Related papers: Requirements for building effective Hamiltonians u…
In order to extend the density-matrix renormalization-group (DMRG) method to two-dimensional systems, we formulate two alternative methods to prepare the initial states. We find that the number of states that is needed for accurate energy…
This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…
Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians.…
Density matrix renormalization group (DMRG) or matrix product states (MPS) is the most effective and accurate method for studying one-dimensional quantum many-body systems. However, the application of DMRG to two-dimensional systems is not…
Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
Dynamic Mode Decomposition (DMD) is a data-driven method related to Koopman operator theory that extracts information about dominant dynamics from data snapshots. In this paper we examine techniques to accelerate the application of DMD to…
Minimizing the energy of an $N$-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions (conditions for the 2-RDM to represent an ensemble $N$-electron…
Given the recent developments in quantum techniques, modeling the physical Hamiltonian of a target quantum many-body system is becoming an increasingly practical and vital research direction. Here, we propose an efficient strategy combining…
Dynamical decoupling (DD) is a key technique for suppressing decoherence and preserving the performance of quantum algorithms. We introduce a measurement-based DD (MDD) protocol that determines control unitary gates from partial…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…
We investigate Riemannian gradient flows for preparing ground states of a desired Hamiltonian on a quantum device. We show that the number of steps of the corresponding Riemannian gradient descent (RGD) algorithm that prepares a ground…
Quantum machine learning (QML) requires powerful, flexible and efficiently trainable models to be successful in solving challenging problems. We introduce density quantum neural networks, a model family that prepares mixtures of trainable…
One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application…
Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization…
We study a proof-of-principle example of the recently proposed hybrid quantum-classical simulation of strongly correlated fermion models in the thermodynamic limit. In a "two-site" dynamical mean-field theory (DMFT) approach we reduce the…
Engineering effective Hamiltonians is essential for advancing quantum technologies including quantum simulation, sensing, and computing. This paper presents a general framework for effective Hamiltonian engineering, enabling robust,…
Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a…
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…