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quantum algorithms for transport coefficients in gauge theories

Physical Review D 2021年第9期104卷 094514-094514页

作者： Thomas D. Cohen Henry Lamm Scott Lawrence Yukari Yamauchi Department of Physics University of Maryland College Park Maryland 20742 USA Fermi National Accelerator Laboratory Batavia Illinois 60510 USA Department of Physics University of Colorado Boulder Colorado 80309 USA

In the future, ab initio quantum simulations of heavy ion collisions may become possible with large-scale fault-tolerant quantum computers. We propose a quantum algorithm for studying these collisions by looking at a class of observables requiring dramatically smaller volumes: transport coefficients. These form nonperturbative inputs into theoretical models of heavy ions; thus, their calculation reduces theoretical uncertainties without the need for a full-scale simulation of the collision. We derive the necessary lattice operators in the Hamiltonian formulation and describe how to obtain them on quantum computers. Additionally, we discuss ways to efficiently prepare the relevant thermal state of a gauge theory.

关键词： Lattice QCD quantum algorithms Relativistic heavy-ion collisions

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Benchmarking adaptative variational quantum algorithms on QUBO instances

Benchmarking adaptative variational quantum algorithms on QU...

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2023 International Workshop on AI for quantum and quantum for AI, AIQxQIA 2023

作者： Turati, Gloria Dacrema, Maurizio Ferrari Cremonesi, Paolo Politecnico di Milano Italy

Adaptative Variational quantum algorithms (adapt-VQAs) are innovative algorithms that can dynamically adjust their circuit by adding and removing gates. While various adaptative methods have been proposed, a comprehensive comparison among them is still missing in the literature. This paper aims to fill this gap by benchmarking three adaptative algorithms against the fixed-structure QAOA. Our findings reveal that the adaptative methods generate circuits leading to solutions with approximation ratios comparable with QAOA, but use fewer gates. This leads to a decrease in computational time and an increased resilience to noise. © 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

关键词： Adaptative VQAs Benchmark NISQ quantum algorithms QUBO

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Simulating Strongly Coupled Many-Body Systems With quantum algorithms

Simulating Strongly Coupled Many-Body Systems With Quantum A...

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作者： Hlatshwayo, Manqoba Q. Western Michigan University

学位级别：Ph.D., Doctor of Philosophy

The complexity of the nuclear many-body problem is a severe obstacle to finding a general and accurate numerical approach needed to simulate medium-mass and heavy nuclei. Even with the advent of exascale classical computing, the impediment of exponential growth of the Hilbert space renders the problem intractable for most classical calculations. In the last few years, quantum algorithms have become an attractive alternative for practitioners because quantum computers are more efficient in simulating quantum physics than classical computers. While a fully fault-tolerant universal quantum computer will not be realized soon, this dissertation explores quantum algorithms for simulating nuclear physics suitable for noisy intermediate-scale quantum (NISQ) devices. To achieve high simulation accuracy on the currently available NISQ hardware, one must design noise-resilient algorithms and utilize techniques that suppress noise errors while maximizing quantum gate fidelity. This work satisfies this desideratum by employing variational quantum algorithms, error-mitigation techniques, and numerically engineered high-fidelity custom gates. First, an efficient encoding scheme for the Lipkin model is proposed, and the quantum equation of motion algorithm is shown to have a special quantum benefit for simulating strongly coupled many-body systems. Second, microwave pulses to perform custom two-qubit gates on a superconducting quantum computer are engineered. This results in significantly higher gate fidelity and lower execution duration than the default quantum hardware gates. Lastly, simulations are done for model nuclear Hamiltonians, and the results from using IBM superconducting quantum computers are in close agreement with classical calculations. Therefore, this study contributes toward transformative nuclear physics simulations on near-term quantum computers.

关键词： Nuclear theory quantum algorithms quantum equation of motion Optimal control Classical computers

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quantum algorithms for Schrieffer-Wolff transformation

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Physical Review Research 2022年第4期4卷 043023-043023页

作者： Zongkang Zhang Yongdan Yang Xiaosi Xu Ying Li Graduate School of China Academy of Engineering Physics Beijing 100193 China

The Schrieffer-Wolff transformation aims to solve degenerate perturbation problems and give an effective Hamiltonian that describes the low-energy dynamics of the exact Hamiltonian in the low-energy subspace of an unperturbed Hamiltonian. This unitary transformation decoupling the low-energy and high-energy subspaces for the transformed Hamiltonian can be realized by quantum circuits. We give a fully quantum algorithm for realizing the SW transformation. We also propose a hybrid quantum-classical algorithm for finding the effective Hamiltonian on NISQ hardware, where a general cost function is used to indicate the decoupling degree. Numerical simulations without or with noise and experiments on quantum computer ibmq_manila are implemented for a Heisenberg chain model. Our results verify the algorithm and show its validity on near-term quantum computers.

