Collective Microwave Response for Multiple Gate-Defined Double Quantum Dots.

We fabricate and characterize a hybrid quantum device that consists of five gate-defined double quantum dots (DQDs) and a high-impedance NbTiN transmission resonator. The controllable interactions between DQDs and the resonator are spectroscopically explored by measuring the microwave transmission through the resonator in the detuning parameter space. Utilizing the high tunability of the system parameters and the high cooperativity (Ctotal > 17.6) interaction between the qubit ensemble and the resonator, we tune the charge-photon coupling and observe the collective microwave response changing from linear to nonlinear. Our results present the maximum number of DQDs coupled to a resonator and manifest a potential platform for scaling up qubits and studying collective quantum effects in semiconductor-superconductor hybrid cavity quantum electrodynamics systems.

Molecular transistors as substitutes for quantum information applications.

Applications of quantum information science (QIS) generally rely on the generation and manipulation of qubits. Still, there are ways to envision a device with a continuous readout, but without the entangled states. This concise perspective includes a discussion on an alternative to the qubit, namely the solid-state version of the Mach-Zehnder interferometer, in which the local moments and spin polarization replace light polarization. In this context, we provide some insights into the mathematics that dictates the fundamental working principles of quantum information processes that involve molecular systems with large magnetic anisotropy. Transistors based on such systems lead to the possibility of fabricating logic gates that do not require entangled states. Furthermore, some novel approaches, worthy of some consideration, exist to address the issues pertaining to the scalability of quantum devices, but face the challenge of finding the suitable materials for desired functionality that resemble what is sought from QIS devices.

Ultrafast coherent control of a hole spin qubit in a germanium quantum dot.

Operation speed and coherence time are two core measures for the viability of a qubit. Strong spin-orbit interaction (SOI) and relatively weak hyperfine interaction make holes in germanium (Ge) intriguing candidates for spin qubits with rapid, all-electrical coherent control. Here we report ultrafast single-spin manipulation in a hole-based double quantum dot in a germanium hut wire (GHW). Mediated by the strong SOI, a Rabi frequency exceeding 540 MHz is observed at a magnetic field of 100 mT, setting a record for ultrafast spin qubit control in semiconductor systems. We demonstrate that the strong SOI of heavy holes (HHs) in our GHW, characterized by a very short spin-orbit length of 1.5 nm, enables the rapid gate operations we accomplish. Our results demonstrate the potential of ultrafast coherent control of hole spin qubits to meet the requirement of DiVincenzo's criteria for a scalable quantum information processor.

Anisotropic g-Factor and Spin-Orbit Field in a Germanium Hut Wire Double Quantum Dot.

Holes in nanowires have drawn significant attention in recent years because of the strong spin-orbit interaction, which plays an important role in constructing Majorana zero modes and manipulating spin-orbit qubits. Here, from the strongly anisotropic leakage current in the spin blockade regime for a double dot, we extract the full g-tensor and find that the spin-orbit field is in plane with an azimuthal angle of 59° to the axis of the nanowire. The direction of the spin-orbit field indicates a strong spin-orbit interaction along the nanowire, which may have originated from the interface inversion asymmetry in Ge hut wires. We also demonstrate two different spin relaxation mechanisms for the holes in the Ge hut wire double dot: spin-flip co-tunneling to the leads, and spin-orbit interaction within the double dot. These results help establish feasibility of a Ge-based quantum processor.

Long-Distance Superexchange between Semiconductor Quantum-Dot Electron Spins.

Because of their long coherence times and potential for scalability, semiconductor quantum-dot spin qubits hold great promise for quantum information processing. However, maintaining high connectivity between quantum-dot spin qubits, which favor linear arrays with nearest neighbor coupling, presents a challenge for large-scale quantum computing. In this work, we present evidence for long-distance spin-chain-mediated superexchange coupling between electron spin qubits in semiconductor quantum dots. We weakly couple two electron spins to the ends of a two-site spin chain. Depending on the spin state of the chain, we observe oscillations between the distant end spins. We resolve the dynamics of both the end spins and the chain itself, and our measurements agree with simulations. Superexchange is a promising technique to create long-distance coupling between quantum-dot spin qubits.

Correlated spectrum of distant semiconductor qubits coupled by microwave photons.

We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator. Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons. These patterns are in excellent agreement with a simulation using the Tavis-Cummings model, and allow us to readily identify different parameter regimes for both qubits in the detuning space. This method could potentially be an important component in the overall spectroscopic toolbox for quickly characterizing certain collective properties of multiple cavity quantum electrodynamics (QED) coupled qubits.

Giant Anisotropy of Spin Relaxation and Spin-Valley Mixing in a Silicon Quantum Dot.

