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arXiv:1006.2735 · Physical Review B

A configuration interaction analysis of exchange in double quantum dots

Erik Nielsen, Richard P. Muller

Published Jun 14, 2010• 3 citations
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Abstract

We describe in detail a full configuration interaction (CI) method designed to analyze systems of quantum dots. This method is capable of exploring large regions of parameter space, like more approximate approaches such as Heitler London and Hund Mulliken, though it is not limited to weakly coupled dots. In particular, this method is well-suited to the analysis of solid state quantum-dot-based qubits, and we consider the case of a double quantum dot (DQD) singlet-triplet qubit. Past analyses have used techniques which are either substantially restricted in the regimes they can be used, or device specific and unsuited to exploration of a large regions of parameter space. We analyze how the DQD exchange energy, which is central to the operation of qubit rotation gates, depends on a generic set of system parameters including magnetic field, DQD detuning, dot size, and dot separation. We discuss the implications of these results to the construction of real devices. We provide a benchmark of the CI by directly comparing results from the CI method with exact results for two electrons in a single parabolic potential (dot).

DOI
10.48550/arxiv.1006.2735

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We describe in detail a full configuration interaction (CI) method designed to analyze systems of quantum dots. This method is capable of exploring large regions of parameter space, like more approximate approaches such as Heitler London and Hund Mulliken, though it is not limited to weakly coupled dots. In particular, this method is well-suited to the analysis of solid state quantum-dot-based qubits, and we consider the case of a double quantum dot (DQD) singlet-triplet qubit. Past analyses have used techniques which are either substantially restricted in the regimes they can be used, or device specific and unsuited to exploration of a large regions of parameter space. We analyze how the DQD exchange energy, which is central to the operation of qubit rotation gates, depends on a generic set of system parameters including magnetic field, DQD detuning, dot size, and dot separation. We discuss the implications of these results to the construction of real devices. We provide a benchmark of the CI by directly comparing results from the CI method with exact results for two electrons in a single parabolic potential (dot).
We consider qubit coupling resulting from the capacitive coupling between two double quantum dot (DQD) singlet-triplet qubits. Calculations of the coupling when the two DQDs are detuned symmetrically or asymmetrically are performed using a full configuration interaction (CI). The full CI reveals behavior that is not observed by more commonly used approximations such as Heitler London or Hund Mulliken, particularly related to the operation of both DQDs in the (0,2) charge sector. We find that there are multiple points in detuning space where a two-qubit entangling gate can be realized, and that tradeoffs between coupling magnitude and sensitivity to fluctuations in detuning make a case for operating the gate in the (0,2) regime not commonly considered.
We discuss the microscopic modeling of exchange interactions between double semiconductor quantum dots used as spin qubits. Starting from a reference full configuration interaction (CI) calculation for the two-particle wave functions, we build a reduced basis set of dressed states that can describe the ground-state singlets and triplets over the whole operational range with as few as 100 basis functions (as compared to a few thousands for the full CI). This enables fast explorations of the exchange interactions landscape as well as efficient time-dependent simulations. We apply this methodology to a double hole quantum dot in germanium and discuss the physics of exchange interactions in this system. We show that the net exchange splitting results from a complex interplay among interdot tunneling, Coulomb exchange, and correlations. We analyze, moreover, the effects of confinement, strains, and Rashba interactions on the anisotropic exchange and singlet-triplet mixings at finite magnetic field. We finally illustrate the relevance of this methodology for time-dependent calculations on a singlet-triplet qubit.
Achieving low-error, exchange-interaction operations in quantum dots for quantum computing imposes simultaneous requirements on the exchange energy's dependence on applied voltages. A double quantum dot qubit, approximated with a quadratic potential, is solved using a full configuration interaction method. This method is more accurate than Heitler-London and Hund-Mulliken approaches and captures new and significant qualitative behavior. We show that multiple regimes can be found in which the exchange energy's dependence on the bias voltage between the dots is compatible with current quantum error correction codes and state-of-the-art electronics. Identifying such regimes may prove valuable for the construction and operation of quantum gates that are robust to charge fluctuations, particularly in the case of dynamically corrected gates.
We consider a double quantum dot (DQD) qubit which contains six electrons instead of the usual one or two. In this spin qubit, quantum information is encoded in a low-lying singlet-triplet space much as in the case of a two-electron DQD qubit. We find that initialization, manipulation, and readout can be performed similarly to the two-electron case, and that energy gaps remain large enough that these operations can be performed robustly. We consider DQD potentials with parameters chosen to be representative of current experimental capabilities. Results are obtained using two complementary full configuration interaction methods.
By leveraging a GPU-accelerated Schrödinger-Poisson (SP) solver, we characterize exchange coupling in a hole spin double-qubit device involving a double quantum dot (DQD) system formed inside a 5-gate silicon fin field-effect transistor (FinFET) similar to real experimental structures. The self-consistent SP simulations rely on a finite difference discretization of the 3D volume and on a Luttinger-Kohn 6x6 kp Hamiltonian accounting for magnetic fields and strain distribution. They return the gate-induced confined electronic states and the corresponding electrostatic potential hosting the DQD. These quantities serve as inputs to a two-particle Hamiltonian that is constructed from single-particle Slater determinants through the configuration interaction (CI) method. By diagonalizing this two-particle Hamiltonian, the eigenstates and eigenenergies of the DQD system are obtained, together with their exchange coupling. We show that our simulation framework, using a reduced number of basis states, is capable of reproducing the magneto-electrostatic behavior of the devices of interest, as predicted from theory and observed experimentally. We finally leverage our approach to determine the optimal operating conditions of a two-qubit quantum logic gate implemented in a Si FinFET structure.
We present a theoretical study of a four-electron four-quantum-dot system based on molecular-orbital methods, which hosts a pair of singlet-triplet spin qubits. We took into account the admixture of electron wave functions in all dots, and we found that this mixing of wave functions has consequences to the energy spectrum, exchange interaction, and gate crosstalk of the system. Specifically, we found that when the two singlet-triplet qubits are close enough, some of the states are no longer dominated by the computational basis states, and the exchange interaction cannot simply be understood as the energy difference between the singlet and triplet states. Using the Hund-Mulliken calculation of the Hubbard parameters, we characterized the effective exchange interaction of the system, and we found good agreement with results calculated by taking energy differences where applicable. We studied the two commonly conceived schemes coupling two qubits, namely the exchange and capacitive coupling, and we found that when the interqubit distance is at certain intermediate values, the two kinds of coupling are comparable in strength, complicating the analyses of the evolution of the two qubits. We also investigated the gate crosstalk in the system due to the quantum-mechanical mixing of electron states, and we found that while this effect is typically very weak, it should not be ignored if the spacing between the qubits is similar to or less than the distance between the double dots that constitute the qubit.