Related papers: Dense outputs from quantum simulations
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
We present a method to construct a continuous extension (otherwise known as dense output) for a numerical routine in the special case of the numerical solution being a scalar-valued function exhibiting rapid oscillations. Such cases call…
We provide theory, algorithms, and simulations of non-equilibrium quantum systems using a one-dimensional (1D) completely-positive (CP), matrix-product (MP) density-operator ($\rho$) representation. By generalizing the matrix product…
Over the past decade we have seen an explosion of demonstrations of quantum coherence in atomic, optical, and condensed matter systems. These developments have placed a new emphasis on the production of robust and optimal quantum control…
Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…
In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
Countless applications cast their computational core in terms of dense linear algebra operations. These operations can usually be implemented by combining the routines offered by standard linear algebra libraries such as BLAS and LAPACK,…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
$\mathcal{PT}$-symmetric system has attracted extensive attention in recent years because of its unique properties and applications. How to simulate $\mathcal{PT}$-symmetric system in traditional quantum mechanical system has not only…
Open quantum systems are ubiquitous in the physical sciences, with widespread applications in the areas of chemistry, condensed matter physics, material science, optics, and many more. Not surprisingly, there is significant interest in…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
We present a time-dependent quantum algorithm for nuclear inelastic scattering in the time-dependent basis function on qubits approach. This algorithm aims to quantum simulate a subset of the nuclear inelastic scattering problems that are…
There is a pressing need for more accurate computational simulations of the opto-electronic properties of defects in materials to aid in the development of quantum sensing platforms. In this work, we explore how quantum computers could be…
This paper presents a hybrid classical-quantum program for density estimation and supervised classification. The program is implemented as a quantum circuit in a high-dimensional quantum computer simulator. We show that the proposed quantum…