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Optimization problems in finance, physics and computer science are typically very hard to tackle in classical computing and quantum computing could help speed up computations and provide efficient methods for tackling large problems.…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We describe a hybrid quantum-classical approach to treat quantum many-body systems in the thermodynamic limit. This is done by combining numerical linked-cluster expansions (NLCE) with the variational quantum eigensolver (VQE). Here, the…
The ability of quantum computers to overcome the exponential memory scaling of many-body problems is expected to transform quantum chemistry. Quantum algorithms require accurate representations of electronic states on a quantum device, but…
Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Despite the promise of leveraging near- to intermediate-term…
In the noisy-intermediate-scale-quantum era, Variational Quantum Eigensolver (VQE) is a promising method to study ground state properties in quantum chemistry, materials science, and condensed physics. However, general quantum eigensolvers…
The performance of quantum algorithms for eigenvalue problems, such as computing Hamiltonian spectra, depends strongly on the overlap of the initial wavefunction and the target eigenvector. In a basis of Slater determinants, the…
We perform a systematic investigation of variational forms (wave function Ans\"atze), to determine the ground state energies and properties of two-dimensional model fermionic systems on triangular lattices (with and without periodic…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
The recently developed Projective Quantum Eigensolver (PQE) offers an elegant procedure to evaluate the ground state energies of molecular systems on quantum computers. However, the noise in available quantum hardware can result in…
Recent quantum algorithms pertaining to electronic structure theory primarily focus on threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more…
Accurately capturing electron correlation in large-scale molecular systems remains one of the foremost challenges in quantum chemistry and a primary driver for the development of quantum algorithms. Classical configuration-interaction…
Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource…
Quantum computers can be used to calculate the electronic structure and estimate the ground state energy of many-electron molecular systems. In the present study, we implement the Variational Quantum Eigensolver (VQE) algorithm, as a hybrid…
Variational quantum eigensolvers (VQEs) combine classical optimization with efficient cost function evaluations on quantum computers. We propose a new approach to VQEs using the principles of measurement-based quantum computation. This…
The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm…
The near-term utility of quantum computers is hindered by hardware constraints in the form of noise. One path to achieving noise resilience in hybrid quantum algorithms is to decrease the required circuit depth -- the number of applied…
Computational chemistry is one of the most promising applications of quantum computing, mostly thanks to the development of the Variational Quantum Eigensolver (VQE) algorithm. VQE is being studied extensively and numerous optimisations of…
The variational quantum eigensolver (VQE) is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. This hybrid quantum/classical algorithm involves implementing a sequence of…
Accurately treating electron correlation in the wavefunction is a key challenge for both classical and quantum computational chemistry. Classical methods have been developed which explicitly account for this correlation by incorporating…