We demonstrate a substantial improvement in the spin-exchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factor of six increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotation-axis fluctuations due to nuclear field noise rather than direct exchange noise.

Electron spins in semiconductors are promising qubits because their long coherence times enable nearly 10 9 coherent quantum gate operations. However, developing a scalable high-fidelity two-qubit gate remains challenging. Here, we demonstrate an entangling gate between two double-quantum-dot spin qubits in GaAs by using a magnetic field gradient between the two dots in each qubit to suppress decoherence due to charge noise. When the magnetic gradient dominates the voltage-controlled exchange interaction between electrons, qubit coherence times increase by an order of magnitude. Using randomized benchmarking, we measure single-qubit gate fidelities of~99%, and through self-consistent quantum measurement, state, and process tomography, we measure an entangling gate fidelity of 90%. In the future, operating double quantum dot spin qubits with large gradients in nuclear-spin-free materials, such as Si, should enable a two-qubit gate fidelity surpassing the threshold for fault-tolerant quantum information processing.npj Quantum Information (2017) 3:3 ; doi:10.1038/s41534-016-0003-1 INTRODUCTIONThe quantum phase coherence of isolated spins in semiconductors 1-7 can persist for long times, reaching tens of milliseconds for electron spins 8 and tens of minutes for nuclear spins. 9 Such long coherence times enable single-qubit gate fidelities exceeding the threshold for fault-tolerant quantum computing 8 and make spins promising qubits. However, entangling spins is difficult because magnetic interactions between spins are weak. For electrons, this challenge can be met by exploiting the charge of the electron for electric-dipole 10 or gate-controlled exchange coupling 2 between spins. In these methods, however, the qubit energy depends on electric fields, and charge noise in the host material limits singlequbit coherence.11 Charge noise also affects other qubit platforms. For example, heating due to charge noise is a limiting factor in the coherence of trapped ion qubits, 12 and the transmon superconducting qubit was designed to suppress noise from charge fluctuations in superconducting islands.13 Strategies such as composite pulses, 14, 15 dynamical decoupling, 11 and sweet-spot operation [16][17][18] have been developed to mitigate the effects of charge noise.In this work, we present a technique to suppress decoherence caused by charge noise. The key idea is to apply a large transverse qubit energy splitting that does not depend on electric fields and, therefore, suppresses the effects of charge fluctuations. We implement this scheme with two singlet-triplet qubits, each of which consists of two electrons in a double-quantum-dot.

We demonstrate operation of a small Fabry-Perot interferometer in which highly coherent Aharonov-Bohm oscillations are observed in the integer and fractional quantum Hall regimes. Using a novel heterostructure design, Coulomb effects are drastically suppressed. Coherency of edge mode interference is characterized by the energy scale for thermal damping, T0 = 206mK at ν = 1. Selective backscattering of edge modes originating in the N = 0, 1, 2 Landau levels allows for independent determination of inner and outer edge mode velocities. Clear Aharonov-Bohm oscillations are observed at fractional filling factors ν = 2/3 and ν = 1/3. Our device architecture provides a platform for measurement of anyonic braiding statistics. arXiv:1901.08452v1 [cond-mat.mes-hall]

A two-level system resonantly interacting with an ac magnetic or electric field constitutes the physical basis of diverse phenomena and technologies. However, Schrödinger's equation for this seemingly simple system can be solved exactly only under the rotating wave approximation, which neglects the counter-rotating field component. When the ac field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch-Siegert (BS) shift. Here, we report the vacuum BS shift, which is induced by the ultrastrong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity. Specifically, an ultra-high-mobility 2D electron gas inside a high-Q terahertz cavity in a quantising magnetic field revealed ultra-narrow Landau polaritons, which exhibited a vacuum BS shift up to 40 GHz. This shift, clearly distinguishable from the photon-field selfinteraction effect, represents a unique manifestation of a strong-field phenomenon without a strong field. sions. We thank Yoichi Kawada, Hironori Takahashi, and Hamamatsu Photonics K.K. for fabricating the achromatic THz quarter wave plate. J.K.

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-...

