Related papers: Block Lanczos method for excited states on a quant…

Lanczos-type algorithms are well known for their inherent instability. They typically breakdown when relevant orthogonal polynomials do not exist. Current approaches to avoiding breakdown rely on jumping over the non-existent polynomials to…

We present a Lanczos algorithm utilizing multiple grids that reduces the memory requirements both on disk and in working memory by one order of magnitude for RBC/UKQCD's 48I and 64I ensembles at the physical pion mass. The precision of the…

Advances in quantum simulator technology is increasingly required because research on quantum algorithms is becoming more sophisticated and complex. State vector simulation utilizes CPU and memory resources in computing nodes exponentially…

Solving electronic structure problems is considered one of the most promising applications of quantum computing. However, due to limitations imposed by the coherence time of qubits in the Noisy Intermediate Scale Quantum (NISQ) era or the…

The pair coupled cluster doubles (pCCD) method (where the excitation manifold is restricted to electron pairs) has a series of interesting features. Among others, it provides ground-state energies very close to what is obtained with…

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…

An iterative version of the qubit coupled cluster (QCC) method [I.G. Ryabinkin et al., J. Chem. Theory Comput. 14, 6317 (2019)] is proposed. The new method seeks to find ground electronic energies of molecules on noisy intermediate-scale…

We present matrix-product state (MPS) based band Lanczos method as solver for quantum cluster methods such as the variational cluster approximation. While a na\"ive implementation of MPS as cluster solver would barely improve its range of…

We establish rigourously the scaling properties of the Lanczos process applied to an arbitrary extensive Many-Body System which is carried to convergence n to infinity and the thermodynamic limit N to infinity taken. In this limit the…

We adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a…

We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…

The prediction of electronic structure for strongly correlated molecules represents a promising application for near-term quantum computers. Significant attention has been paid to ground state wavefunctions, but excited states of molecules…

A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry…

Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in…

The ability of near-term quantum computers to represent classically-intractable quantum states has brought much interest in using such devices for estimating the ground and excited state energies of fermionic Hamiltonians. The usefulness of…

The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the…

We introduce a quantum extension of dynamic programming, a fundamental computational method that efficiently solves recursive problems using memory. Our innovation lies in showing how to coherently generate recursion step unitaries by using…

Computing the null space of a large sparse matrix $A$ is a challenging computational problem, especially if the nullity -- the dimension of the null space -- is not small. When applying a block Lanczos method to $A^\mathsf{T} A$ for this…

Lattice QCD has historically produced energy results interpretable as either estimates relying on implicit assumptions about asymptotic behavior or one-sided upper bounds. New Lanczos methods providing two-sided bounds with less-restrictive…

We propose efficient algorithms with logarithmic step complexities for the generation of entangled $GHZ_N$ and $W_N$ states useful for quantum networks, and we demonstrate an implementation on the IBM quantum computer up to $N=16$. Improved…