Selected topics of quantum computing for nuclear physics

Nuclear physics,whose underling theory is described by quantum gauge field coupled with matter,is fundamentally important and yet is formidably challenge for simulation with classical computers.Quantum computing provides a perhaps transformative approach for studying and understanding nuclear physics.With rapid scaling-up of quantum processors as well as advances on quantum algorithms,the digital quantum simulation approach for simulating quantum gauge fields and nuclear physics has gained lots of attention.In this review,we aim to summarize recent efforts on solving nuclear physics with quantum computers.We first discuss a formulation of nuclear physics in the language of quantum computing.In particular,we review how quantum gauge fields(both Abelian and non-Abelian)and their coupling to matter field can be mapped and studied on a quantum computer.We then introduce related quantum algorithms for solving static properties and real-time evolution for quantum systems,and show their applications for a broad range of problems in nuclear physics,including simulation of lattice gauge field,solving nucleon and nuclear structures,quantum advantage for simulating scattering in quantum field theory,non-equilibrium dynamics,and so on.Finally,a short outlook on future work is given.

Exact quantum dynamics for two-level systems with time-dependent driving

It is well known that the time-dependent Schrrödinger equation can only be solved exactly in very rare cases,even for two-level quantum systems.Thus,finding the exact quantum dynamics under a time-dependent Hamiltonian is not only fundamentally important in quantum physics but also facilitates active quantum manipulations for quantum information processing.In this work,we present a method for generating nearly infinite analytically assisted solutions to the Schrödinger equation for a qubit under time-dependent driving.These analytically assisted solutions feature free parameters with only boundary restrictions,making them applicable in a variety of precise quantum manipulations.Due to the general form of the time-dependent Hamiltonian in our approach,it can be readily implemented in various experimental setups involving qubits.Consequently,our scheme offers new solutions to the Schrödinger equation,providing an alternative analytical framework for precise control over qubits.

Simulation of optimal work extraction for quantum systems with work storage

The capacity to extract work from a quantum heat machine is not only of practical value but also lies at the heart of understanding quantum thermodynamics.In this paper,we investigate optimal work extraction for quantum systems with work storage,where extracting work is completed by a unitary evolution on the composite system.We consider the physical requirement of energy conservation both strictly and on average.For both,we construct their corresponding unitaries and propose variational quantum algorithms for optimal work extraction.We show that maximal work extraction in general can be feasible when energy conservation is satisfied on average.We demonstrate with numeral simulations using a continuous-variable work storage.Our work show an implementation of a variational quantum computing approach for simulating work extraction in quantum systems.

Spin-polarized pairing induced by the magnetic field in the Bernal bilayer graphene

Recent experimental findings have demonstrated the occurrence of superconductivity in Bernal bilayer graphene when induced by a magnetic field.In this study,we conduct a theoretical investigation of the potential pairing symmetry within this superconducting system.By developing a theoretical model,we primarily calculate the free energy of the system with p+ip-wave parallel spin pairing,p+ip-wave anti-parallel spin pairing and d+i d-wave pairing symmetry.Our results confirm that the magnetic field is indeed essential for generating the superconductivity.We discover that the p+ip-wave parallel spin pairing leads to a lower free energy for the system.The numerical calculations of the energy band structure,zero-energy spectral function and density of states for each of the three pairing symmetries under consideration show a strong consistency with the free energy results.

Unravelling biotoxicity of graphdiyne:Molecular dynamics simulation of the interaction between villin headpiece protein and graphdiyne

Recently,there has been a growing prevalence in the utilization of graphdiyne(GDY)in the field of biomedicine,attributed to its distinctive physical structure and chemical properties.Additionally,its biocompatibility has garnered increasing attention.However,there is a lack of research on the biological effects and physical mechanisms of GDYprotein interactions at the molecular scale.In this study,the villin headpiece subdomain(HP35)served as a representative protein model.Molecular dynamics simulations were employed to investigate the interaction process between the HP35 protein and GDY,as well as the structural evolution of the protein.The data presented in our study demonstrate that GDY can rapidly adsorb HP35 protein and induce denaturation to one of the a-helix structures of HP35 protein.This implies a potential cytotoxicity concern of GDY for biological systems.Compared to graphene,GDY induced less disruption to HP35 protein.This can be attributed to the presence of natural triangular vacancies in GDY,which prevents p–p stacking action and the limited interaction of GDY with HP35 protein is not conducive to the expansion of protein structures.These findings unveil the biological effects of GDY at the molecular level and provide valuable insights for the application of GDY in biomedicine.

