On the use of cross polarization in solid-state NMR:1 H spinlock versus adiabatic demagnetization in the rotating frame

Cross polarization(CP)is a widely used solid-state nuclear magnetic resonance(NMR)technique for enhancing the polarization of dilute S spins from much larger polarization of abundant I spins such as 1 H.To achieve such a polarization transfer,the I spin should either be spin-locked or be converted to the dipolar ordered state through adiabatic demagnetization in the rotating frame.In this work,we analyze the spin dynamics of the Hartmann-Hahn CP(HHCP)utilizing the 1 H spin-locking,and the dipolar-order CP(DOCP)having the 1 H adiabatic demagnetization.We further propose an adiabatic demagnetization CP(ADCP)where a constant radio-frequency pulse is applied on the S spin while 1 H is adiabatically demagnetized.Our analyses indicate that ADCP utilizes the adiabatic passage to effectively achieve the polarization transfer from the 1 H to S spins.In addition,the dipolar ordered state generated during the 1 H demagnetization process could also be converted into the observable S polarization through DOCP,further enhancing the polarized signals.It is shown by both static and magic-angle-spinning(MAS)NMR experiments that ADCP has dramatically broadened the CP matching condition over the other CP schemes.Various samples have been used to demonstrate the polarization transfer efficiency of this newly proposed ADCP scheme.

Pore shrinkage capacity of Shajiang black soils(Vertisols)on the North China Plain and its influencing factors

Different pore sizes present different pore shrinkage capacities in a nonrigid soil.However,the shrinkage capacities of different pore sizes and their influencing factors are not clear.We aimed to quantify the shrinkage capacities of different pore sizes(large pores,>50μm;medium pores,0.2-50μm;fine pores,<0.2μm)and determine how soil properties impact soil shrinkage capacity at the regional scale.Two sampling transects from west to east(360 km long,35 samples)and from north to south(190 km long,29 samples)were selected to investigate soil shrinkage capacity and physicochemical properties of at0-20 cm depth in the Vertisol(locally known as Shajiang black soil)region of the North China Plain.The results showed that soil total shrinkage capacity,indicated by the coefficient of linear extensibility(COLE),had a mean value of 0.041-0.051 in the west-east and north-south transects.Large pores had higher pore shrinkage index(PSI)values(0.103-0.109)than medium(0.077-0.096)and fine(0.087-0.091)pores.The PSI of fine pores showed a fluctuating increasing trend from northwest to southeast,and the fine pore shrinkage capacity determined the COLE(r^(2)=0.789,P<0.001).The PSI of large pores had a significant relationship with soil bulk density(r=0.281,P<0.05)and organic carbon(r=-0.311,P<0.05),whereas those of medium and fine pores were correlated with soil clay content(r=0.381 and 0.687,respectively,P<0.001).In addition,the PSI of fine pores was also correlated with montmorillonite content(r=0.387,P<0.01).It can be concluded that the PSI of large pores is related to anthropogenically influenced soil properties with low stability,whereas those of medium and fine pores are related to pedogenic properties.The high variability in anthropogenic and pedogenic factors explains the spatial pattern of Vertisol shrinkage capacity on the North China Plain.

Noisy intermediate-scale quantum computers

Quantum computers have made extraordinary progress over the past decade,and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers.Quantum advantage,the tipping point heralding the quantum era,has been accomplished along with several waves of breakthroughs.Quantum hardware has become more integrated and architectural compared to its toddler days.The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold.Meanwhile,quantum computation research has established a new norm by embracing industrialization and commercialization.The joint power of governments,private investors,and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field,now at the beginning of the noisy intermediate-scale quantum era.Here,we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes,and then summarizing the next-stage challenges.Furthermore,we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.

Hydrologic separation and their contributions to N loss in an agricultural catchment in hilly red soil region

The impacts of hydrological processes on N loss is of great value to understand the N transport at catchment scale,which is far from clear. Rainfall, soil water, groundwater and stream water and their N concentrations were monitored from March 2017 to February 2018 in Sunjia agricultural catchment of the red soil critical zone. Objectives of this study were:(1) to determine the dynamics of N concentration of different waters and their N loads;(2) to assess their contributions to N load of streamflow in the paddy and upland mixed agricultural catchment. Our results showed that the N concentrations of soil water(4.8 mg L^(-1)) and groundwater(6.0 mg L^(-1)) were the highest, approximately 2 to 5 times higher than those of stream water(2.7 mg L^(-1)), rain water(1.7 mg L^(-1)) and irrigation water(1.2 mg L^(-1)). The N net loss of the catchment(38.2 kg ha^(-1) yr^(-1))accounted for 15% of the total fertilizer N input. Rainy season(April–June) was a high-risk period of N loss, contributing to more than one third of the total annual loss amount. Using end-member mixing analysis model(EMMA), we found groundwater(whose discharge accounted for 25% of the catchment streamflow) was an important source for the N loss in the agricultural catchment. Even in this catchment with coexisting upland and paddy field ecosystems, identified end-members could be used to predict the N load well(R^2>0.87, p<0.001). These results can deepen our understanding of the relationship between hydrological process and N transport in the red soil critical zone and are also helpful to improve the water and fertilizer management in subtropical agricultural catchment.

