The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are constrained in their accuracy due to the computational limits. The VQE may be used to model complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. This review aims to provide an overview of the progress that has been made on the different parts of the algorithm. All the different components of the algorithm are reviewed in detail including representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process, the post-processing mitigation of errors, and best practices are suggested. We identify four main areas of future research:(1) optimal measurement schemes for reduction of circuit repetitions; (2) large scale parallelization across many quantum computers;(3) ways to overcome the potential appearance of vanishing gradients in the optimization process, and how the number of iterations required for the optimization scales with system size; (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced.

The Variational Quantum Eigensolver: a review of methods and best practices

The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios, its applicability across various problem instances, and considerations of hardware-specific challenges such as error susceptibility and noise resilience. Additionally, we conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm. We aim to provide insights into key questions about the algorithm, such as whether it can outperform classical algorithms and under what circumstances it should be used. Towards this goal, we offer specific practical points in a form of a short guide. 

A review on Quantum Approximate Optimization Algorithm and its variants

Quantum computing for near-term applications in generative chemistry and drug discovery.

Originally a part of the study of physics, quantum mechanics is fast becoming an interdisciplinary field. Quantum computing offers the potential to reach the higher levels of accuracy and security associated with a much faster speedup. Many different approaches have been proposed to building a quantum computer. Seeking the best solution for quantum computers is the mission of both practitioners and researchers. Quantum mechanics is a creative technique that has the potential to redefine information-related disciplines. Unique properties of quantum superposition and entanglement will enable powerful computational scale at a faster and more efficient speed than classical computers, and quantum computing is attracting attention for implementation across broader industries. This study attempts to depict the roadmaps of quantum computing and industrial information integration as they move into the future, based on reviewing the extant popular literature. 

Quantum computing and industrial information integration: A review

Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics.-5.4pc]Please note that the spelling of the following author names in the manuscript differs from the spelling provided in the article metadata: D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. The spelling provided in the manuscript has been retained; please confirm. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation as well as to simulate lattice gauge theory dynamics. 

Fermionic quantum processing with programmable neutral atom arrays

We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field. 

/pdf/a-quantum-computing-view-on-unitary-coupled-cluster-theory-3ghr9s9n.pdf

A quantum computing view on unitary coupled cluster theory

Abstract: Applying a digital strategy is proven to be one way to reduce the infection rate of COVID-19. As a fundamental part of it, database is capable to create a data repository to predict uncertain impacts of the pandemic. The research proposed a database design for project C-Beta that emphasized on creating an ideal system to record and monitor the daily health condition of people with COVID-19. Mainly, the research adopted Connolly and begg principles of Database Software Development Life Cycle. As a result, the database design activities produced blueprints in the forms of data dictionary, ERD, and user views. The database design delivered in the research included with several features namely user verification, restricted research membership, and flexibility in survey creation. Based on analysis and design phase, C-Beta provides a method to collect data for COVID-19 clinical study. Researchers who utilize C-Beta is able to manage multiple surveys and extract all collected records at the same time. 

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A quantum computing view on unitary coupled cluster theory

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