Purification of copper foils driven by single crystallization

High-purity copper(Cu) with excellent thermal and electrical conductivity, is crucial in modern technological applications, including heat exchangers, integrated circuits, and superconducting magnets. The current purification process is mainly based on the zone/electrolytic refining or anion exchange, however, which excessively relies on specific integrated equipment with ultra-high vacuum or chemical solution environment, and is also bothered by external contaminants and energy consumption. Here we report a simple approach to purify the Cu foils from 99.9%(3N) to 99.99%(4N) by a temperature-gradient thermal annealing technique, accompanied by the kinetic evolution of single crystallization of Cu.The success of purification mainly relies on(i) the segregation of elements with low effective distribution coefficient driven by grain-boundary movements and(ii) the high-temperature evaporation of elements with high saturated vapor pressure.The purified Cu foils display higher flexibility(elongation of 70%) and electrical conductivity(104% IACS) than that of the original commercial rolled Cu foils(elongation of 10%, electrical conductivity of ~ 100% IACS). Our results provide an effective strategy to optimize the as-produced metal medium, and therefore will facilitate the potential applications of Cu foils in precision electronic products and high-frequency printed circuit boards.

Rydberg-Atom Terahertz Heterodyne Receiver with Ultrahigh Spectral Resolution

Terahertz heterodyne receivers with high sensitivity and spectral resolution are crucial for various applications.Here,we present a room-temperature atomic terahertz heterodyne receiver that achieves ultrahigh sensitivity and frequency resolution.At a signal frequency of 338.7 GHz,we obtain a sensitivity of 2.88±0.09V·cm^(−1)·Hz^(−1/2) for electric field measurements.The calibrated linear dynamical range spans approximately 89 dB,ranging from−110 dBV/cm to−21 dBV/cm.We demodulate a 400 symbol stream encoded in 4-state phase-shift keying,demonstrating excellent phase detection capability.By scanning the frequency of the local oscillator,we realize a terahertz spectrometer with Hz level frequency resolution.This resolution is more than two orders of magnitude higher than that of existing terahertz spectrometers.The demonstrated terahertz heterodyne receiver holds promising potential for working across the entire terahertz spectrum,significantly advancing its practical applications.

Variational quantum eigensolvers by variance minimization

The original variational quantum eigensolver(VQE)typically minimizes energy with hybrid quantum-classical optimization that aims to find the ground state.Here,we propose a VQE based on minimizing energy variance and call it the variance-VQE,which treats the ground state and excited states on the same footing,since an arbitrary eigenstate for a Hamiltonian should have zero energy variance.We demonstrate the properties of the variance-VQE for solving a set of excited states in quantum chemistry problems.Remarkably,we show that optimization of a combination of energy and variance may be more efficient to find low-energy excited states than those of minimizing energy or variance alone.We further reveal that the optimization can be boosted with stochastic gradient descent by Hamiltonian sampling,which uses only a few terms of the Hamiltonian and thus significantly reduces the quantum resource for evaluating variance and its gradients.

Variational Quantum Eigensolver with Mutual Variance-Hamiltonian Optimization

The zero-energy variance principle can be exploited in variational quantum eigensolvers for solving general eigenstates but its capacity for obtaining a specified eigenstate,such as ground state,is limited as all eigenstates are of zero energy variance.We propose a variance-based variational quantum eigensolver for solving the ground state by searching in an enlarged space of wavefunction and Hamiltonian.With a mutual variance-Hamiltonian optimization procedure,the Hamiltonian is iteratively updated to guild the state towards to the ground state of the target Hamiltonian by minimizing the energy variance in each iteration.We demonstrate the performance and properties of the algorithm with numeral simulations.Our work suggests an avenue for utilizing guided Hamiltonian in hybrid quantum-classical algorithms.

Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems

Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex.Here,we propose a variational quantum algorithm for solving the non-Hermitian Hamiltonian by minimizing a type of energy variance,where zero variance can naturally determine the eigenvalues and the associated left and right eigenstates.Moreover,the energy is set as a parameter in the cost function and can be tuned to scan the whole spectrum efficiently by using a two-step optimization scheme.Through numerical simulations,we demonstrate the algorithm for preparing the left and right eigenstates,verifying the biorthogonal relations,as well as evaluating the observables.We also investigate the impact of quantum noise on our algorithm and show that its performance can be largely improved using error mitigation techniques.Therefore,our work suggests an avenue for solving non-Hermitian quantum many-body systems with variational quantum algorithms on near-term noisy quantum computers.

Interaction induced non-reciprocal three-level quantum transport

Besides its fundamental importance, non-reciprocity has also found many potential applications in quantum technology. Recently, many quantum systems have been proposed to realize non-reciprocity, but stable non-reciprocal process is still experimentally difficult in general, due to the needed cyclical interactions in artificial systems or operational difficulties in solid state materials. Here, we propose a new kind of interaction induced non-reciprocal operation, based on the conventional stimulated-Raman-adiabatic-passage (STIRAP) setup, which removes the experimental difficulty of requiring cyclical interaction, and thus it is directly implementable in various quantum systems. Furthermore, we also illustrate our proposal on a chain of three coupled superconducting transmons, which can lead to a non-reciprocal circulator with high fidelity without a ring coupling configuration as in the previous schemes or implementations. Therefore, our protocol provides a promising way to explore fundamental non-reciprocal quantum physics as well as realize non-reciprocal quantum device.

Variational quantum simulation of the quantum critical regime

The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures.While it is of great physical interest,simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity.Herein,we propose a variational approach,which minimizes the variational free energy,to simulate and locate the quantum critical regime on a quantum computer.The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state,in which the entropy can be analytically obtained from the initial state,and thus the free energy can be accessed conveniently.With numeral simulation,using the one-dimensional Kitaev model as a demonstration we show that the quantum critical regime can be identified by accurately evaluating the temperature crossover line.Moreover,the dependencies of both the correlation length and the phase coherence time with temperature are evaluated for the thermal states.Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.

Modulation of CO adsorption on 4,12,2-graphyne by Fe atom doping and applied electric field

Adsorption characteristics of CO adsorbed on pristine 4,12,2-graphyne(4,12,2-G)and Fe-doped 4,12,2-graphyne(Fe-4,12,2-G)are studied by first-principles calculations.It is shown that CO is only physically adsorbed on pristine 4,12,2-G.Fe atoms can be doped into 4,12,2-G stably and lead to band gap opening.After doping,the interaction between Fe-4,12,2-G and CO is significantly enhanced and chemisorption occurs.The maximum adsorption energy reaches-1.606 e V.Meanwhile,the charge transfer between them increases from 0.009e to 0.196e.Moreover,the electric field can effectively regulate the adsorption ability of the Fe-4,12,2-G system,which is expected to achieve the capture and release of CO.Our study is helpful to promote applications of two-dimensional carbon materials in gas sensing and to provide new ideas for reversible CO sensor research.

Synchronization and Phase Shaping of Single Photons with High-Efficiency Quantum Memory

Time synchronization and phase shaping of single photons both play fundamental roles in quantum information applications that rely on multi-photon quantum interference.Phase shaping typically requires separate modulators with extra insertion losses.Here,we develop an all-optical built-in phase modulator for single photons using a quantum memory.The fast phase modulation of a single photon in both step and linear manner are verified by observing the efficient quantum-memory-assisted Hong-Ou-Mandel interference between two single photons,where the anti-coalescence effect of bosonic photon pairs is demonstrated.The developed phase modulator may push forward the practical quantum information applications.

Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators

We investigate the quantum entanglement in a non-Hermitian kicking system.In the Hermitian case,the out-of-time ordered correlators(OTOCs)exhibit the unbounded power-law increase with time.Correspondingly,the linear entropy,which is a common measurement of entanglement,rapidly increases from zero to almost unity,indicating the formation of quantum entanglement.For strong enough non-Hermitian driving,both the OTOCs and linear entropy rapidly saturate as time evolves.Interestingly,with the increase of non-Hermitian kicking strength,the long-time averaged value of both OTOCs and linear entropy has the same transition point where they exhibit the sharp decrease from a plateau,demonstrating the disentanglment.We reveal the mechanism of disentanglement with the extension of Floquet theory to non-Hermitian systems.

Dynamically Characterizing the Structures of Dirac Points via Wave Packets

Topological non-trivial band structures are the core problem in the field of topological materials.We investigate the topological band structure in a system with controllable Dirac points from the perspective of wave packet dynamics.By adding a third-nearest-neighboring coupling to the graphene model,additional pairs of Dirac points emerge.The emergence and annihilation of Dirac points result in hybrid and parabolic points,and we show that these band structures can be revealed by the dynamical behaviors of wave packets.In particular,for the gapped hybrid point,the motion of the wave packet shows a one-dimensional Zitterbewegung motion.Furthermore,we also show that the winding number associated with the Dirac point and parabolic point can be determined via the center of mass and spin texture of wave packets,respectively.The results of this work could motivate new experimental methods to characterize a system’s topological signatures through wave packet dynamics,which may also find applications in systems of other exotic topological materials.

Quantum Secure Multiparty Computation with Symmetric Boolean Functions

We propose a class of n-variable Boolean functions which can be used to implement quantum secure multiparty computation.We also give an implementation of a special quantum secure multiparty computation protocol.An advantage of our protocol is that only 1 qubit is needed to compute the n-tuple pairwise AND function,which is more efficient comparing with previous protocols.We demonstrate our protocol on the IBM quantum cloud platform,with a probability of correct output as high as 94.63%.Therefore,our protocol presents a promising generalization in realization of various secure multipartite quantum tasks.

Increasing the efficiency of post-selection in direct measurement of the quantum wave function

Direct weak or strong measurement of quantum wave function based on post-selections has been widely explored;however, the efficiency of the measurement is heavily limited by the success probability of post-selection. Here we propose a modified scheme to directly measure photon’s wave function by simply inserting a liquid crystal plate before the postselection stage. Numerical simulations demonstrate that our modified method can significantly increase the efficiency of post selection. Our proposal would speed up the quantum wave function measurement with high resolution and high fidelity.

Fast quantum state transfer and entanglement for cavity-coupled many qubits via dark pathways

Quantum state transfer(QST)and entangled state generation(ESG)are important building blocks for modern quantum information processing.To achieve these tasks,convention wisdom is to consult the quantum adiabatic evolution,which is time-consuming,and thus is of low fidelity.Here,using the shortcut to adiabaticity technique,we propose a general method to realize high-fidelity fast QST and ESG in a cavity-coupled many qubits system via its dark pathways,which can be further designed for high-fidelity quantum tasks with different optimization purpose.Specifically,with a proper dark pathway,QST and ESG between any two qubits can be achieved without decoupling the others,which simplifies experimental demonstrations.Meanwhile,ESG among all qubits can also be realized in a single step.In addition,our scheme can be implemented in many quantum systems,and we illustrate its implementation on superconducting quantum circuits.Therefore,we propose a powerful strategy for selective quantum manipulation,which is promising in cavity coupled quantum systems and could find many convenient applications in quantum information processing.

Impurity effect as a probe for the pairing symmetry of graphene-based superconductors

We study theoretically the single impurity effect on graphene-based superconductors.Four different pairing symmetries are discussed.Sharp in-gap resonant peaks are found near the impurity site for the d+id pairing symmetry and the p+ip pairing symmetry when the chemical potential is large.As the chemical potential decreases,the in-gap states are robust for the d+id pairing symmetry while they disappear for the p+ip pairing symmetry.Such in-gap peaks are absent for the fully gapped extended s-wave pairing symmetry and the nodal f-wave pairing symmetry.The existence of the ingap resonant peaks can be explained well based on the sign-reversal of the superconducting gap along different Fermi pockets and by analyzing the denominator of the T-matrix.All of the features may be checked by the experiments,providing a useful probe for the pairing symmetry of graphene-based superconductors.