# “Quantum algorithm” Science-Research, Aprir 2022, Week 1 — summary from Astrophysics Data System and Arxiv

## Astrophysics Data System — summary generated by Brevi Assistant

In this work, we present a Gauss-Newton based quantum algorithm for combinatorial optimization troubles that swiftly converges to among the ideal solutions without being trapped in neighborhood minima or plateaus. Quantum optimization formulas have been explored for years, yet extra recent investigations have gotten on variational quantum formulas, which often experience the abovementioned problems. Resolving the eigenproblem of the Laplacian matrix of a fully linked graph has wide applications in data science, machine learning, and photo processing, etc. Here, we propose an efficient quantum algorithm to address it based on a basic presumption that the element of each vertex and its norms can be accessed through a quantum random gain access to data framework. Testing combinatorial optimization issues are common in scientific research and engineering. First, we present an intuitive technique for synthesizing and examining discrete optimization troubles, in which the issue and matching mathematical primitives are shared utilizing a discrete quantum intermediate depiction that is encoding-independent. Fidelity is a fundamental step for the distance of two quantum states, which is essential both from a theoretical and useful perspective. As a corresponding result, we show that fidelity evaluation to any non-trivial constant additive precision is hard generally, by providing a sample complexity lower bound that depends polynomially on the measurement. We propose a series of quantum algorithms for calculating a large range of quantum declines and distances, including the von Neumann worsening, quantum Rényi decline, trace range, and fidelity. The key idea of our quantum algorithms is to extend block-encoding from unitary operators in previous work to quantum states. Solving linear systems of formulas is of essential relevance in numerous areas of scientific research. Quantum algorithm has exponential velocity in solving the straight systems Ax⃗ = b⃗ for well-conditioned and sporadic coefficient matrix A with dimension N × N. In this paper, we present a quantum algorithm to address matrix equations of the kind AX = B, where X = (X⃗_1,x⃗_2,…x⃗_n), B = (B⃗_1,b⃗_2,…b⃗_n), X⃗_k and b⃗_k are system vectors.

*Please keep in mind that the text is machine-generated by the Brevi Technologies’ Natural language Generation model, and we do not bear any responsibility. The text above has not been edited and/or modified in any way.*

## Source texts:

- https://ui.adsabs.harvard.edu/abs/2022arXiv220313939T/abstract — A Gauss-Newton based Quantum Algorithm for Combinatorial Optimization.
- https://ui.adsabs.harvard.edu/abs/2022arXiv220314451L/abstract — A quantum algorithm for solving eigenproblem of the Laplacian matrix of a fully connected graph.
- https://ui.adsabs.harvard.edu/abs/2022arXiv220314432S/abstract — Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems.
- https://ui.adsabs.harvard.edu/abs/2022arXiv220315993G/abstract — Improved Quantum Algorithms for Fidelity Estimation.
- https://ui.adsabs.harvard.edu/abs/2022arXiv220313522W/abstract — New Quantum Algorithms for Computing Quantum Entropies and Distances.
- https://ui.adsabs.harvard.edu/abs/2022LaPhL.19e5202X/abstract — Quantum algorithm for solving matrix equations of the form AX = B.

## Arxiv — summary generated by Brevi Assistant

In this work, we present a Gauss-Newton based quantum algorithm for combinatorial optimization problems that rapidly converges to among the optimum options without being entraped in neighborhood minima or plateaus. Quantum optimization algorithms have been explored for years, yet much more current investigations have been on variational quantum algorithms, which typically experience the previously mentioned issues. The Density Matrix Renormalization Group algorithm has been extremely successful for calculating the ground states of one-dimensional quantum many-body systems. Much more significantly, it permits to build a DMRG algorithm which, like the standard DMRG for ground states, iteratively minimizes the global optimization problem for neighborhoods of the same type, with the energy assembling monotonically in principle. Integrity is a basic measure for the nearness of 2 quantum states, which is necessary both from an academic and useful perspective. If circuit descriptions for the appropriate states are provided, we show that the task is hard for the intricacy course called quantum statistical absolutely no expertise via a decrease to a closely relevant outcome by Watrous. Hereditary formulas are heuristic optimization strategies influenced by Darwinian development, which are defined by efficiently finding durable remedies for optimization issues. Quantum machine learning has been recognized as one of the vital areas that can enjoy advantages from near-term quantum gadgets, beside optimization and quantum chemistry. We offer understanding into why the efficiency of a VQA-based Q-learning algorithm crucially depends upon the observables of the quantum model and demonstrate how to pick appropriate observables based on the learning task available. The search for new computational tasks of quantum chemistry that can be performed on existing quantum computer systems is necessary for the advancement of quantum computing and quantum chemistry. Although calculations of chemical responses have a broad array of applications in quantum chemical calculations, a quantum algorithm for acquiring activation energy E_a which establishes the rate of chemical reactions, has not been performed.

*Please keep in mind that the text is machine-generated by the Brevi Technologies’ Natural language Generation model, and we do not bear any responsibility. The text above has not been edited and/or modified in any way.*

## Source texts:

- https://arxiv.org/abs/2203.13939v2 — A Gauss-Newton based Quantum Algorithm for Combinatorial Optimization.
- https://arxiv.org/abs/2203.16350v1 — Density Matrix Renormalization Group Algorithm For Mixed Quantum States.
- https://arxiv.org/abs/2203.15993v1 — Improved Quantum Algorithms for Fidelity Estimation.
- https://arxiv.org/abs/2203.15039v1 — Quantum Genetic Algorithm with Individuals in Multiple Registers.
- https://arxiv.org/abs/2103.15084v2 — Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning.
- https://arxiv.org/abs/2009.06803v2 — Quantum algorithm for a chemical reaction path optimization by using a variational quantum algorithm and a reaction path generation.

# Brief Info about Brevi Assistant

The Brevi assistant is a novel way to automatically summarize, assemble, and consolidate multiple text documents, research papers, articles, publications, reports, reviews, feedback, etc., into one compact abstractive form.

At Brevi Assistant, we integrated the most popular open-source databases to empower Researchers, Teachers, and Students to find relevant Contents/Abstracts and to always be up to date about their fields of interest.

Also, users can automate the topics and sources of interest to receive weekly or monthly summaries.