相关论文: Simulation of linear non-Hermitian boundary-value …

In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…

Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…

We present an efficient classical algorithm based on the construction of a unitary quantum circuit for simulating the Isotropic Wave Equation (IWE) in one, two, or three dimensions. Using an analogy with the massless Dirac equation, second…

We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the many-body wave functions with high complexity. Quantum neural network provides a…

The quantum singular value transformation is a powerful quantum algorithm that allows one to apply a polynomial transformation to the singular values of a matrix that is embedded as a block of a unitary transformation. This paper shows how…

The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational…

We present a variational quantum algorithm that solves the one-dimensional diffusion problem with a space-dependent diffusion constant $D(x)$. This problem is relevant for the exchange of hydroxide ions across a multi-layer membrane in an…

A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…

Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit…

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum…

Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be…

In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors…

Quantum simulation can help us study poorly understood topics such as high-temperature superconductivity and drug design. However, existing quantum simulation algorithms for current quantum computers often have drawbacks that impede their…

Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…

The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…

Quantum algorithms for simulating quantum systems provide a clear and provable advantage over classical algorithms in fault-tolerant settings. There is also interest in quantum algorithms and their implementation in Noisy Intermediate Scale…

Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…