We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and non-invasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of ∼ 7 ns at the charge degeneracy point, where the qubit level splitting is first-order-insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with numerical simulations and predictions from a 1/f noise model. PACS numbers: 85.35.Gv, 03.67.Lx, 73.21.La The key requirement that a quantum computer be scalable has motivated recent work exploring coherent control of two-level systems in the solid state. A large effort has focused on quantum dots, where quantum control of both single spin and two spin "singlet-triplet" qubits has been demonstrated [1][2][3][4]. While progress has been rapid, reliable two-qubit gates are required in order to scale to larger system sizes [5]. Proposals for two-qubit gates rely on a charge-noise-susceptible exchange interaction [2,[6][7][8][9]. Developing a quantitative understanding of the charge noise environment, and how it impacts quantum coherence, is therefore crucial for quantum dot approaches to quantum information processing.Early demonstrations of quantum coherence in the solid-state took place using charge qubits, which can have ∼ 100 ps gate operation times and relatively long coherence times [10,11]. Nakamura et al. demonstrated charge coherence in a superconducting Cooper pair box (CPB), where the state of the qubit is determined by the number of Cooper pairs on a superconducting island [10,12]. In semiconductor systems, a charge qubit can be formed by isolating an electron in a tunnel-coupled double quantum dot (DQD) [13,14]. Here the state of the qubit is set by the position of the electron in the double well potential. Coherent control of a GaAs charge qubit has been demonstrated [13,15], along with correlated two qubit interactions [16]. However, precise values of the coherence time are unknown in GaAs, since state readout in past experiments involved transport through the DQD with strong coupling to the leads, typically limiting coherence times to ∼ 1 ns due to cotunnelling [13]. In addition, each dot contained a few tens of electrons, potentially complicating the qubit level structure.In this Letter, we demonstrate coherent control of a tunable GaAs charge qubit containing a single electron. In previous experiments, voltage pulses were applied to the drain contact of the DQD for quantum control [13,16]. Here we demonstrate a scalable approach to generating charge coherence by applying non-adiabatic voltage pulses to the surface depletion gates. State read-

We introduce a solid-state qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gate-voltage pulses. We demonstrate two-axis control at a detuning sweet spot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A π/2-gate time of 2.5 ns and a coherence time of 19 μs, using multipulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment.

Rapid coherent control of electron spin states is required for implementation of a spin-based quantum processor. We demonstrated coherent control of electronic spin states in a double quantum dot by sweeping an initially prepared spin-singlet state through a singlet-triplet anticrossing in the energy-level spectrum. The anticrossing serves as a beam splitter for the incoming spin-singlet state. When performed within the spin-dephasing time, consecutive crossings through the beam splitter result in coherent quantum oscillations between the singlet state and a triplet state. The all-electrical method for quantum control relies on electron-nuclear spin coupling and drives single-electron spin rotations on nanosecond time scales.

Quantum-dot spin qubits characteristically use oscillating magnetic or electric fields, or quasi-static Zeeman field gradients, to realize full qubit control. For the case of three confined electrons, exchange interaction between two pairs allows qubit rotation around two axes, hence full control, using only electrostatic gates. Here, we report initialization, full control, and single-shot readout of a three-electron exchange-driven spin qubit. Control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in less than 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements and non-orthogonal control axes.

We report the dispersive charge-state readout of a double quantum dot in the few-electron regime using the in situ gate electrodes as sensitive detectors. We benchmark this gate-sensing technique against the well established quantum point contact (QPC) charge detector and find comparable performance with a bandwidth of ∼ 10 MHz and an equivalent charge sensitivity of ∼ 6.3 × 10 −3 e/ √ Hz. Dispersive gate-sensing alleviates the burden of separate charge detectors for quantum dot systems and promises to enable readout of qubits in scaled-up arrays.Non-invasive charge detection has emerged as an important tool for uncovering new physics in nanoscale devices at the single-electron level and allows readout of spin qubits in a variety of material systems [1][2][3][4][5][6][7][8][9]. For quantum dots defined electrostatically by the selective depletion of a two dimensional electron gas (2DEG), the conductance of a proximal quantum point contact (QPC) [4][5][6][7]9] or single electron transistor (SET) [3,8] can be used to detect the charge configuration in a regime where direct transport is not possible. This method can, in principle, reach quantum mechanical limits for sensitivity [10] and has enabled the detection of single electron spin-states [4, 7, 11] with a 98% readout fidelity in a single-shot [12].An alternate approach to charge-state detection, long used in the context of single electron spectroscopy [13], is based on the dispersive signal from shifts in the quantum capacitance [14,15] when electrons undergo tunnelling. Similar dispersive interactions are now the basis for readout in a variety of quantum systems including atoms in an optical resonator [16], superconducting qubits [17][18][19] and nanomechanical devices [20].In this Letter we report dispersive readout of quantum dot devices using the standard, in situ gate electrodes coupled to lumped-element resonators as highbandwidth, sensitive charge-transition sensors.We demonstrate the sensitivity of this gate-sensor in the fewelectron regime, where these devices are commonly operated as charge or spin qubits [21] and benchmark its performance against the well established QPC charge sensor. We find that because the quantum capacitance is sufficiently large in these devices, gate-sensors have similar sensitivity to QPC sensors. In addition, we show that gate-sensors can operate at elevated temperatures in comparison to QPCs.Previous investigations, in the context of circuit quantum electrodynamics (c-QED), have engineered a dispersive interaction between many-electron dots and superconducting coplanar waveguide resonators [22][23][24][25]. Recently, the charge and spin configuration of double quantum dots has also been detected by dispersive changes in a radio frequency resonator coupled directly to the source or drain contacts of the device [25][26][27][28]. The present work advances these previous studies by demonstrating that the gates, already in place to define the quantum dot system, can also act as fast and sensitive readout detectors in the single...