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

Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to be achieved. In this work, we define a task called…

Quantum signal processing (QSP) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of…

We present a simplified exposition of some pieces of [Gily\'en, Su, Low, and Wiebe, STOC'19, arXiv:1806.01838], which introduced a quantum singular value transformation (QSVT) framework for applying polynomial functions to block-encoded…

Quantum singular value transformation (QSVT) is a framework that has been shown to unify many primitives in quantum algorithms. In this work, we leverage the QSVT framework in two directions. We first show that the QSVT framework can…

We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…

A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single qubit quantum channels $\{T_t\}$ specified by a generator $\mathcal{L}$. This algorithm requires only…

We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian…

We propose an algorithm for encoding of linear kinetic plasma problems in quantum circuits. The focus is made on modeling electrostatic linear waves in one-dimensional Maxwellian electron plasma. The waves are described by the linearized…

Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…

We propose using variational quantum algorithms (VQAs) to simulate established quantum algorithms under realistic noise conditions, aiming to surpass the fidelity of theoretical circuits in noisy environments. Focusing on the Quantum…

The last few years have seen rapid development of applications of quantum computation to quantum field theory. The first algorithms for quantum simulation of scattering have been proposed in the context of scalar and fermionic theories,…

We present a variational quantum algorithm (VQA) to solve the nonlinear one-dimensional Bratu equation. By formulating the boundary value problem within a variational framework and encoding the solution in a parameterized quantum neural…

Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…

The many-body nature of nuclear physics problems poses significant computational challenges. These challenges become even more pronounced when studying the resonance states of nuclear systems, which are governed by the non-Hermitian…

Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…

Entanglement is a defining property of quantum systems. For a subsystem of a larger quantum system, one can formally define an operator known as the modular Hamiltonian, which is closely linked to the entanglement properties of that…

Non-Hermitian physics has emerged as a rich field of study, with applications ranging from $PT$-symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or…

We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…

We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…