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The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum…
Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The Variational Quantum Eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we…
The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
We introduce a family of variational quantum algorithms called quantum iterative power algorithms (QIPA) that outperform existing hybrid near-term quantum algorithms of the same kind. We demonstrate the capabilities of QIPA as applied to…
We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed…
We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of Continuous-Variable Quantum Computing…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical…
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a…
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…
We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $[E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by…
Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…
We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting…
Quantum computing has been increasingly applied in nuclear physics. In this work, we combine quantum computing with the complex scaling method to address the resonance problem. Due to the non-Hermiticity introduced by complex scaling,…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
Most non-relativistic interacting quantum many-body systems, such as atomic and molecular ensembles or materials, are naturally described in terms of continuous-space Hamiltonians. The simulation of their ground-state properties on digital…
Simulating the Hubbard model is of great interest to a wide range of applications within condensed matter physics, however its solution on classical computers remains challenging in dimensions larger than one. The relative simplicity of…