Measurement of coupled quantum systems plays a central role in quantum information processing. We have realized independent single-shot read-out of two electron spins in a double quantum dot. The read-out method is all-electrical, cross-talk between the two measurements is negligible, and read-out fidelities are ~86% on average. This allows us to directly probe the anticorrelations between two spins prepared in a singlet state and to demonstrate the operation of the two-qubit exchange gate on a complete set of basis states. The results provide a possible route to the realization and efficient characterization of multiqubit quantum circuits based on single quantum dot spins.

Spin-based electronics or spintronics relies on the ability to store, transport and manipulate electron spin polarization with great precision. In its ultimate limit, information is stored in the spin state of a single electron, at which point quantum information processing also becomes a possibility. Here, we demonstrate the manipulation, transport and readout of individual electron spins in a linear array of three semiconductor quantum dots. First, we demonstrate single-shot readout of three spins with fidelities of 97% on average, using an approach analogous to the operation of a charge-coupled device (CCD). Next, we perform site-selective control of the three spins, thereby writing the content of each pixel of this 'single-spin charge-coupled device'. Finally, we show that shuttling an electron back and forth in the array hundreds of times, covering a cumulative distance of 80 μm, has negligible influence on its spin projection. Extrapolating these results to the case of much larger arrays points at a diverse range of potential applications, from quantum information to imaging and sensing.

We report that the electron spin-relaxation time T 1 in a GaAs quantum dot with a spin-1=2 ground state has a 180°periodicity in the orientation of the in-plane magnetic field. This periodicity has been predicted for circular dots as being due to the interplay of Rashba and Dresselhaus spin orbit contributions. Different from this prediction, we find that the extrema in the T 1 do not occur when the magnetic field is along the [110] and ½110 crystallographic directions. This deviation is attributed to an elliptical dot confining potential. The T 1 varies by more than 1 order of magnitude when rotating a 3 T field, reaching about 80 ms for the optimal angle. We infer from the data that in our device the signs of the Rashba and Dresselhaus constants are opposite. The high control reached in the manipulation of a single electron spin in a semiconductor environment [1] is encouraging for future application of this natural two-level system for quantum computation technology. In GaAs, InAs, and other III-V quantum dots it has been shown that this manipulation can be realized using exclusively electrical fields [2,3]. Coupling of the electric field to the spins is mediated by the spin-orbit (SO) interaction naturally provided by the semiconductor host environment. The semiconductor environment also implies that the electron is intimately in contact with phonons, charge fluctuations, and nuclear spins, and these interactions are responsible for the relaxation and dephasing process of the electron spin.During the last ten years, a significant experimental [4-10] and theoretical [11][12][13][14][15] effort has been devoted to understanding the effect of electron spin relaxation in lateral quantum dots (QDs). At magnetic fields of the order of Tesla, spin relaxation in GaAs dots was found to be dominated by the SO interaction in combination with piezoelectric phonons. Two contributions to the SO interaction usually dominate. The local electric field due to a crystal with bulk inversion asymmetry generates a Dresselhaus (D) SO contribution [16] which, for electrons confined in the plane (xy, with x and y along the [100] and [010] crystallographic directions, respectively) of the quantum well, can be written as H D ¼ βð−σ x P x þ σ y P y Þ=ℏ, with ℏ the Planck constant, β the Dresselhaus SO coupling strength, P the electron kinematic momentum, and σ the vector of Pauli matrices. In addition, the electric field associated with the asymmetric confining potential along the heterostructure growth direction (z along [001]) gives rise to the Rashba (R) SO contribution [17], H R ¼ αðσ y P x − σ x P y Þ=ℏ, with α the Rashba SO coupling strength. The effect of the SO interaction can be viewed as an effective magnetic field B SO acting on the conduction electron spin, with an amplitude and direction that depend on the electron momentum [see Fig. 1(b)]. The interplay of R and D coupling gives rise to an anisotropy in the direction and magnitude of B SO in the plane of the quantum well. As a result, spin relaxation in a quantum dot is ...

