The effects of spin-orbit coupling on the two-electron spectra in lateral coupled quantum dots are investigated analytically and numerically. It is demonstrated that in the absence of magnetic field, the exchange interaction is practically unaffected by spin-orbit coupling, for any interdot coupling, boosting prospects for spin-based quantum computing. The anisotropic exchange appears at finite magnetic fields. A numerically accurate effective spin Hamiltonian for modeling spin-orbit-induced two-electron spin dynamics in the presence of magnetic field is proposed. DOI: 10.1103/PhysRevLett.104.126401 PACS numbers: 71.70.Gm, 71.70.Ej, 73.21.La, 75.30.Et The electron spins in quantum dots are natural and viable qubits for quantum computing [1], as evidenced by the impressive recent experimental progress [2,3] in spin detection and spin relaxation [4,5], as well as in coherent spin manipulation [6,7]. In coupled dots, the two-qubit quantum gates are realized by manipulating the exchange coupling which originates in the Coulomb interaction and the Pauli principle [1,8]. How is the exchange modified by the presence of the spin-orbit coupling? In general, the usual (isotropic) exchange changes its magnitude while a new, functionally different form of exchange, called anisotropic, appears, breaking the spin-rotational symmetry. Such changes are a nuisance from the perspective of the error correction [9], although the anisotropic exchange could also induce quantum gating [10,11].The anisotropic exchange of coupled localized electrons has a convoluted history [12][13][14][15][16][17][18]. The question boils down to determining the leading order in which the spin-orbit coupling affects both the isotropic and anisotropic exchange. At zero magnetic field, the second order was suggested [19], with later revisions showing the effects are absent in the second order [12,20].Here, we perform numerically exact calculations of the isotropic and anisotropic exchange in realistic GaAs coupled quantum dots in the presence of both the Dresselhaus and Bychkov-Rashba spin-orbit interactions [21]. We establish that in zero magnetic field, the secondorder spin-orbit effects are absent at all interdot couplings. Neither is the isotropic exchange affected, nor is the anisotropic exchange present. At finite magnetic fields, the anisotropic coupling appears. We derive a spin-exchange Hamiltonian describing this behavior, generalizing the existing descriptions; we do not rely on weak coupling approximations such as the Heitler-London one. The model is proven highly accurate by comparison with our numerics, and we propose it as a realistic effective model for the twospin dynamics in coupled quantum dots.Our microscopic description is the single band effective mass envelope function approximation; we neglect multiband effects [22,23]. We consider a two-electron double dot whose lateral confinement is defined electrostatically by metallic gates on the top of a semiconductor heterostructure. The heterostructure, grown along the [001] direction,...
Classical simulation of quantum computers will continue to play an essential role in the progress of quantum information science, both for numerical studies of quantum algorithms and for modelings noise and errors. Here we introduce the latest release of the Intel Quantum Simulator (IQS), formerly known as qHiPSTER. The high-performance computing (HPC) capability of the software allows users to leverage the available hardware resources provided by supercomputers, as well as available public cloud computing infrastructure. To take advantage of the latter platform, together with the distributed simulation of each separate quantum state, IQS offers the possibility of simulating a pool of related circuits in parallel. We highlight the technical implementation of the distributed algorithm and details about the new pool functionality. We also include some basic benchmarks (up to 42 qubits) and performance results obtained using HPC infrastructure. Finally, we use IQS to emulate a scenario in which many quantum devices are running in parallel to implement the quantum approximate optimization algorithm, using particle swarm optimization as the classical subroutine. The results demonstrate that the hyperparameters of this classical optimization algorithm depends on the total number of quantum circuit simulations one has the bandwidth to perform. The Intel Quantum Simulator has been released open-source with permissive licensing and is designed to simulate a large number of qubits, to emulate multiple quantum devices running in parallel, and/or to study the effects of decoherence and other hardware errors on calculation results. *
A global quantitative picture of the phonon-induced two-electron spin relaxation in GaAs double quantum dots is presented using highly accurate numerics. Wide regimes of interdot coupling, magnetic field magnitude and orientation, and detuning are explored in the presence of a nuclear bath. Most important, the giant magnetic anisotropy of the singlet-triplet relaxation can be controlled by detuning switching the principal anisotropy axes: a protected state becomes unprotected upon detuning and vice versa. It is also established that nuclear spins can dominate spin relaxation for unpolarized triplets even at high magnetic fields, contrary to common belief. DOI: 10.1103/PhysRevLett.108.246602 PACS numbers: 72.25.Rb, 03.67.Lx, 71.70.Ej, 73.21.La Electron spins in quantum dots [1] are among perspective candidates for a controllable quantum coherent system in spintronics [2,3]. Spin qubits in GaAs quantum dots, the current state of the art [4,5], are coupled to two main environment baths: nuclear spins and phonons [6]. The nuclei dominate decoherence, which is on microsecond time scales. But only phonons are an efficient energy sink for the relaxation of the energy-resolved spin states, leading to spin lifetimes as long as seconds [7].The extraordinary low relaxation is boosted by orders of magnitude at spectral crossings, unless special conditions-such geometries we call easy passages-are met [8,9]. Spectral crossings seem inevitable in the manipulation based on the Pauli spin blockade [1,10], the current choice in spin qubit experiments [11]. On the other hand, a fast spin relaxation channel may be desired, e.g., in the dynamical nuclear polarization [12][13][14].The single-electron spin relaxation is well understood [15,16]: it proceeds through acoustic phonons, in proportion to their density of states, which increases with the transferred energy. The matrix element of the phonon electric field between spin opposite states is nonzero due to spin-orbit coupling or nuclear spins. At anticrossings, the matrix element is enhanced by orders of magnitude, even though the anticrossing gap is minute ($ eV). The relaxation rate can be either enhanced or suppressed, depending on whether the energy or the matrix element effects dominate.The two electron relaxation rates were measured in single [17][18][19] and in double [20][21][22] dots. Theoretical works so far mostly focused on single dots [23,24], or vertical double dots [25,26], in which the symmetry of the confinement potential lowers the numerical demands. A slightly deformed dot was considered in Refs. [27,28], and a lateral coupled double dot in silicon in Ref. [29]. What is key for spin-qubit manipulation and most relevant for ongoing experiments, is the case of weakly coupled and biased coupled dots. In addition, the relative roles of the spin-orbit and hyperfine interactions in the spin relaxation in GaAs quantum dots have not yet been established.The analysis of the two-electron double dot relaxation is challenging because many parameters need to be consider...
In cryo-electron microscopy (EM), molecular structures are determined from large numbers of projection images of individual particles. To harness the full power of this single-molecule information, we use the Bayesian inference of EM (BioEM) formalism. By ranking structural models using posterior probabilities calculated for individual images, BioEM in principle addresses the challenge of working with highly dynamic or heterogeneous systems not easily handled in traditional EM reconstruction. However, the calculation of these posteriors for large numbers of particles and models is computationally demanding. Here we present highly parallelized, GPU-accelerated computer software that performs this task efficiently. Our flexible formulation employs CUDA, OpenMP, and MPI parallelization combined with both CPU and GPU computing. The resulting BioEM software scales nearly ideally both on pure CPU and on CPU+GPU architectures, thus enabling Bayesian analysis of tens of thousands of images in a reasonable time. The general mathematical framework and robust algorithms are not limited to cryo-electron microscopy but can be generalized for electron tomography and other imaging experiments.
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