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arXiv:1210.6590 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Measure of decoherence in quantum error correction for solid-state quantum computing

Alexey A. Melnikov, Leonid Evgenevich Fedichkin

Published Jan 3, 2013• 7 citations
arXivHTMLPDF

Abstract

We considered the interaction of semiconductor quantum register with noisy environment leading to various types of qubit errors. We analysed both phase and amplitude decays during the process of electron-phonon interaction. The performance of quantum error correction codes (QECC) which will be inevitably used in full scale quantum information processors was studied in realistic conditions in semiconductor nanostructures. As a hardware basis for quantum bit we chose the quantum spatial states of single electron in semiconductor coupled double quantum dot system. The modified 5- and 9-qubit quantum error correction (QEC) algorithms by Shor and DiVincenzo without error syndrome extraction were applied to quantum register. 5-qubit error correction procedures were implemented for Si charge double dot qubits in the presence of acoustic phonon environment. ¬-matrix, Choi{Jamio lkowski state and measure of decoherence techniques were used to quantify qubit faulttolerance. Our results showed that the introduction of above quantum error correction techniques at small phonon noise levels provided quadratic improvement of output error rates. The effciency of 5-qubits quantum error correction algorithm in semiconductor quantum information processors was demonstrated.

DOI
10.1117/12.2016639

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We considered the interaction of semiconductor quantum register with noisy environment leading to various types of qubit errors. We analysed both phase and amplitude decays during the process of electron-phonon interaction. The performance of quantum error correction codes (QECC) which will be inevitably used in full scale quantum information processors was studied in realistic conditions in semiconductor nanostructures. As a hardware basis for quantum bit we chose the quantum spatial states of single electron in semiconductor coupled double quantum dot system. The modified 5- and 9-qubit quantum error correction (QEC) algorithms by Shor and DiVincenzo without error syndrome extraction were applied to quantum register. 5-qubit error correction procedures were implemented for Si charge double dot qubits in the presence of acoustic phonon environment. ¬-matrix, Choi{Jamio lkowski state and measure of decoherence techniques were used to quantify qubit faulttolerance. Our results showed that the introduction of above quantum error correction techniques at small phonon noise levels provided quadratic improvement of output error rates. The effciency of 5-qubits quantum error correction algorithm in semiconductor quantum information processors was demonstrated.
We implement the DiVincenzo-Shor 5 qubit quantum error correcting code into a solid-state quantum register. The quantum register is a multi charge-qubit system in a semiconductor environment, where the main sources of noise are phase decoherence and relaxation. We evaluate the decay of the density matrix for this multi-qubit system and perform regular quantum error corrections. The performance of the error correction in this realistic system is found to yield an improvement of the fidelity. The fidelity can be maintained arbitrarily close to one by sufficiently increasing the frequency of error correction. This opens the door for arbitrarily long quantum computations.
This review synthesizes current understanding of decoherence pathways across leading hardware platforms and explains why several experimentally observed noise features—drift, burst events, coherent components, correlated and non-Markovian structure, and leakage—can be disproportionately damaging for QEC. Decoherence remains the dominant impediment to scalable quantum computing because it is not a single error mechanism but a system-level phenomenon arising from materials defects, electromagnetic loss, control electronics, measurement backaction, and the broader environment in which a processor operates. Quantum error correction (QEC) is designed to algorithmically suppress physical noise, yet its practical success depends on how closely real devices satisfy the assumptions under which fault tolerance is proved: approximate locality, weak temporal correlations, sufficiently stochastic error statistics, low leakage, and reliable syndrome extraction. We then evaluate fundamental and engineering challenges that shape the viability of QEC at scale: syndrome measurement fidelity, correlated error suppression, decoding latency and classical co-processing, architectural constraints (connectivity, crosstalk, calibration overhead), and the resource cost of implementing a universal fault-tolerant gate set. Recent demonstrations of below-threshold behaviour and “break-even” regimes show that QEC is transitioning from theory to practice, but also clarify what remains unresolved: maintaining stable noise below fault-tolerance targets over long times, scaling to many logical qubits with low correlated-error rates, and integrating hardware-aware codes and decoders. We conclude with research priorities that treat decoherence and QEC as part of a co-designed stack spanning device physics, control, architecture, and algorithms.
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.