Electron spins in gate-defined quantum dots provide a promising platform for quantum computation. In particular, spin-based quantum computing in gallium arsenide takes advantage of the high quality of semiconducting materials, reliability in fabricating arrays of quantum dots and accurate qubit operations. However, the effective magnetic noise arising from the hyperfine interaction with uncontrolled nuclear spins in the host lattice constitutes a major source of decoherence. Low-frequency nuclear noise, responsible for fast (10 ns) inhomogeneous dephasing, can be removed by echo techniques. High-frequency nuclear noise, recently studied via echo revivals, occurs in narrow-frequency bands related to differences in Larmor precession of the three isotopes Ga,Ga and As (refs 15,16,17). Here, we show that both low- and high-frequency nuclear noise can be filtered by appropriate dynamical decoupling sequences, resulting in a substantial enhancement of spin qubit coherence times. Using nuclear notch filtering, we demonstrate a spin coherence time (T) of 0.87 ms, five orders of magnitude longer than typical exchange gate times, and exceeding the longest coherence times reported to date in Si/SiGe gate-defined quantum dots.

The entropy of an electronic system offers important insights into the nature of its quantum mechanical ground state. This is particularly valuable in cases where the state is difficult to identify by conventional experimental probes, such as conductance. Traditionally, entropy measurements are based on bulk properties, such as heat capacity, that are easily observed in macroscopic samples but are unmeasurably small in systems that consist of only a few particles [1, 2]. In this work, we develop a mesoscopic circuit to directly measure the entropy of just a few electrons, and demonstrate its efficacy using the well understood spin statistics of the first, second, and third electron ground states in a GaAs quantum dot [3][4][5][6][7][8]. The precision of this technique, quantifying the entropy of a single spin-1 2 to within 5% of the expected value of k B ln 2, shows its potential for probing more exotic systems. For example, entangled states or those with non-Abelian statistics could be clearly distinguished by their low-temperature entropy [9][10][11][12][13].Our approach is analogous to the milestone of spin-tocharge conversion achieved over a decade ago, in which the infinitesimal magnetic moments of a single spin were detected by transforming them into the presence or absence of an electron charge [14,15]. Following this example, we perform an entropy-to-charge conversion, making use of the Maxwell relationthat connects changes in entropy, particle number, and temperature (S, N , and T , respectively) to changes in the chemical potential, µ, a quantity that is simple to measure and control. The Maxwell relation in Eq. 1 forms the basis of two theoretical proposals to measure non-Abelian exchange of Moore-Read quasiparticles in the ν = 5 2 state via their entropy [9,10]. Reference 10 proposes a strategy by which quasiparticle entropy could be deduced from a V m id V p G sens N − 1 N ∂S/∂N = 0 b V m id V m id V p N − 1 N ∂S/∂N > 0 c Vp δGsens Vp δGsens I heat I sens V sens V p G sens δG sens AC DC 500nm FIG. 1.Measurement protocol (a) Scanning electron micrograph of a device similar to the one measured. Electrostatic gates (gold) define the circuit in a 2D electron gas (2DEG), with grey gates grounded. Squares indicate ohmic contacts to the 2DEG. The temperature of the electron reservoir in the middle (red) is oscillated using AC current, I heat , at frequency f heat through the quantum point contact (QPC) on the left. A portion of the 5 µm-wide reservoir has been removed here for clarity. The occupation of the quantum dot, tunnel coupled to the right side the reservoir, is tuned by Vp and monitored by Isens through the charge sensor QPC. Isens is split into DC and AC components, the latter being measured by a lock-in amplifier at 2f heat . (b) and (c) Simulated DC charge sensor signal, Gsens, for a transition from N − 1 → N electrons at two temperatures (T Red > T Blue ), showing two possible cases for ∂S ∂N . Insets show the corresponding difference, δGsens, between hot and cold curves.the temperature-depende...

Using a singlet-triplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over six orders of magnitude in frequency, from 1 mHz to 1 kHz, is flat below 10 mHz, and falls as 1/f 2 for frequency f 1 Hz. Increasing the applied magnetic field from 0.1 T to 0.75 T suppresses electronmediated spin diffusion, which decreases spectral content in the 1/f 2 region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the few-pulse regime ( 16 π-pulses), where transverse Overhauser fluctuations dominate dephasing, to the many-pulse regime ( 32 π-pulses), where longitudinal Overhauser fluctuations with a 1/f spectrum dominate.