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arXiv:2409.02301 · Physical review. B./Physical review. B

Theory of charge stability diagrams in coupled quantum dot qubits

Nathan L. Foulk, S. Das Sarma

Published Nov 25, 2024• 5 citations
arXivHTMLPDF

Abstract

We predict large regions of the charge stability diagram using a multiband and multielectron configuration interaction model of a double quantum dot system. We account for many-body interactions within each quantum dot using full configuration interaction and solve for single-particle density operators. This allows charge states to be predicted more accurately than the extensively used classical capacitance model or the single-band Hubbard model. The resulting single-particle mixed states then serve as inputs into an atomic orbital picture that allows for the explicit calculation of the underlying Hubbard model parameters by performing the appropriate integrals. This numerical approach allows for arbitrary choices of electrostatic potential and gate geometry. A common assumption when calculating charge stability diagrams from the Hubbard model is that the charge stability diagrams are periodic, but we find that the tunnel couplings for valence electrons in dots with $N=3$ electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.

DOI
10.1103/physrevb.110.205428

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We predict large regions of the charge stability diagram using a multiband and multielectron configuration interaction model of a double quantum dot system. We account for many-body interactions within each quantum dot using full configuration interaction and solve for single-particle density operators. This allows charge states to be predicted more accurately than the extensively used classical capacitance model or the single-band Hubbard model. The resulting single-particle mixed states then serve as inputs into an atomic orbital picture that allows for the explicit calculation of the underlying Hubbard model parameters by performing the appropriate integrals. This numerical approach allows for arbitrary choices of electrostatic potential and gate geometry. A common assumption when calculating charge stability diagrams from the Hubbard model is that the charge stability diagrams are periodic, but we find that the tunnel couplings for valence electrons in dots with N=3N=3N=3 electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.
We complete our recently introduced theoretical framework treating the double-quantum-dot system with a generalized form of Hubbard model. The effects of all quantum parameters involved in our model on the charge-stability diagram are discussed in detail. A general formulation of the microscopic theory is presented and, truncating at one orbital per site, we study the implication of different choices of the model confinement potential on the Hubbard parameters as well as the charge-stability diagram. We calculate the charge-stability diagram keeping three orbitals per site and find that the effect of additional higher-lying orbitals on the subspace with lowest-energy orbitals only can be regarded as a small renormalization of Hubbard parameters, thereby justifying our practice of keeping only the lowest orbital in all other calculations. The role of the harmonic-oscillator frequency in the implementation of the Gaussian model potential is discussed, and the effect of an external magnetic field is identified to be similar to choosing a more localized electron wave function in microscopic calculations. The full matrix form of the Hamiltonian, including all possible exchange terms and several peculiar charge-stability diagrams due to unphysical parameters, is presented in the Appendices, thus emphasizing the critical importance of a reliable microscopic model in obtaining the system parameters defining the Hamiltonian.
Serial triple quantum dot (STQD) systems have received extensive attention in the past decade, not only because quantum dot scaling up is an indispensable ingredient for integrations, but also due to the fact that specific charge states of STQD can be employed to achieve fast full-electrical manipulation of spin qubits. For the latter, a comprehensive understanding of the relationship between neighboring charge occupancy states of STQD is essential for three-electron exchange-only spin qubit-based quantum computations. Charge stability diagram is usually employed to map out the charge occupation states about the plunger gate voltages of STQDs and to study the degeneracy among charge occupation states. Experimentally, two- rather than three-dimensional charge stability diagram was obtained in a lot of early studies by keeping one of plunger gates unchanged to reduce complexity. The obtained two-dimensional diagram can only provide limited information and is subject to blurred boundary of charge occupation states due to the low tunneling current and the energy level broading effects. It is, therefore, challenge to searching for the working points where quantum manipulation can be performed promptly and accurately. In principle, three-dimensional charge occupation stability diagram can be efficiently constructed by numerical simulations based on constant interaction (CI) model. In this study, we calculate the electrochemical potential of STQD about three plunger gate voltages by using the CI model-based capacitance network to reproduce any desired two-dimensional charge stability diagram. The simulated diagram not only well accords with the diagrams obtained from the early experimental data of STQD, but also provides high clarity of the charge state boundaries with tunable parameters. The systematical study of two-dimensional charge stability diagram reviews the energy degeneracy triple and quadruple points of STQD charge occupation states and concludes the energy degeneracy points in three types to compare with experimental data. For each of the energy degeneracy points, we discuss both the electron and hole transport by using the electrochemical potential alignment schematics. We reveal the common and unique triple points of STQD in comparison with those of double quantum dot. The quadruple points of STQD are also addressed in the manipulation of quantum cellular automata and quantum logical gate. The comprehensive understanding of these energy degeneracy points can efficiently guide experiments to build an optimal working point of the STQD system for quantum computations and simulations.
