A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

In this article,we focus on the short time strong solution to a compressible quantum hydrodynamic model.We establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic model in terms of the gradient of the velocity,the second spacial derivative of the square root of the density,and the first order time derivative and first order spacial derivative of the square root of the density.

Experimental quantum state compression from two identical qubits to a qutrit

In the realm of modern information technology,data compression technology occupies a pivotal position.With advancements in quantum information technology,the need to compress large-scale qubits ensembles has become urgent,aiming to reduce the demand on quantum storage resources.However,existing quantum state compression schemes generally face a limitation:the particles before and after compression must reside in the same dimensional space.In specific scenarios,compressing qubits into particles of higher dimensions not only enhances the efficiency of quantum state compression but also further reduces the usage of quantum storage resources.Here we experimentally demonstrated a quantum state compression between particles of different dimensions,successfully compressing two qubits into a single qutrit.The average fidelity of the resulting qutrit with the ideal quantum state is 0.8835.Our study may have potential applications in future quantum information,such as increasing quantum communication bandwidth and reducing storage resource consumption in quantum computing.

Noise-resistant quantum state compression readout

Qubit measurement is generally the most error-prone operation that degrades the performance of near-term quantum devices,and the exponential decay of readout fidelity severely impedes the development of large-scale quantum information processing.Given these disadvantages, we present a quantum state readout method, named compression readout, that naturally avoids large multi-qubit measurement errors by compressing the quantum state into a single qubit for measurement. Our method generally outperforms direct measurements in terms of accuracy, and the advantage grows with the system size. Moreover, because only one-qubit measurements are performed, our method requires solely a fine readout calibration on one qubit and is free of correlated measurement error, which drastically diminishes the demand for device calibration. These advantages suggest that our method can immediately boost the readout performance of near-term quantum devices and will greatly benefit the development of large-scale quantum computing.

Single-photon frequency-modulated continuous-wave Lidar based on quantum compressed sensing

Frequency-modulated continuous-wave(FMCW)Lidar has the characteristics of high-ranging accuracy,noise immunity,and synchronous speed measurement,which makes it a candidate for the next generation of vehicle Lidar.In this work,an FMCW Lidar working at the single-photon level is demonstrated based on quantum compressed sensing,and the target distance is recovered from the sparse photon detection,in which the detection sensitivity,bandwidth,and compression ratio are improved significantly.Our Lidar system can achieve 3 GHz bandwidth detection at photon count rates of a few thousand,making ultra-long-distance FMCW Lidar possible.

On the Blowing up of Solutions to One-dimensional Quantum Navier-Stokes Equations

The blow-up in finite time for the solutions to the initial-boundary value problem associated to the one-dimensional quantum Navier-Stokes equations in a bounded domain is proved. The model consists of the mass conservation equation and a momentum balance equation, including a nonlinear third-order differen- tial operator, with the quantum Bohm potential, and a density-dependent viscosity. It is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after a finite time, if the viscosity constant is not bigger than the scaled Planck constant. The proof is inspired by an observable constructed by Gamba, Gualdani and Zhang, which has been used to study the blowing up of solutions to quantum hydrodynamic models.

OPTIMAL DECAY RATE OF THE COMPRESSIBLE QUANTUM NAVIER-STOKES EQUATIONS

For quantum fluids governed by the compressible quantum Navier-Stokes equations in R;with viscosity and heat conduction, we prove the optimal L;- L;decay rates for the classical solutions near constant states. The proof is based on the detailed linearized decay estimates by Fourier analysis of the operators, which is drastically different from the case when quantum effects are absent.

GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE THREE-DIMENSIONAL FULL COMPRESSIBLE QUANTUM EQUATIONS

We consider the quantum Navier-Stokes equations for the viscous, compressible, heat conducting fluids on the three-dimensional torus T3. The model is based on a system which is derived by Jungel, Matthes and Milisic [15]. We made some adjustment about the relation of the viscosities of quantum terms. The viscosities and the heat conductivity coefficient are allowed to depend on the density, and may vanish on the vacuum. By several levels of approxima- tion we prove the global-in-time existence of weak solutions for the large initial data.