In silicon quantum dots (QDs), at a certain magnetic field commonly referred to as the "hot spot," the electron spin relaxation rate (T_{1}^{-1}) can be drastically enhanced due to strong spin-valley mixing. Here, we experimentally find that with a valley splitting of 78.2±1.6 µeV, this hot spot in spin relaxation can be suppressed by more than 2 orders of magnitude when the in-plane magnetic field is oriented at an optimal angle, about 9° from the [100] sample plane. This directional anisotropy exhibits a sinusoidal modulation with a 180° periodicity. We explain the magnitude and phase of this modulation using a model that accounts for both spin-valley mixing and intravalley spin-orbit mixing. The generality of this phenomenon is also confirmed by tuning the electric field and the valley splitting up to 268.5±0.7 µeV.

Assessment and analysis of agricultural non-point source pollution loads in China: 1978-2017.

China's successful agriculture development has resulted in public concerned environmental problems. However, continuous and detailed data about Chinese agricultural non-point source pollution (ANPSP) loads are lacking. To assess and analyze Chinese ANPSP loads from 1978 to 2017, an inventory analysis was performed, and a socioeconomic and spatiotemporal analysis in the scale of provinces was conducted. The results showed that the pollution loads of chemical oxygen demand (COD), total nitrogen (TN) and total phosphorus (TP) increased by 91.0%, 196.2% and 244.1%, respectively, and their variation underwent a free development stage, reform promotion stage, market regulation stage and policy incentive stage. The results of the pollution source analysis showed that over the past 40 years, the total percent contribution to COD by livestock and poultry breeding (LPB) and rural household waste (RHW) accounted for 83.1%-96.6%, the total percent contribution to TN by mineral fertilizers (MF) and LPB accounted for 72.3%-80.8%, and the total percent contribution to TP by LPB, RHW and MF accounted for 69.1%-88.6%. In addition, Shandong, Guangdong, Sichuan, and Henan were the top producers of ANPSP loads, and their COD, TN, and TP loads accounted for approximately 32%, 30%, and 35% of the national totals, respectively. The discharge intensity of COD, TN and TP decreased by 79.2%, 67.8%, and 62.6%, respectively. The discharge intensity exhibited a phasic feature that aligned with the national economic plan in the temporal scale and was closely related to the agricultural conditions in the spatial scale.

Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot.

In this paper, we investigate how to achieve high-fidelity electron spin transport in a GaAs double quantum dot. Our study examines fidelity loss in spin transport from multiple perspectives. We first study incoherent fidelity loss due to hyperfine and spin-orbit interaction. We calculate fidelity loss due to the random Overhauser field from hyperfine interaction, and spin relaxation rate due to spin-orbit interaction in a wide range of experimental parameters with a focus on the occurrence of spin hot spots. A safe parameter regime is identified in order to avoid these spin hot spots. We then analyze systematic errors due to non-adiabatic transitions in the Landau-Zener process of sweeping the interdot detuning, and propose a scheme to take advantage of possible Landau-Zener-Stückelberg interference to achieve high-fidelity spin transport at a higher speed. At last, we study another systematic error caused by the correction to the electron g-factor from the double dot potential, which can lead to a notable phase error. In all, our results should provide a useful guidance for future experiments on coherent electron spin transport.

Coherent transfer of electron spin correlations assisted by dephasing noise.

Quantum coherence of superposed states, especially of entangled states, is indispensable for many quantum technologies. However, it is vulnerable to environmental noises, posing a fundamental challenge in solid-state systems including spin qubits. Here we show a scheme of entanglement engineering where pure dephasing assists the generation of quantum entanglement at distant sites in a chain of electron spins confined in semiconductor quantum dots. One party of an entangled spin pair, prepared at a single site, is transferred to the next site and then adiabatically swapped with a third spin using a transition across a multi-level avoided crossing. This process is accelerated by the noise-induced dephasing through a variant of the quantum Zeno effect, without sacrificing the coherence of the entangled state. Our finding brings insight into the spin dynamics in open quantum systems coupled to noisy environments, opening an avenue to quantum state manipulation utilizing decoherence effects.

Spin-orbit coupling and electric-dipole spin resonance in a nanowire double quantum dot.

We study the electric-dipole transitions for a single electron in a double quantum dot located in a semiconductor nanowire. Enabled by spin-orbit coupling (SOC), electric-dipole spin resonance (EDSR) for such an electron can be generated via two mechanisms: the SOC-induced intradot pseudospin states mixing and the interdot spin-flipped tunneling. The EDSR frequency and strength are determined by these mechanisms together. For both mechanisms the electric-dipole transition rates are strongly dependent on the external magnetic field. Their competition can be revealed by increasing the magnetic field and/or the interdot distance for the double dot. To clarify whether the strong SOC significantly impact the electron state coherence, we also calculate relaxations from excited levels via phonon emission. We show that spin-flip relaxations can be effectively suppressed by the phonon bottleneck effect even at relatively low magnetic fields because of the very large g-factor of strong SOC materials such as InSb.

