.