An improved differential evolution algorithm for learning high-fidelity quantum controls

Precisely and efficiently designing control pulses for the preparation of quantum states and quantum gates are the fundamental tasks for quantum computation.Gradient-based optimal control methods are the routine to design such pulses.However,the gradient information is often difficult to calculate or measure,especially when the system is not well calibrated or in the presence of various uncertainties.Gradient-free evolutionary algorithm is an alternative choice to accomplish this task but usually with low-efficiency.Here,we design an efficient mutation rule by using the information of the current and the former individuals together.This leads to our improved differential evolution algorithm,called da DE.To demonstrate its performance,we numerically benchmark the pulse optimization for quantum states and quantum gates preparations on small-scale NMR system.Further numerical comparisons with conventional differential evolution algorithms show that da DE has great advantages on the convergence speed and robustness to several uncertainties including pulse imperfections and measurement errors.

Quantum state and process tomography via adaptive measurements

We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography(AUPT) protocol of d2+d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate(/8 phase gate), and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.

Experimental preparation of topologically ordered states via adiabatic evolution

Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological orders can arise in two-dimensional spin-lattice models. In this paper, we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution. The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators. Each sector is highly entangled, as shown from the completely reconstructed density matrices. This paves the way towards exploring the properties of topological orders and the application of topological orders in topological quantum memory.

Experimental demonstration of nonlinear quantum metrology with optimal quantum state

Nonlinear quantum metrology may exhibit better precision scalings. For example, the uncertainty of an estimated phase may scale as ??∝1/(N^2) under quadratic phase accumulation, which is 1/N times smaller than the linear counterpart, where N is probe number. Here, we experimentally demonstrate the nonlinear quantum metrology by using a spin-I(I > 1/2) nuclear magnetic resonance(NMR) ensemble that can be mapped into a system of N=2I spin-1/2 particles and the quadratic interaction can be utilized for the quadratic phase accumulation. Our experimental results show that the phase uncertainty can scale as ??∝1/(N^2-1)by optimizing the input states, when N is an odd number. In addition, the interferometric measurement with quadratic interaction provides a new way for estimating the quadrupolar coupling strength in an NMR system. Our system may be further extended to exotic nonlinear quantum metrology with higher order many-body interactions.

Nitrogen fertilization degrades soil aggregation by increasing ammonium ions and decreasing biological binding agents on a Vertisol after 12 years

Degraded soil aggregation arising from nitrogen(N)fertilization has been reported in many studies;however,the mechanisms have not yet been clarified.Elucidating the impact of N fertilization on soil aggregation would help to improve soil structure and sustain high crop production.The objective of this study was to determine the impact of long-term N fertilization on soil aggregation and its association with binding and dispersing agents.A 12-year(2008–2019)N fertilization field experiment on a Vertisol was performed,covering a wide range of N application rates(0,360,450,540,630,and 720 kg ha-1 year-1)and including straw management(straw return and straw removal)in a wheat(Triticum aestivum L.)-maize(Zea mays L.)cropping system.Soil samples of 0–20 cm depth were collected from 12 field treatments with 3 replications in 2019.Soil aggregate stability(mean weight diameter(MWD))and contents of soil organic carbon(SOC),glomalin-related soil protein(GRSP),microbial biomass carbon(MBC),and mineral N(NH4+and NO3-)were determined.Long-term N fertilization under straw removal conditions reduced soil MWD by 12%–18%at N rates from 0 to 720 kg ha-1 compared to that under straw return(P<0.05).Soil MWD was positively associated with pH(P<0.05)and MBC(P<0.05),but negatively correlated with NH4+(P<0.05)and NO3-(P<0.05).Compared with the straw removal treatment,the straw incorporation treatment significantly improved the contents of aggregating agents(SOC,GRSP,and MBC)(P<0.001),but did not affect that of the dispersing agent(NH4+)(P>0.05);consequently,it improved soil aggregation.Overall,our results indicate that long-term N fertilization may degrade soil aggregation because of the increases in monovalent ions(H+and NH4+)and the decrease in MBC during soil acidification,especially when the applied N dose exceeded 360 kg ha-1 year-1.Our finding can minimize the negative structural impacts on Vertisol.

