Abstract One of the ultimate missions of lattice quantum chromodynamics (QCD) is to simulate atomic nuclei from the first principles of the strong interaction. This is an extremely hard task for current computational technology, but might be reachable in the coming quantum computing era. In this paper, we discuss the computational complexities of classical and quantum simulations of lattice QCD. It is shown that the quantum simulation scales better as a function of nucleon number and thus will outperform classical simulation for large nuclei.
Abstract One of the ultimate missions of lattice quantum chromodynamics (QCD) is to simulate atomic nuclei from the first principles of the strong interaction. This is an extremely hard task for current computational technology, but might be reachable in the coming quantum computing era. In this paper, we discuss the computational complexities of classical and quantum simulations of lattice QCD. It is shown that the quantum simulation scales better as a function of nucleon number and thus will outperform classical simulation for large nuclei.
High-energy nuclear physics aims to explore and understand the physics of matter composed of quarks and gluons. However, it is intrinsically difficult to simulate high-energy nuclear physics from the first principle based quantum chromodynamics by using classical computers. In recent years, quantum computing has received intensive attention because it is expected to provide an ultimate solution for simulating high-energy nuclear physics. In this paper, we firstly review recent advances in quantum simulation of high-energy nuclear physics. Then we introduce some standard quantum algorithms, such as state preparation and measurements of light-cone correlation function. Finally, we demonstrate the advantage of quantum computing for solving the real-time evolution and the sign problems by studying hadronic scattering amplitude and phase structure of finite-temperature and finite-density matter, respectively.
Abstract Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract
Abstract: Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract:
Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach -applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.
Abstract A hallmark of the computational campaign in nuclear and particle physics is the lattice-gauge-theory program. It continues to enable theoretical predictions for a range of phenomena in nature from the underlying Standard Model. The emergence of a new computational paradigm based on quantum computing, therefore, can introduce further advances in this program. In particular, it is believed that quantum computing will make possible first-principles studies of matter at extreme densities, and in and out of equilibrium, hence improving our theoretical description of the early universe, astrophysical environments, and high-energy particle collisions. Developing and advancing a quantum-computing-based lattice-gauge-theory program, therefore, have turned into a vibrant and fast-moving area of research in theoretical nuclear and particle physics. These lecture notes introduce the topic of quantum computing lattice gauge theories in a pedagogical manner, with an emphasis on theoretical and algorithmic aspects of the program, and on the most common approaches and practices, to keep the presentation focused and useful. The Hamiltonian formulation of lattice gauge theories is introduced within the Kogut–Susskind framework, the notion of Hilbert space and physical states is discussed, and some elementary numerical methods for performing Hamiltonian simulations are discussed. Quantum-simulation preliminaries and digital quantum-computing basics are presented, which set the stage for concrete examples of gauge-theory quantum-circuit design and resource analysis. A step-by-step analysis is provided for a simpler Abelian gauge theory, and an overview of our current understanding of the cost of quantum computing quantum chromodynamics is presented in the end. Examples and exercises supplement the material, and reinforce the concepts and methods introduced throughout.
One goal in understanding quantum chromodynamics (QCD) includes solving how quarks and gluons combine to form the hadrons and nuclei seen in nature. With lattice QCD, progress has been made regarding the calculation of masses and couplings. However, the real-time evolution and the critical behavior at finite density of strong particles in colliders, stars, or after the big bang remain a challenging problem despite their potential to detect the existence of new physics. The tensor methods for lattice field theories provide a route to handle strongly correlated systems across different subfields using renormalization group methods or quantum computing.