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Accurate calculation of strongly correlated electronic systems requires proper treatment of both static and dynamic correlations, which remains challenging for conventional methods. To address this, we present VQE-PDFT,aquantum-classical…

Quantum Physics · Physics 2026-04-20 Yibo Chen , Zirui Sheng , Weitang Li , Yong Zhang , Xun Xu , Jun-Han Huang , Yuxiang Li

The variational quantum eigensolver (VQE) is generally regarded as a promising quantum algorithm for near-term noisy quantum computers. However, when implemented with the deep circuits that are in principle required for achieving a…

Quantum Physics · Physics 2025-06-05 Simone Cantori , Andrea Mari , David Vitali , Sebastiano Pilati

The Variational Quantum Eigensolver (VQE) is a promising tool for simulating ground states of quantum many-body systems on noisy quantum computers. Its effectiveness relies heavily on the ansatz, which must be both hardware-efficient for…

Quantum Physics · Physics 2025-06-05 Alina Joch , Götz S. Uhrig , Benedikt Fauseweh

The variational quantum eigensolver (VQE) is a promising algorithm for demonstrating quantum advantage in the noisy intermediate-scale quantum (NISQ) era. However, optimizing VQE from random initial starting parameters is challenging due to…

Quantum Physics · Physics 2023-10-20 Abid Khan , Bryan K. Clark , Norm M. Tubman

The Variational Quantum Eigensolver (VQE) is a promising algorithm for quantum computing applications in chemistry and materials science, particularly in addressing the limitations of classical methods for complex systems. This study…

Quantum Physics · Physics 2025-02-25 Nia Pollard , Kamal Choudhary

The Variational Quantum Eigensolver (VQE) is a fundamental algorithm in quantum computing, yet a coherent geometric characterization of VQE remains missing due to fragmented analyses across fixed-ansatz and adaptive-circuit formulations. In…

Quantum Physics · Physics 2026-05-28 Zhen Qin

Quantum computing presents a promising path toward precise quantum chemical simulations, particularly for systems that challenge classical methods. This work investigates the performance of the Variational Quantum Eigensolver (VQE) in…

Quantum Physics · Physics 2025-10-28 Zakaria Boutakka , Nouhaila Innan , Muhammed Shafique , Mohamed Bennai , Z. Sakhi

Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications,…

Quantum Physics · Physics 2025-02-04 Kim A. Nicoli , Luca J. Wagner , Lena Funcke

We present a novel quantum algorithm for approximating the ground-state in quantum many-body systems, particularly suited for Noisy Intermediate-Scale Quantum (NISQ) devices. Our approach integrates Variational Quantum Eigensolvers (VQE)…

Quantum Physics · Physics 2024-03-18 Yihao Liu , Min-Quan He , Z. D. Wang

Hybrid algorithms that combine quantum and classical resources have become commonplace in quantum computing. The variational quantum eigensolver (VQE) is routinely used to solve prototype problems. Currently, hybrid algorithms use no more…

Quantum Physics · Physics 2024-08-27 Manpreet Singh Jattana

Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The Variational Quantum Eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we…

Quantum Physics · Physics 2022-09-28 M. Cerezo , Kunal Sharma , Andrew Arrasmith , Patrick J. Coles

The Variational Quantum Eigensolver (VQE), as a hybrid quantum-classical algorithm, is an important tool for effective quantum computing in the current noisy intermediate-scale quantum (NISQ) era. However, the traditional hardware-efficient…

Strongly Correlated Electrons · Physics 2025-11-20 Shaohui Yao , Wenyu Wang

The variational quantum eigensolver (VQE) is one of the most promising algorithms for low-lying eigenstates calculation on Noisy Intermediate-Scale Quantum (NISQ) computers. Specifically, VQE has achieved great success for ground state…

Numerical Analysis · Mathematics 2025-12-19 Hengzhun Chen , Yingzhou Li , Bichen Lu , Jianfeng Lu

We describe the contextual subspace variational quantum eigensolver (CS-VQE), a hybrid quantum-classical algorithm for approximating the ground state energy of a Hamiltonian. The approximation to the ground state energy is obtained as the…

Quantum Physics · Physics 2021-05-19 William M. Kirby , Andrew Tranter , Peter J. Love

Most literature in the Variational Quantum Eigensolver (VQE) algorithm focuses on finding the ground state of a physical system, by minimizing a quantum-computed cost-function. When excited states are required, the cost-function is usually…

Quantum Physics · Physics 2022-04-12 Kyle Sherbert , Marco Buongiorno Nardelli

Variational quantum eigensolver (VQE) emerged as a first practical algorithm for near-term quantum computers. Its success largely relies on the chosen variational ansatz, corresponding to a quantum circuit that prepares an approximate…

Quantum Physics · Physics 2020-07-10 D. Chivilikhin , A. Samarin , V. Ulyantsev , I. Iorsh , A. R. Oganov , O. Kyriienko

The number of measurements demanded by hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) is prohibitively high for many problems of practical value. For such problems, realizing quantum advantage will…

Quantum Physics · Physics 2021-03-24 Guoming Wang , Dax Enshan Koh , Peter D. Johnson , Yudong Cao

Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We…

Quantum Physics · Physics 2024-06-05 Jan Lukas Bosse , Raul Santos , Ashley Montanaro

The still-maturing noisy intermediate-scale quantum (NISQ) technology faces strict limitations on the algorithms that can be implemented efficiently. In quantum chemistry, the variational quantum eigensolver (VQE) algorithm has become…

Quantum Physics · Physics 2021-06-29 Daniel Claudino , Bo Peng , Nicholas P. Bauman , Karol Kowalski , Travis S. Humble

The variational quantum eigensolver (VQE) is one of the most representative quantum algorithms in the noisy intermediate-size quantum (NISQ) era, and is generally speculated to deliver one of the first quantum advantages for the…

Quantum Physics · Physics 2022-04-13 Shi-Xin Zhang , Zhou-Quan Wan , Chee-Kong Lee , Chang-Yu Hsieh , Shengyu Zhang , Hong Yao