Related papers: Laplace transform based quantum eigenvalue transfo…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
The polar decomposition for a matrix $A$ is $A=UB$, where $B$ is a positive Hermitian matrix and $U$ is unitary (or, if $A$ is not square, an isometry). This paper shows that the ability to apply a Hamiltonian $\pmatrix{ 0 & A^\dagger \cr A…
We introduce a hybrid oscillator-qubit formulation of linear combination of Hamiltonian simulation (LCHS) for solving linear ordinary differential equations. Instead of representing the quadrature rule with a discrete-variable (DV) ancilla…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one's…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
The utility of effective model spaces in quantum simulations of non-relativistic quantum many-body systems is explored in the context of the Lipkin-Meshkov-Glick model of interacting fermions. We introduce an iterative…
Consider a symmetric matrix $A(v)\in\RR^{n\times n}$ depending on a vector $v\in\RR^n$ and satisfying the property $A(\alpha v)=A(v)$ for any $\alpha\in\RR\backslash{0}$. We will here study the problem of finding $(\lambda,v)\in\RR\times…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Linear combination of Hamiltonian simulation (LCHS) connects the general linear non-unitary dynamics with unitary operators and serves as the mathematical backbone of designing near-optimal quantum linear differential equation algorithms.…
The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…
We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} ,…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…
Time symmetry in quantum mechanics, where the current quantum state is determined jointly by both the past and the future, offers a more comprehensive description of physical phenomena. This symmetry facilitates both forward and backward…
We present a new machine learning technique which calculates a real-valued, time independent, finite dimensional Hamiltonian matrix from only experimental data. A novel cost function is given along with a proof that the cost function has…