关键词： quantum algorithms quantum computation

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A Taxonomy of quantum algorithms: The core ideas of existing quantum algorithms and their impli-cations on cryptography

A Taxonomy of Quantum Algorithms: The core ideas of existing...

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作者： ANDERS STIGSSON UNIVERSITY OF GOTHENBURG CHALMERS UNIVERSITY OF TECHNOLOGY

学位级别：硕士

With quantum computers coming up as one of the fastest growing areas in multiple research areas, such as computer science and physics, a taxonomy of the existing quantum algorithms is necessary. However, before this thesis, no taxonomy which in- cluded many of the existing quantum algorithms could be found. We have filled that gap with this thesis. The result is a taxonomy with 31 algorithms. Each algorithm are classified into different groups depending on the characteristics and the core idea that the algorithm uses. We have focused on three different core ideas distributed as 33% using the quantum Fourier Transform, 27% uses Amplitude Amplification and 15% uses quantum Walks with the remaining 25% being classified as "Other". On top of this, we also discuss the security implications on the cryptographic schemes used today, once quantum computers become reality. A taxonomy about an area that expands as fast as quantum computing is never finished, but we believe that this thesis provides a good base for future work in the area. This thesis can also be used as an introduction to quantum computing for students with a base knowledge about computer science and mathematics.

关键词： quantum computers quantum algorithms computer science cryptography

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quantum algorithms for quantum dynamics: A performance study on the spin-boson model

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Physical Review Research 2021年第4期3卷 043212-043212页

作者： Alexander Miessen Pauline J. Ollitrault Ivano Tavernelli IBM Quantum IBM Research – Zürich 8803 Rüschlikon Switzerland Institute for Theoretical Physics ETH Zürich 8093 Zürich Switzerland

quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial limitations of available noisy and near-term quantum hardware. On the other hand, variational quantum algorithms (VQAs) have become an indispensable alternative, enabling small-scale simulations on present-day hardware. However, despite the recent development of VQAs for quantum dynamics, a detailed assessment of their efficiency and scalability is yet to be presented. To fill this gap, we applied a VQA based on McLachlan's principle to simulate the dynamics of a spin-boson model subject to varying levels of realistic hardware noise as well as in different physical regimes, and discuss the algorithm's accuracy and scaling behavior as a function of system size. We observe a good performance of the variational approach used in combination with a general, physically motivated wave function ansatz, and compare it to the conventional first-order Trotter evolution. Finally, based on this, we make scaling predictions for the simulation of a classically intractable system. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage for the solution of time-dependent problems.

关键词： quantum algorithms quantum simulation

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A Comparison of quantum algorithms for the Maximum Clique Problem

A Comparison of Quantum Algorithms for the Maximum Clique Pr...

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作者： Haverly, Andrew R. Rochester Institute of Technology

学位级别：M.S., Master of Science/Master of Surgery

Two of the most promising computational models for quantum computing are the qubit-based model and the continuous variable model, which result in two different computational approaches, namely the qubit gate model and boson sampling. The qubit gate model is a universal form of quantum computation that relies heavily on the principles of superposition and entanglement to solve problems using qubits based on technologies ranging from magnetic fields created from superconducting materials to the spins of valence electrons in atoms. Boson sampling is a non-universal form of quantum computation that uses bosons as continuous-variable values for its computation. Both models show promising prospects for useful quantum advantages over classical computers, but these models are fundamentally different, not only on their technologies but on their applications. Each model excels in different sets of applications. A direct comparison for solving a problem using qubit gate models and boson sampling allows one to better understand not only the individual technologies, but how to decide which model is better suited to solving a given problem and how to start development on solving the given problem. This thesis uses the maximum clique problem to examine the application development process in the qubit gate model and boson sampling as well as a comparison of other known algorithms to the maximum clique problem. The maximum clique problem is an NP-Hard problem concerned with finding the largest fully-connected subgraph. The qubit gate model algorithm to the maximum clique problem is a novel algorithm.

