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...

Circulators are nonreciprocal circuit elements that are integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their nonreciprocity arises from the interference of microwaves over the centimeter scale of the signal wavelength, in the presence of bulky magnetic media that breaks time-reversal symmetry. Here, we realize a completely passive on-chip microwave circulator with size 1=1000th the wavelength by exploiting the chiral, "slow-light" response of a two-dimensional electron gas in the quantum Hall regime. For an integrated GaAs device with 330 μm diameter and about 1-GHz center frequency, a nonreciprocity of 25 dB is observed over a 50-MHz bandwidth. Furthermore, the nonreciprocity can be dynamically tuned by varying the voltage at the port, an aspect that may enable reconfigurable passive routing of microwave signals on chip.

We demonstrate a low loss, chip-level frequency multiplexing scheme for readout of scaled-up spin qubit devices. By integrating separate bias tees and resonator circuits on-chip for each readout channel, we realise dispersive gate-sensing in combination with charge detection based on two rf quantum point contacts (rf-QPCs). We apply this approach to perform multiplexed readout of a double quantum dot in the few-electron regime, and further demonstrate operation of a 10-channel multiplexing device. Limitations for scaling spin qubit readout to large numbers of multiplexed channels is discussed.Scaling-up quantum systems to the extent needed for fault-tolerant operation introduces new challenges not apparent in the operation of single or few-qubit devices. Spin qubits based on gate-defined quantum dots [1] are, in principle, scalable, firstly because of their small (sub-micron) footprint, and secondly, since spins are largely immune to electrical disturbance, they exhibit low crosstalk when densely integrated [2]. At the fewqubit level, readout of spin-states is via quantum point contact (QPC) or single electron transistor (SET) charge sensors, proximal to each quantum dot [3][4][5][6][7][8]. These readout sensors pose a significant challenge to scale-up however, in that they require separate surface gates and large contact leads, crowding the device and tightly constraining the on-chip architecture.The recently developed technique of dispersive gatesensing (DGS) overcomes this scaling limitation by making use of the gates, already in place to define the quantum dots, as additional charge sensors [9]. The gates act as readout detectors by sensing small changes in the quantum capacitance associated with the tunnelling of single electrons. In turn, shifts in capacitance are measured by the response of a radio-frequency (rf) LC resonator that includes the gate. In principle, all of the quantum dot gates used for electron confinement can also be used as dispersive sensors, simultaneously collecting more of the readout signal that is spread over the total device capacitance and thus increasing the signal to noise ratio. Enabling all-gate readout, as well as multichannel rf-QPC or rf-SET charge sensing, requires the development of multiplexing schemes that scale to large numbers of readout sensors and qubits.Here we report an on-chip approach to frequency multiplexing for the simultaneous readout of scaled-up spin qubit devices. We demonstrate 3-channel readout of a few-electron double quantum dot, combining two rfQPCs and a dispersive gate-sensor as well as the operation of a 10-channel planar multiplexing (MUX) circuit. Similar approaches to frequency multiplexing have been demonstrated for distributed resonators in the context of kinetic inductance detectors [10], superconducting qubits [11,12] and rf-SETs [13][14][15]. The present work advances previous demonstrations by lithographically integrating the feed-lines, bias tees, and resonators, which are fabricated on a sapphire chip using low-loss superconducting niob...

Incorporating ferromagnetic dopants into three-dimensional topological insulator thin films has recently led to the realisation of the quantum anomalous Hall effect. These materials are of great interest since they may support electrical currents that flow without resistance, even at zero magnetic field. To date, the quantum anomalous Hall effect has been investigated using low-frequency transport measurements. However, transport results can be difficult to interpret due to the presence of parallel conductive paths, or because additional non-chiral edge channels may exist. Here we move beyond transport measurements by probing the microwave response of a magnetised disk of Cr-(Bi,Sb)2Te3. We identify features associated with chiral edge plasmons, a signature that robust edge channels are intrinsic to this material system. Our results provide a measure of the velocity of edge excitations without contacting the sample, and pave the way for an on-chip circuit element of practical importance: the zero-field microwave circulator.