We investigate phonon-induced spin and charge relaxation mediated by spin-orbit and hyperfine interactions for a single electron confined within a double quantum dot. A simple toy model incorporating both direct decay to the ground state of the double dot and indirect decay via an intermediate excited state yields an electron spin relaxation rate that varies non-monotonically with the detuning between the dots. We confirm this model with experiments performed on a GaAs double dot, demonstrating that the relaxation rate exhibits the expected detuning dependence and can be electrically tuned over several orders of magnitude. Our analysis suggests that spin-orbit mediated relaxation via phonons serves as the dominant mechanism through which the double-dot electron spin-flip rate varies with detuning.Controlling individual spins is central to spin-based quantum information processing [1][2][3] and also enables precision metrology [4,5]. While rapid control can be achieved by coupling the spins of electrons in semiconductor quantum dots [1, 2] to electric fields via the electronic charge state [3,[6][7][8][9][10][11][12][13][14], spin-charge coupling also leads to relaxation of the spins through fluctuations in their electrostatic environment. Phonons serve as an inherent source of fluctuating electric fields in quantum dots [2] and give rise to both charge and spin relaxation through the electron-phonon interaction. In GaAs quantum dots, the direct coupling of spin to the strain field produced by phonons is expected to be inefficient [15,16]. The dominant mechanisms of phonon-induced spin relaxation are therefore indirect and involve spin-charge coupling due to primarily spin-orbit [15][16][17][18][19][20][21] and hyperfine [22][23][24][25][26][27] interactions. Confining an electron within a double quantum dot (DQD) provides a high degree of control over the charge state [28][29][30][31], so that relaxation rates can be varied over multiple orders of magnitude by adjusting the energy level detuning between the dots [25,[32][33][34][35].Here, we investigate the interplay of spin and charge relaxation via phonons for a single electron confined to a DQD in the presence of spin-orbit and hyperfine interactions. We present a simple model together with measurements of the electron spin relaxation rate in a GaAs DQD, both of which yield a non-monotonic dependence on the detuning between the dots (see Fig. 3). The experiments provide confirmation of the model and demonstrate the existence of spin "hot spot" features [18-20, 36, 37] at nonzero values of detuning, where relaxation is enhanced by several orders of magnitude. The opposite behavior is observed at zero detuning, where the spin-flip rate exhibits a local minimum. Theoretically, spin hot spots are predicted to occur due to the complete mixing of spin and orbital states at avoided energy crossings associated with spin-orbit coupling [18,19,36]. From a practical standpoint, adjusting the detuning to these points represents a potential method for rapid allelectrical...

We investigate the electric manipulation of a single-electron spin in a single gate-defined quantum dot. We observe that so-far neglected differences between the hyperfine- and spin-orbit-mediated electric dipole spin resonance conditions have important consequences at high magnetic fields. In experiments using adiabatic rapid passage to invert the electron spin, we observe an unusually wide and asymmetric response as a function of the magnetic field. Simulations support the interpretation of the line shape in terms of four different resonance conditions. These findings may lead to isotope-selective control of dynamic nuclear polarization in quantum dots.

This paper studies the stability conditions of a discrete-time switched linear system in the presence of affine parametric uncertainties and an unknown time delay. Based on a discrete Lyapunov functional, sufficient conditions are investigated to determine the upper bound of admissible time delay in the discrete-time switched system. Furthermore, the average dwell time method, which is an effective tool for stability analysis of switched systems, is used to derive the exponential stability conditions. These conditions characterize the switching signal, which does not depend on any uncertainties. Finally, numerical examples are provided to verify and compare the theoretical results.

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This paper studies the problem of robust stabilization for a class of nonlinear discrete-time switched systems with polytopic uncertainties and unknown state delay. Moreover, the control signal is assumed to be constrained. The objective of the proposed controller is to stabilize the switched system under arbitrary switching signals based on the switched Lyapunov function approach. Therefore, based on the constrained robust model predictive control method and an appropriate Lyapunov–Krasovskii functional, the sufficient conditions to guarantee the asymptotical stability of the switched system are developed as linear matrix inequalities. Through online solving an optimization problem, the predictive state-feedback controller is designed. Furthermore, in this delay-dependent approach, only the upper bound of time-delay should be known. Appropriate transient response, ability to handle constraints, and nonconstrained switching signal are the other advantages of the proposed method. Finally, the performance of the proposed approach is compared with a similar approach through a numerical example. As well as, to show the applicability of the proposed controller, it is applied to a drinking water supply network, as an application example.