Self-consistent Schrödinger-Poisson calculations are a powerful tool for predicting the behavior of layered semiconductor quantum dot devices. However, characterization of charge stability diagrams through fully simulated gate-voltage sweeps is computationally expensive. Combining a Multi-Domain Multi-Model (MDMM) approach with an automated tuning routine, we identify gate voltages associated with selected charge configurations. This small set of self-consistent simulations can be augmented with Full Configuration Interaction (FCI) energy calculations to extract charging energies, lever arms, and interdot Coulomb interactions to directly parameterize a Hubbard model for rapid charge stability diagram generation. For an Intel Tunnel Falls Si/SiGe device, we demonstrate the Hubbard model's ability to reproduce charge stability diagrams at a fraction of the computational cost in comparison to voltage bias sweeps. We further compare the simulated diagrams to experimental data and demonstrate qualitative agreement. Our result represents a step towards predictive digital twin models for semiconductor quantum dot devices. Finally, we apply this workflow towards lever arm engineering in a second device, demonstrating that the method extends to multiple architectures.
In this article, we studied the effect of a single charge trap on the charge stability diagram of a quantum dot-based single electron transistor. The anomalies in the Coulomb characteristic diagram of the quantum dot, system energy, occupation probabilities, and conductivity of the quantum dot have been investigated. These anomalies are caused by the electrostatic interaction of the quantum dot with the charge trap. The trap is capacitively connected to the quantum dot and can be empty or occupied by an electron; considering a few quantum states of the system, we solved the master equation using Fermi's golden rule to obtain the tunneling rates and the matrix of tunneling coefficients. Then, calculating the inverse of the matrix of coefficients, the probability of each quantum state has been obtained. Validation of the analysis is performed by comparing the simulation results with the experimental data. Finally, we have demonstrated that our study provides a tool to detect the charge presence in a trap near a quantum dot, which can potentially be used for the readout of quantum gates.
A quantitative description of the exchange interaction in quantum dots is relevant for modeling gate operations of spin qubits. By measuring the amplitude and frequency of exchange-driven qubit state oscillations, we measure the detuning dependence of the exchange coupling in a GaAs double quantum dot over three orders of magnitude. Both 1D and 3D full configuration interaction simulations can replicate the observed behavior. Extending a Hubbard model by including excited states increases the range of detuning where it provides a good fit, thus elucidating the underlying physics.
The spin of an electron confined in semiconductor quantum dots is currently a promising candidate for quantum bit (qubit) implementations. Taking advantage of the existing CMOS integration technologies, such devices can offer a platform for large scale quantum computation. However, a quantum mechanical framework bridging a device's physical design and operational parameters to the qubit's energy space is lacking. Furthermore, the spin to charge coupling introduced by intrinsic or induced spin-orbit interaction (SOI) exposes the qubits to charge noise compromising their coherence properties and inducing quantum gate errors. We present here a comodeling framework for double quantum dot (DQD) devices and their charge noise environments. We use a combination of an electrostatic potential solver, full configuration interaction quantum mechanical methods, and two-level-fluctuator models to study the quantum gate performance in realistic device designs and operation conditions. We utilize the developed models together alongside the single electron solutions of the quantum dots to simulate one- and two-qubit gates in the presence of charge noise. We find an inverse correlation between quantum gate errors and quantum dot confinement frequencies. We calculate X-gate fidelities >97>97%>97 in the simulated Si-MOS devices at a typical TLF density of ${10}^{11}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. We also find that exchange driven two-qubit SWAP gates show higher sensitivity to charge noise with fidelities down to 9191%91 in the presence of the same density of TLFs. We further investigate the one- and two-qubit gate fidelities at different TLF densities. We find that given the small size of the quantum dots, sensitivity of a quantum gate to the distance between the noise sources and the quantum dot creates a strong variability in the quantum gate fidelities, which can compromise the device yields in scaled qubit technologies.