Related papers: A Quantum Algorithm for Solving Linear Differentia…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and…
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \in \mathbb{R}^{n \times d}$ and a vector $b$, the goal is to find $x'$ such that $ \| Ax' - b \|_2^2 \leq (1+\epsilon) \min_{x} \| A x - b…
We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…