Related papers: Quantum Heaviside Eigen Solver
Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce…
Non-Hermitian operators naturally arise in the description of open quantum systems, which exhibit features such as resonances and decay processes, where the associated eigenvalues are complex. Standard quantum algorithms, including the…
We present a framework for computing the solution to Hamiltonian eigenproblems in a subspace defined by bit-strings sampled from a quantum computer. Hamiltonians are represented using an extended alphabet that includes projection and ladder…
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…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
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…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…
Developing efficient quantum computing algorithms is essential for tackling computationally challenging problems across various fields. This paper presents a novel quantum algorithm, XZ24, for efficiently computing the eigen-energy spectra…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…
With physical quantum computers becoming increasingly accessible, research on their applications across various fields has advanced rapidly. In this paper, we present the first study of quantum cosmology conducted on physical quantum…
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…
The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for quantum simulation that can be run on near-term quantum hardware. A challenge in VQE -- as well as any other heuristic algorithm for finding ground states…
The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium sized Hermitian generalized…
The determination of the ground and low-lying excited states is critical in many studies of quantum chemistry and condensed-matter physics. Recent theoretical work proposes a variational quantum eigensolver using ancillary qubits to…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…