Doppler effect induced spin relaxation boom.

We study an electron spin qubit confined in a moving quantum dot (QD), with our attention on both spin relaxation, and the product of spin relaxation, the emitted phonons. We find that Doppler effect leads to several interesting phenomena. In particular, spin relaxation rate peaks when the QD motion is in the transonic regime, which we term a spin relaxation boom in analogy to the classical sonic boom. This peak indicates that a moving spin qubit may have even lower relaxation rate than a static qubit, pointing at the possibility of coherence-preserving transport for a spin qubit. We also find that the emitted phonons become strongly directional and narrow in their frequency range as the qubit reaches the supersonic regime, similar to Cherenkov radiation. In other words, fast moving excited spin qubits can act as a source of non-classical phonons. Compared to classical Cherenkov radiation, we show that quantum dot confinement produces a small but important correction on the Cherenkov angle. Taking together, these results have important implications to both spin-based quantum information processing and coherent phonon dynamics in semiconductor nanostructures.

Tunable Hybrid Qubit in a GaAs Double Quantum Dot.

We experimentally demonstrate a tunable hybrid qubit in a five-electron GaAs double quantum dot. The qubit is encoded in the (1,4) charge regime of the double dot and can be manipulated completely electrically. More importantly, dot anharmonicity leads to quasiparallel energy levels and a new anticrossing, which help preserve quantum coherence of the qubit and yield a useful working point. We have performed Larmor precession and Ramsey fringe experiments near the new working point and find that the qubit decoherence time is significantly improved over a charge qubit. This work shows a new way to encode a semiconductor qubit that is controllable and coherent.

Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere.

Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov-Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs.

Scaling of decoherence for a system of uncoupled spin qubits.

Significant experimental progresses in recent years have generated continued interest in quantum computation. A practical quantum computer would employ thousands if not millions of coherent qubits, and maintaining coherence in such a large system would be imperative for its utility. As an attempt at understanding the quantum coherence of multiple qubits, here we study decoherence of a multi-spin-qubit state under the influence of hyperfine interaction, and clearly demonstrate that the state structure is crucial to the scaling behavior of n-spin decoherence. Specifically, we find that coherence times of a multi-spin state at most scale with the number of qubits n as √n, while some states with higher symmetries have scale-free coherence with respect to n. Statistically, convergence to these scaling behavior is generally determined by the size of the Hilbert space m, which is usually much larger than n (up to an exponential function of n), so that convergence rate is very fast as we increase the number of qubits. Our results can be extended to other decoherence mechanisms, including in the presence of dynamical decoupling, which allow meaningful discussions on the scalability of spin-based quantum coherent technology.

Valley-based noise-resistant quantum computation using Si quantum dots.

We devise a platform for noise-resistant quantum computing using the valley degree of freedom of Si quantum dots. The qubit is encoded in two polarized (1,1) spin-triplet states with different valley compositions in a double quantum dot, with a Zeeman field enabling unambiguous initialization. A top gate gives a difference in the valley splitting between the dots, allowing controllable interdot tunneling between opposite valley eigenstates, which enables one-qubit rotations. Two-qubit operations rely on a stripline resonator, and readout on charge sensing. Sensitivity to charge and spin fluctuations is determined by intervalley processes and is greatly reduced as compared to conventional spin and charge qubits. We describe a valley echo for further noise suppression.

Fast hybrid silicon double-quantum-dot qubit.

We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers S(2)=3/4 (S=1/2) and S(z)=-1/2, with the two different states being singlet and triplet in the doubly occupied dot. Gate operations can be implemented electrically and the qubit is highly tunable, enabling fast implementation of one- and two-qubit gates in a simpler geometry and with fewer operations than in other proposed quantum dot qubit architectures with fast operations. Moreover, the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.

Controllable anisotropic exchange coupling between spin qubits in quantum dots.

The exchange coupling between quantum dot spin qubits is isotropic, which restricts the types of quantum gates that can be formed. Here, we propose a method for controlling anisotropic interactions between spins arranged in a bus geometry. The symmetry is broken by an external magnetic field, resulting in XXZ-type interactions that can efficiently generate maximally entangled Greenberger-Horne-Zeilinger states or universal gate sets for exchange-only quantum computing. We exploit the XXZ couplings to propose a qubit scheme, based on double dots.