Related papers: Quantum variational embedding for ground-state ene…
The sum-of-squares method can give rigorous lower bounds on the energy of quantum Hamiltonians. Unfortunately, typically using this method requires solving a semidefinite program, which can be computationally expensive. Further, the…
We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…
Computing electronic structures of quantum systems is a key task underpinning many applications in photonics, solid-state physics, and quantum technologies. This task is typically performed through iterative algorithms to find the energy…
The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems.…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…
We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…
A new theoretical approach is presented that combines the Hartree-Fock variational scheme with the exact solution of the pairing problem in the finite orbital space. Using this formulation in the sd-space as an example, we show that the…
We present a quantum-classical hybrid algorithm for calculating the ground state and its energy of the quantum many-body Hamiltonian by proposing an adaptive construction of a quantum state for the quantum-selected configuration interaction…
Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based post-quantum cryptography, coding theory, and computer algebra. In this work, we study the…
I describe a simple algorithm for numerically finding the ground state and low-lying excited states of a quantum system. The algorithm is an adaptation of the relaxation method for solving Poisson's equation, and is fundamentally based on…
A versatile and efficient variational approach is developed to solve in- and out-of-equilibrium problems of generic quantum spin-impurity systems. Employing the discrete symmetry hidden in spin-impurity models, we present a new canonical…
How can we use a quantum computer to detect the entanglement structure of a quantum state? Bouland et al. (2024) recently provided an algorithm that, given multiple input copies of the state, finds the "hidden cuts"-partitions into fully…
We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over quantum circuits via infinitesimal unitary transformations,…
Hybrid quantum-classical approaches offer potential solutions to quantum chemistry problems, yet they often manifest as constrained optimization problems. Here, we explore the interconnection between constrained optimization and generalized…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
The area law for entanglement entropy fundamentally reflects the complexity of quantum many-body systems, demonstrating ground states of local Hamiltonians to be represented with low computational complexity. While this principle is…
Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. These task-oriented algorithms work in a hybrid loop combining a quantum processor and classical optimization. Using a specific…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…