Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0805.2370

Quantitative Evaluation of Decoherence and Applications for Quantum-Dot Charge Qubits

Leonid Evgenevich Fedichkin, Vladimir Privman A

Published May 15, 2008• 2 citations
arXivHTMLPDF

Abstract

We review results on evaluation of loss of information in quantum registers due to their interactions with the environment. It is demonstrated that an optimal measure of the level of quantum noise effects can be introduced via the maximal absolute eigenvalue norm of deviation of the density matrix of a quantum register from that of ideal, noiseless dynamics. For a semiconductor quantum dot charge qubits interacting with acoustic phonons, explicit expressions for this measure are derived. For a broad class of environmental modes, this measure is shown to have the property that for small levels of quantum noise it is additive and scales linearly with the size of the quantum register.

DOI
10.48550/arxiv.0805.2370

Related papers

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

Alexey A. Melnikov, Leonid Evgenevich Fedichkin

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.

arXiv:1210.6590•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 3, 2013•7 citations

Evaluation of Decoherence for Quantum Control and Computing

Arkady Fedorov, Leonid Evgenevich Fedichkin, Vladimir Privman A

Different approaches in quantifying environmentally-induced decoherence are considered. We identify a measure of decoherence, derived from the density matrix of the system of interest, that quantifies the environmentally induced error, i.e., deviation from the ideal isolated-system dynamics. This measure can be shown to have several useful features. Its behavior as a function of time has no dependence on the initial conditions, and is expected to be insensitive to the internal dynamical time scales of the system, thus only probing the decoherence-related time dependence. For a spin-boson model - a prototype of a qubit interacting with environment - we also demonstrate the property of additivity: in the regime of the onset of decoherence, the sum of the individual qubit error measures provides an estimate of the error for a several-qubit system, even if the qubits are entangled, as expected in quantum-computing applications. This makes it possible to estimate decoherence for several-qubits quantum computer gate designs for which explicit calculations are exceedingly difficult.

arXiv:cond-mat/0401248•Journal of Computational and Theoretical Nanoscience•Jun 30, 2004•18 citations

Error rate of a charge qubit coupled to an acoustic phonon reservoir

Leonid Evgenevich Fedichkin, Arkady Fedorov

We analyze decoherence of an electron in a double dot due to the interaction with acoustic phonons. For large tunneling rates between the quantum dots, the main contribution to decoherence comes from the phonon emission relaxation processes, while for small tunneling rates, the virtual-phonon, dephasing processes dominate. Our results show that in common semiconductors, such as Si and GaAs, the latter mechanism determines the upper limit for the double-dot charge qubit performance measure.

arXiv:quant-ph/0309024•Physical Review A•Mar 17, 2004•128 citations

Subdecoherent information encoding in a quantum-dot array

Paolo Zanardi A, Fausto Rossi

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.

arXiv:quant-ph/9808036•Physical review. B, Condensed matter•Mar 15, 1999•47 citations

Quantum Dynamics and Coherence of Qubits

Vladimir Privman A

Abstract — We review results in theoretical modeling of quantum systems in support of the studies of decoherence and qubit interactions for quantum information processing. The developed modeling tools have been applied to semiconductor materials and nanostructures that show promise for implementation of coherent, controlled quantum dynamics at the level of registers of several quantum bits (qubits), such as spins. Field-theoretical techniques have been utilized to address decoherence and more generally the origin and effects of quantum noise and the loss of entanglement in quantum dynamics of qubits and several-qubit registers. Qubit coupling mechanisms via the indirect exchange interaction have been investigated, and quantum computing designs have been evaluated for scalability. We also describe general and specific research challenges, the solution of which will advance the field of modeling “open quantum systems ” to further our understanding of how environmental influences affect quantum coherence and its loss during quantum dynamics.

•Aug 21, 2011•0 citations

Quantum Information in Semiconductors: Noiseless Encoding in a Quantum-Dot Array

Paolo Zanardi A, Fausto Rossi

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.

arXiv:quant-ph/9804016•Physical Review Letters•Nov 23, 1998•184 citations
We review results on evaluation of loss of information in quantum registers due to their interactions with the environment. It is demonstrated that an optimal measure of the level of quantum noise effects can be introduced via the maximal absolute eigenvalue norm of deviation of the density matrix of a quantum register from that of ideal, noiseless dynamics. For a semiconductor quantum dot charge qubits interacting with acoustic phonons, explicit expressions for this measure are derived. For a broad class of environmental modes, this measure is shown to have the property that for small levels of quantum noise it is additive and scales linearly with the size of the quantum register.
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.
Different approaches in quantifying environmentally-induced decoherence are considered. We identify a measure of decoherence, derived from the density matrix of the system of interest, that quantifies the environmentally induced error, i.e., deviation from the ideal isolated-system dynamics. This measure can be shown to have several useful features. Its behavior as a function of time has no dependence on the initial conditions, and is expected to be insensitive to the internal dynamical time scales of the system, thus only probing the decoherence-related time dependence. For a spin-boson model - a prototype of a qubit interacting with environment - we also demonstrate the property of additivity: in the regime of the onset of decoherence, the sum of the individual qubit error measures provides an estimate of the error for a several-qubit system, even if the qubits are entangled, as expected in quantum-computing applications. This makes it possible to estimate decoherence for several-qubits quantum computer gate designs for which explicit calculations are exceedingly difficult.
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.
Abstract — We review results in theoretical modeling of quantum systems in support of the studies of decoherence and qubit interactions for quantum information processing. The developed modeling tools have been applied to semiconductor materials and nanostructures that show promise for implementation of coherent, controlled quantum dynamics at the level of registers of several quantum bits (qubits), such as spins. Field-theoretical techniques have been utilized to address decoherence and more generally the origin and effects of quantum noise and the loss of entanglement in quantum dynamics of qubits and several-qubit registers. Qubit coupling mechanisms via the indirect exchange interaction have been investigated, and quantum computing designs have been evaluated for scalability. We also describe general and specific research challenges, the solution of which will advance the field of modeling “open quantum systems ” to further our understanding of how environmental influences affect quantum coherence and its loss during quantum dynamics.
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.