Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism

Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NISQ)computing.In this paper,we use the bit-flip averaging(BFA)method to mitigate frequent readout errors in quantum generative adversarial networks(QGAN)for image generation,which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance,successfully solving problems with high cost of measurement for traditional error mitigation methods.Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method,the Kullback-Leibler(KL)divergence of the generated images converges to 0.04,0.05,and 0.1 for readout error probabilities of p=0.01,p=0.05,and p=0.1,respectively.Additionally,by evaluating the fidelity of the quantum states representing the images,we observe average fidelity values of 0.97,0.96,and 0.95 for the three readout error probabilities,respectively.These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models.

Improved decoy-state quantum key distribution with uncharacterized heralded single-photon sources

Encoding system plays a significant role in quantum key distribution(QKD).However,the security and performance of QKD systems can be compromised by encoding misalignment due to the inevitable defects in realistic devices.To alleviate the influence of misalignments,a method exploiting statistics from mismatched basis is proposed to enable uncharacterized sources to generate secure keys in QKD.In this work,we propose a scheme on four-intensity decoy-state quantum key distribution with uncharacterized heralded single-photon sources.It only requires the source states are prepared in a two-dimensional Hilbert space,and can thus reduce the complexity of practical realizations.Moreover,we carry out corresponding numerical simulations and demonstrate that our present four-intensity decoy-state scheme can achieve a much higher key rate compared than a three-intensity decoy-state method,and meantime it can obtain a longer transmission distance compared than the one using weak coherent sources.

Quantum dynamics within curved thin layers with deviation

Combining the deviation between thin layers' adjacent surfaces with the confining potential method applied to the quantum curved systems,we derive the effective Schr?dinger equation describing the particle constrained within a curved layer,accompanied by a general geometric potential V_(gq) composed of a compression-corrected geometric potential V_(gq)~*and a novel potential V_(gq)~(**) brought by the deviation.Applying this analysis to the cylindrical layer emerges two types of deviation-induced geometric potential,resulting from the the cases of slant deviation and tangent deviation,respectively,which strongly renormalizes the purely geometric potential and contribute to the energy spectrum based on a very substantial deepening of bound states they offer.

Calculation of Valence Subband Structures for Strained Quantum-Wells by Plane Wave Expansion Method Within 6×6 Luttinger-Kohn Model

The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.

Quantum Boltzmann equation solved by Monte Carlo method for nano-scale semiconductor devices simulation

A two-dimensional （2D） full band self-consistent ensemble Monte Carlo （MC） method for solving the quantum Boltzmann equation, including collision broadening and quantum potential corrections, is developed to extend the MC method to the study of nano-scale semiconductor devices with obvious quantum mechanical （QM） effects. The quantum effects both in real space and momentum space in nano-scale semiconductor devices can be simulated. The effective mobility in the inversion layer of n and p channel MOSFET is simulated and compared with experimental data to verify this method. With this method 50nm ultra thin body silicon on insulator MOSFET are simulated. Results indicate that this method can be used to simulate the 2D QM effects in semiconductor devices including tunnelling effect.

An enhanced image binarization method incorporating with Monte-Carlo simulation

We proposed an enhanced image binarization method.The proposed solution incorporates Monte-Carlo simulation into the local thresholding method to address the essential issues with respect to complex background,spatially-changed illumination,and uncertainties of block size in traditional method.The proposed method first partitions the image into square blocks that reflect local characteristics of the image.After image partitioning,each block is binarized using Otsu’s thresholding method.To minimize the influence of the block size and the boundary effect,we incorporate Monte-Carlo simulation into the binarization algorithm.Iterative calculation with varying block sizes during Monte-Carlo simulation generates a probability map,which illustrates the probability of each pixel classified as foreground.By setting a probability threshold,and separating foreground and background of the source image,the final binary image can be obtained.The described method has been tested by benchmark tests.Results demonstrate that the proposed method performs well in dealing with the complex background and illumination condition.

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation.Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.

An analysis of the radar backscatter from oil-covered sea surfaces using moment method and Monte-Carlo simulation: preliminary results

An analysis of the radar backscattering from the ocean surface covered by oil spill is presented using a mi- crowave scattering model and Monte-Carlo simulation. In the analysis, a one-dimensional rough sea sur- face is numerically generated with an ocean waveheight spectrum for a given wind velocity. A two-layered medium is then generated by adding a thin oil layer on the simulated rough sea surface. The electric fields backscattered from the sea surface with two-layered medium are computed with the method of moments （MoM）, and the backscattering coefficients are statistically obtained with N independent samples for each oil-spilled surface using the Monte-Carlo technique for various conditions of surface roughness, oil-layer thickness, frequency, polarization and incidence angle. The numerical simulation results are compared with theoretical models for clean sea surfaces and SAR images of an off-spilled sea surface caused by the Hebei （Hebei province, China） Spirit oil tanker in 2007. Further, conditions for better oil spill extraction are sought by the numerical simulation on the effects of wind speed and oil-layer thickness at different inci- dence angles on the backscattering coefficients.