Zero-to ultralow-field nuclear magnetic resonance and its applications

As a complementary analysis tool to conventional high-field nuclear magnetic resonance(NMR),zero-to ultralow-field(ZULF)NMR detects nuclear magnetization signals in the sub-microtesla regime.Spin-exchange relaxation-free(SERF)atomic magnetometers provide a new generation of sensitive detectors for ZULF NMR.Owing to features such as low cost,high resolution,and portability,ZULF NMR has recently attracted considerable attention in chemistry,biology,medicine,and tests of fundamental physics.This review describes the basic principles,methodology,and recent experimental and theoretical development of ZULF NMR as well as its applications in spectroscopy,quantum control,imaging,NMR-based quantum devices,and tests of fundamental physics.The future prospects of ZULF NMR are also discussed.

Floquet-engineered quantum state transfer in spin chains

Quantum state transfer between two distant parties is at the heart of quantum computation and quantum communication.Among the various protocols,the counterdiabatic driving(CD)method,by suppressing the unwanted transitions with an auxiliary Hamiltonian Hcd(t),offers a fast and robust strategy to transfer quantum states.However,Hcd(t)term often takes a complicated form in higherdimensional systems and is difficult to realize in experiment.Recently,the Floquet-engineered method was proposed to emulate the dynamics induced by Hcd(t)without the need for complex interactions in multi-qubit systems,which can accelerate the adiabatic process through the fast-oscillating control in the original Hamiltonian H0(t).Here,we apply this method in the Heisenberg spin chains,with only control of the two marginal couplings,to achieve the fast,high-fidelity,and robust quantum state transfer.Then we report an experimental implementation of our scheme using a nuclear magnetic resonance simulator.The experimental results demonstrate the feasibility of this method in complex many-body system and thus provide a new alternative to realize the high-fidelity quantum state manipulation in practice.

Feedback control for manipulating magnetization in spin-exchange optical pumping system

Control of magnetization plays an important role in the scientific and technological field of manipulating spin systems. In this work, we study the problem of manipulating nuclear magnetization in the spin-exchange optical pumping system, including accelerating the recovery of nuclear polarization and fixing it on a specific desired state. A real-time feedback control strategy is exploited here. We have also done some numerical simulations, with the results clearly demonstrating the effectiveness of our method, that the nuclear magnetization is able to be driven towards the equilibrium state at a much faster speed and also can be stabilized to a target state. We expect that our feedback control method can find applications in gyro experiments.

Generic preparation and entanglement detection of equal superposition states

Quantum superposition is a fundamental principle of quantum mechanics, so it is not surprising that equal superposition states(ESS) serve as powerful resources for quantum information processing. In this work, we propose a quantum circuit that creates an arbitrary dimensional ESS. The circuit construction is efficient as the number of required elementary gates scales polynomially with the number of required qubits. For experimental realization of the method, we use techniques of nuclear magnetic resonance(NMR). We have succeeded in preparing a 9-dimensional ESS on a 4-qubit NMR quantum register. The full tomography indicates that the fidelity of our prepared state with respect to the ideal 9-dimensional ESS is over 96%. We also prove the prepared state is pseudo-entangled by directly measuring an entanglement witness operator. Our result can be useful for the implementation of those quantum algorithms that require an ESS as an input state.

Algorithmic cooling based on cross-relaxation and decoherence-free subspace

Heat-bath algorithmic cooling(HBAC)has been proven to be a powerful and effective method for obtaining high polarization of the target system.Its cooling upper bound has been recently found using a specific algorithm,the partner pairing algorithm(PPAHBAC).It has been shown that by including cross-relaxation,it is possible to surpass the cooling bounds.Herein,by combining cross-relaxation and decoherence-free subspace,we present a two-qubit reset sequence and then generate a new algorithmic cooling(AC)technique using irreversible polarization compression to further surpass the bound.The proposed two-qubit reset sequence can prepare one of the two qubits to four times the polarization of a single-qubit reset operation in PPA-HBAC for low polarization.When the qubit number is large,the cooling limit of the proposed AC is approximately five times as high as the PPA-HBAC.The results reveal that cross-relaxation and decoherence-free subspace are promising resources to create new AC for higher polarization.