Applications such as simulating complicated quantum systems or solving large-scale linear
algebra problems are very challenging for classical computers, owing to the extremely high …

Quantum computers can exploit a Hilbert space whose dimension increases exponentially
with the number of qubits. In experiment, quantum supremacy has recently been achieved …

Previously proposed quantum algorithms for solving linear systems of equations cannot be
implemented in the near term due to the required circuit depth. Here, we propose a hybrid …

We propose a quantum algorithm to solve systems of nonlinear differential equations. Using
a quantum feature map encoding, we define functions as expectation values of parametrized …

Machine learning (ML) has emerged as a formidable force for identifying hidden but
pertinent patterns within a given data set with the objective of subsequent generation of …

Quantum algorithms have been developed for efficiently solving linear algebra tasks.
However, they generally require deep circuits and hence universal fault-tolerant quantum …

Variational quantum algorithms have been proposed to solve static and dynamic problems
of closed many-body quantum systems. Here we investigate variational quantum simulation …

Large machine learning models are revolutionary technologies of artificial intelligence
whose bottlenecks include huge computational expenses, power, and time used both in the …

Recently, several approaches to solving linear systems on a quantum computer have been
formulated in terms of the quantum adiabatic theorem for a continuously varying …

We present substantially generalized and improved quantum algorithms over prior work for
inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we …