Related papers: Quantum Algorithms for Estimating Physical Quantit…
The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here we present two algorithms that, in conjunction with other methods developed…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit…
Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
The mean of a random variable can be understood as a linear functional on the space of probability distributions. Quantum computing is known to provide a quadratic speedup over classical Monte Carlo methods for mean estimation. In this…
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Quantum-chemical simulations are essential for predicting energies of chemical reactions. Accurately solving the many-body Schr\"odinger equation for reagent and product states of most relevant chemical process is, however, unfeasible.…
Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is…
We propose a scheme for quantum computation in optical lattices. The qubits are encoded in the spacial wavefunction of the atoms such that spin decoherence does not influence the computation. Quantum operations are steered by shaking the…
We describe an algorithm for quantum state tomography that converges in polynomial time to an estimate, together with a rigorous error bound on the fidelity between the estimate and the true state. The result suggests that state tomography…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
We present a quantum algorithm for simulating complex many-body systems and finding their ground states, combining the use of tensor networks and density matrix renormalization group (DMRG) techniques. The algorithm is based on von…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…