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

A new hybrid method—combined heat flux method with Monte-Carlo method to analyze thermal radiation

A new hybrid method, Monte-Carlo-Heat-Flux （MCHF） method, was presented to analyze the radiative heat transfer of participating medium in a three-dimensional rectangular enclosure using combined the Monte-Carlo method with the heat flux method. Its accuracy and reliability was proved by comparing the computational results with exact results from classical ＂Zone Method＂.

Monte-Carlo Method for Coalbed Methane Resource Assessment in Key Coal Mining Areas of China

Monte-Carlo method is used for estimating coalbed methane （CBM） resources in key coal mining areas of China. Monte-Carlo method is shown to be superior to the traditional volumetric method with constant parameters in the calculation of CBM resources. The focus of the article is to introduce the main algorithm and the realization of functions estimated by Monte-Carlo method, including selection of parameters, determination of distribution function, generation of pseudo-random numbers, and evaluation of the parameters corresponding to pseudo-random numbers. A specified software on the basis of Monte-Carlo method is developed using Visual C＋＋ for the assessment of the CBM resources. A case study shows that calculation results using Monte-Carlo method have smaller error range in comparison with those using volumetric method.

Pseudospin symmetric solutions of the Dirac equation with the modified Rosen-Morse potential using Nikiforov-Uvarov method and supersymmetric quantum mechanics approach

Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential including the spin-orbit coupling term by using the Nikiforov-Uvarov method and supersymmetric quantum mechanics approach.The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin-orbit coupling quantum number k are presented under the condition of pseudospin symmetry.The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations.The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.

Security Simulation of Continuous-Variable Quantum Key Distribution over Air-to-Water Channel Using Monte Carlo Method

Considering the ocean water＇s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable （CV） quantum key distribution （QKD） based Mr-to-water channel. The effects of the absorp- tion and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle.

A method to calculate effective Hamiltonians in quantum information

Effective Hamiltonian method is widely used in quantum information. We introduce a method to calculate effective Hamiltonians and give two examples in quantum information to demonstrate the method. We also give a relation between the effective Hamiltonian in the Shr?dinger picture and the corresponding effective Hamiltonian in the interaction picture.Finally, we present a relation between our effective Hamiltonian method and the James–Jerke method which is currently used by many authors to calculate effective Hamiltonians in quantum information science.

The Quantum Scattering Study for Ion-pair Formation Reaction Na+I_2→Na^+I_2^- with the LCAC-SW method

The selected-state probabilities of collinear ion-pair formation process Na+I2→Na++I2-on Aten-Laming-Los two-State potential energy surface have been calculated by using LCAC-SW method. The results show that reaction probabilities are oscillatory with collision energy; the threshold energy of this ioniZation reaction is 2.8 ev, which is in modest agreement with experimental result.

The analytical transfer matrix method for quantum reflection

In this paper, the analytical transfer matrix method （ATMM） is applied to study the properties of quantum reflection in three systems： a sech2 barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 Quantum Mechanics （Non-relativistic Theory） （New York： Pergamon）], which proves that ATMM is a simple and effective method for quantum reflection.

The Study of Alcoholysis of 1,2-Thiazetidine-l,l-dioxide with Quantum Chemical Method

The alcoholysis mechanism of 1,2-thiazetidine-1,1-dioxide with methanol, in which the relatively stable product is sulfonate ester, has been investigated by quantum chemical method. Our calculations indicate the reaction for alcoholysis of 1,2-thiazetidine-1,1-dioxide proceeds via two possible mechanisms: concerted and stepwise. In the stepwise mechanism, two possible reaction pathways can be followed while only one possible reaction pathway can be followed in the concerted mechanism.

An optimized encoding method for secure key distribution by swapping quantum entanglement and its extension

Song [Song D 2004 Phys. Rev. A69034301] first proposed two key distribution schemes with the symmetry feature.We find that, in the schemes, the private channels which Alice and Bob publicly announce the initial Bell state or the measurement result through are not needed in discovering keys, and Song’s encoding methods do not arrive at the optimization.Here, an optimized encoding method is given so that the efficiencies of Song’s schemes are improved by 7/3 times. Interestingly, this optimized encoding method can be extended to the key distribution scheme composed of generalized Bell states.

Energy level of an electron in a saddle-potential quantum dot under a uniform magnetic field obtained by the invariant eigenoperator method

We show that the recently proposed invariant eigenoperator method can be successfully applied to solving the energy levels of an electron in a saddle-potential quantum dot under a uniform magnetic field. The Landau diamagnetism decreases with the value wy2 - wx2 due to the existence of the saddle potential.

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation（GRWA） in both qualitative and quantitative aspects.