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...

We perform Landau-Zener-Stückelberg interferometry on a single electron GaAs charge qubit by repeatedly driving the system through an avoided crossing. We observe coherent destruction of tunneling, where periodic driving with specific amplitudes inhibits current flow. We probe the quantum dot occupation using a charge detector, observing oscillations in the qubit population resulting from the microwave driving. At a frequency of 9 GHz we observe excitation processes driven by the absorption of up to 17 photons. Simulations of the qubit occupancy are in good agreement with the experimental data.PACS numbers: 73.21. La, 73.63.Kv, 85.35.Be, 85.35.Ds Semiconductor quantum dots are fruitful systems for exploring phenomena arising from quantum interference effects [1][2][3][4][5][6]. Landau-Zener-Stückelberg (LZS) interferometry has recently emerged as a novel way to study quantum coherence in solid state systems. LZS theory was initially described in the context of atomic collisions and relies on having an effective two-level system with an avoided crossing in the energy level spectrum [7][8][9][10][11]. Repeated sweeps through the avoided crossing result in successive Landau-Zener transitions, allowing control of the final state probability. While the theory was initially applied to atomic collisions, recent advances in the fabrication of solid state quantum devices have made it experimentally accessible in a wide variety of systems, ranging from superconducting qubits [12] to nitrogen vacancy centers in diamond [13,14]. In superconducting qubits, LZS interferometry has been used with great success to determine the energy level diagram and to measure qubit coherence times [12,15,16]. In spin qubits, LZS interferometry has been harnessed to drive coherent singlet-triplet transitions resulting in spin rotations that are much faster than those obtained using conventional electron spin resonance [17,18].In this Rapid Communication we perform LZS interferometry on a single electron GaAs double quantum dot (DQD) charge qubit. The sample geometry is illustrated in the scanning electron microscope (SEM) image shown in Fig. 1(a). Ti/Au gate electrodes are fabricated on top of a GaAs/AlGaAs heterostructure that is grown using molecular beam epitaxy. The gate electrodes selectively deplete regions of the two-dimensional electron gas located 110 nm below the surface of the wafer, forming a DQD containing a single electron. In this experiment, a third dot is used as a charge detector, which allows non-invasive measurements of the charge state occupancy [19]. A fixed 100 mT field is applied perpendicular to the plane of the sample. Despite their simplicity, charge qubits are of great experimental importance as they allow for direct quantum control through electric fields, with coherent control rates dictated by tunnel couplings that can easily approach 10 GHz. They also serve as building blocks for more complex quantum systems, such as spin qubits [20].We focus on the one electron regime, where the DQD contains a single charge...

Solid-state qubits have recently advanced to the level that enables them, in principle, to be scaledup into fault-tolerant quantum computers. As these physical qubits continue to advance, meeting the challenge of realising a quantum machine will also require the engineering of new classical hardware and control architectures with complexity far beyond the systems used in today's fewqubit experiments. Here, we report a micro-architecture for controlling and reading out qubits during the execution of a quantum algorithm such as an error correcting code. We demonstrate the basic principles of this architecture in a configuration that distributes components of the control system across different temperature stages of a dilution refrigerator, as determined by the available cooling power. The combined setup includes a cryogenic field-programmable gate array (FPGA) controlling a switching matrix at 20 millikelvin which, in turn, manipulates a semiconductor qubit.Realising the classical control system of a quantum computer is a formidable scientific and engineering challenge in its own right 1,2 . The hardware that comprises the control interface must be fast relative to the timescales of qubit decoherence, low-noise so as not to further disturb the fragile operation of qubits, and scalable with respect to physical resources, ensuring that the footprint for routing signal lines or the operating power does not grow rapidly as the number of qubits increases 3,4 . As solid-state quantum processors will likely operate below 1 kelvin 5-8 , components of the control system will also need to function in a cryogenic environment, adding further constraints.Similar challenges have long been addressed in the satellite and space exploration community 9 , where the need for high-frequency electronic systems operating reliably in extreme environments has driven the development of new circuits and devices 10 . Quantum computing systems, on the other hand, have to date largely relied on brute-force approaches, controlling a few qubits directly via room temperature electronics that is hardwired to the quantum device at cryogenic temperatures.Here we present a control architecture for operating a cryogenic quantum processor autonomously and demonstrate its basic building blocks using a semiconductor qubit. This architecture addresses many aspects related to scalability of the control interface by embedding multiplexing sub-systems at cryogenic temperatures and separating the high-bandwidth analog control waveforms from the digital addressing needed to select qubits for manipulation. Our demonstration comprises a commercial field-programmable gate array (FPGA) operating at 4 kelvin and controlling a microwave signal switching matrix at 20 mK, which then interfaces with a quantum dot device. Bringing these sub-systems together in the context of our control architecture suggests a path for scaleup of control hardware needed to manipulate the large numbers of qubits in a useful quantum machine. I. CONTROL MICRO-ARCHITECTUREOur control micro-...

We demonstrate fast universal electrical spin manipulation with inhomogeneous magnetic fields. With fast Rabi frequency up to 127 MHz, we leave the conventional regime of strong nuclear-spin influence and observe a spin-flip fidelity >96%, a distinct chevron Rabi pattern in the spectral-time domain, and a spin resonance linewidth limited by the Rabi frequency, not by the dephasing rate. In addition, we establish fast z rotations up to 54 MHz by directly controlling the spin phase. Our findings will significantly facilitate tomography and error correction with electron spins in quantum dots.