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Electronic state calculations using quantum computers are mostly based on second quantization, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is first quantization, which is…
We propose a new variational quantum algorithm named Variational Open Quantum Eigensolver (VOQE) for solving steady states of open quantum systems described by either Lindblad master equations or non-Hermitian Hamiltonians. In VOQE, density…
The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then…
The quantum phase estimation algorithm stands as the primary method for determining the ground state energy of a molecular electronic Hamiltonian on a quantum computer. In this context, the ability to initialize a classically tractable…
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 state preparation lies at the heart of quantum computation and quantum simulations, enabling the investigation of complex manybody systems across physics, chemistry, and data science. While existing methods such as Variational…
The variational quantum eigensolver (VQE), a variational algorithm to obtain an approximated ground state of a given Hamiltonian, is an appealing application of near-term quantum computers. The original work [A. Peruzzo et al.; \textit{Nat.…
As a hybrid quantum-classical algorithm, the variational quantum eigensolver is widely applied in quantum chemistry simulations, especially in computing the electronic structure of complex molecular systems. However, on existing noisy…
One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the…
Constrained problems are frequently encountered in classical and quantum optimization. Particle conservation, in particular, is commonly imposed when studying energy spectra of chemical and solid state systems. Though particle…
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical variational algorithm that produces an upper-bound estimate of the ground-state energy of a Hamiltonian. As quantum computers become more powerful and go beyond the…
Barren plateaus in variational quantum algorithms are typically described by gradient concentration at random initialization. In contrast, rigorous results for the Hessian, even at the level of entry-wise variance, remain limited. In this…
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we…
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…
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…
Barren plateaus are a notorious problem in the optimization of variational quantum algorithms and pose a critical obstacle in the quest for more efficient quantum machine learning algorithms. Many potential reasons for barren plateaus have…
The cascaded variational quantum eigensolver (CVQE) circumvents the need for iterative communication between the quantum and classical processing units that is necessary in the conventional VQE algorithm. While CVQE offers complete freedom…
Adaptive ansatz construction has emerged as a powerful technique for reducing circuit depth and improving optimization efficiency in variational quantum eigensolvers. However, existing adaptive methods, including ADAPT-VQE, rely solely on…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…