关键词： quantum algorithms Maximum clique problem

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The NISQ Analyzer: Automating the Selection of quantum Computers for quantum algorithms 14th

The NISQ Analyzer: Automating the Selection of Quantum Compu...

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14th Symposium and Summer School on Service Oriented Computing

作者： Salm, Marie Barzen, Johanna Breitenbuecher, Uwe Leymann, Frank Weder, Benjamin Wild, Karoline Univ Stuttgart Inst Architecture Applicat Syst Univ Str 38 Stuttgart Germany

ISBN: (纸本)9783030648459;9783030648466

quantum computing can enable a variety of breakthroughs in research and industry in the future. Although some quantum algorithms already exist that show a theoretical speedup compared to the best known classical algorithms, the implementation and execution of these algorithms come with several challenges. The input data determines, for example, the required number of qubits and gates of a quantum algorithm. A quantum algorithm implementation also depends on the used Software Development Kit which restricts the set of usable quantum computers. Because of the limited capabilities of current quantum computers, choosing an appropriate one to execute a certain implementation for a given input is a difficult challenge that requires immense mathematical knowledge about the implemented quantum algorithm as well as technical knowledge about the used Software Development Kits. In this paper, we present a concept for the automated analysis and selection of implementations of quantum algorithms and appropriate quantum computers that can execute a selected implementation with a certain input data. The practical feasibility of the concept is demonstrated by the prototypical implementation of a tool that we call NISQ Analyzer.

关键词： quantum computing quantum algorithms Hardware selection Implementation selection Decision support NISQ analyzer

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Frameworks for quantum algorithms

Frameworks for Quantum Algorithms

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作者： Jeffery, Stacey University of Waterloo

学位级别：master

Due to the difficulty of constructing new quantum algorithms, frameworks that facilitate this construction are of great importance in quantum computing. These frameworks reduce the problem of coming up with a quantum algorithm to that of constructing some combinatorial object that is often much simpler to reason about. The implementation and analysis of an algorithm for the specified problem follow from the properties of this object. A number of such frameworks have been extremely successful in leading to the development of numerous quantum algorithms for a variety of problems. In this thesis, we build on two of these frameworks, the quantum walk search framework, and the span program framework, extending their algorithmic potential. The quantum walk search framework gives a generic quantum analogue to a specific type of classical algorithm based on random walks. If one can construct a classical algorithm of this form, a corresponding quantum algorithm with better complexity immediately follows. In this framework, a generic algorithm is constructed from several subroutines for which implementations must be given for each application. One of these subroutines, a checking subroutine, is run many times throughout the algorithm. This subroutine may be implemented by any quantum algorithm that satisfies the required functionality, including another quantum walk algorithm. By making a slight modification to the quantum walk framework, we can show how to nest a quantum walk algorithm in the checking subroutine of another quantum walk algorithm in a way that gives better complexity than the naive nesting. This modification allows us to reproduce a number of upper bounds previously obtained in another framework, the learning graph framework, including upper bounds for triangle finding, and more generally, subgraph finding for constant-sized subgraphs. Porting these upper bounds over to the setting of quantum walks is desirable because the algorithms achieved in the quantum w

关键词： quantum algorithms quantum walks

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Implementations of quantum algorithms for Solving Linear Systems

Implementations of Quantum Algorithms for Solving Linear Sys...

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作者： Sigurđsson, Sigurdsson Delft University of Technology

学位级别：硕士

In this thesis, I make a comparison of two quantum algorithms for solving systems of linear equations. The two approaches are tested using both simulations of quantum processes and simulations of noisy intermediary-scale quantum computers, i.e., NISQ. Both methods are tested on the same problems to compare sensitivity and runtime efficiency, varying the tests along with different levels of condition numbers, sparsity and regularity. The first of the two methods compared is the method introduced by Harrow, Hassim, and Lloyd referred to as the HHL method, after the author's initials. The second method is by a research team at Los Alamos National Laboratory called the variational quantum linear solver, or VQLS for short. The first method, HHL, was the original discovery of solving linear systems using quantum computing methods and so has served as the backdrop and benchmark for other algorithms doing the same thing. The HHL method showed that an advantage can be had when using quantum computing to solve linear systems, in fact they show that this quantum method can have exponential speed up over the commonly used classical method.

关键词： quantum algorithms Linear Solvers HHL VQLS

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