Related papers: An alternative implementation of the Lanczos algor…
The prevalence of variational methods in near-term quantum computing makes optimizer choice critical, yet selection is frequently intuition-based. We therefore present a systematic benchmark of eight classical optimization algorithms for…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are…
A generalization of the stochastic wave function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unravelling is based on a description of the reduced system in a doubled Hilbert space…
Current widely-used approaches to calculate spectral functions using the density-matrix renormalization group in frequency space either necessarily include an artificial broadening (correction-vector method) or have limited resolution…
Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…
We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of…
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…
We introduce a new implementation of time-dependent density-functional theory which allows the \emph{entire} spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a \emph{single} standard…
Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization. The quantum…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…
Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we…
We present a reduced basis approach to solve the convected Helmholtz equation with several physical parameters. Physical parameters characterize the aeroacoustic wave propagation in terms of the wave and Mach numbers. We compute solutions…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
We consider the quantum mechanical propagator for a particle moving in a $d$-dimensional Lorentz gas, with fixed, hard sphere scatterers. To evaluate this propagator in the semi-classical region, and for times less than the Ehrenfest time,…
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual…
For over 70 years it has been assumed that scalar wave propagation in (ensemble-averaged) random particulate materials can be characterised by a single effective wavenumber. Here, however, we show that there exist many effective…
Compared to the classical Lanczos algorithm, the $s$-step Lanczos variant has the potential to improve performance by asymptotically decreasing the synchronization cost per iteration. However, this comes at a cost. Despite being…
We propose a new variational Monte Carlo (VMC) approach based on the Krylov subspace for large-scale shell-model calculations. A random walker in the VMC is formulated with the $M$-scheme representation, and samples a small number of…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…