The last several years have seen a massive resurgence of interest in the Hamiltonian simulation of relativistic lattice field theories from the nuclear and high energy physics community. This renewal has largely been driven by rapid advancements in quantum computing hardware and increased access to real quantum computers, not just simulators on classical machines. However, significant breakthroughs in hardware and software must occur to develop fault-tolerant quantum computers, which will most likely be necessary for simulations of physically-relevant nuclear systems. In the meantime, there are many theoretical and algorithmic roadblocks to overcome in order to implement gauge theories onto quantum computers. In this plenary, I present a broad overview of digital quantum simulation, including methods and status of current hardware architectures, followed by a description of the challenges faced when simulating lattice gauge theories on quantum computers.
The last several years have seen a massive resurgence of interest in the Hamiltonian simulation of relativistic lattice field theories from the nuclear and high energy physics community. This renewal has largely been driven by rapid advancements in quantum computing hardware and increased access to real quantum computers, not just simulators on classical machines. However, significant breakthroughs in hardware and software must occur to develop fault-tolerant quantum computers, which will most likely be necessary for simulations of physically-relevant nuclear systems. In the meantime, there are many theoretical and algorithmic roadblocks to overcome in order to implement gauge theories onto quantum computers. In this plenary, I present a broad overview of digital quantum simulation, including methods and status of current hardware architectures, followed by a description of the challenges faced when simulating lattice gauge theories on quantum computers.
Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on [Formula: see text] dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways. This article is part of the theme issue 'Quantum technologies in particle physics'.
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.
<!--HTML-->There are many fundamental questions in particle and nuclear physics that cannot be addressed via classical computing techniques. These include the equation of state for finite density nuclear matter, real-time dynamics of quantum field theories from first-principles and non-perturbative aspects of chiral gauge theories. In recent years quantum computing hardware has seen dramatic advancements, which have brought with them the possibility to apply quantum computing to these and other open problems in high energy physics. In this talk, after a brief introduction to quantum computing, I will discuss my recent work towards the quantum simulation of lower-dimensional lattice gauge theories, focusing on the interplay between Gauss’ law, gauge redundancies and (un)favourable resource scaling.
Lattice field theory, along with its algorithmic and hardware ecosystems, has been at the forefront of computational particle and nuclear physics. It continues to deliver impressive results on the hadronic spectrum, structure, decays, and reactions. Yet, this vigorous campaign has fallen short in addressing a range of problems involving dense matter and general dynamical phenomena. The reason is that such problems require an exponential scaling of computing time and space in system size. Quantum simulation, enabled by quantum-computing algorithms and hardware technology, promises a way forward by offering several polynomially efficient algorithms compared with their inefficient classical counterparts. Lattice gauge theorists have engaged in a multi-pronged program to leverage such new possibilities, and have steadily advanced the state of theory, algorithm, and hardware implementations and co-design. In this talk, I motivate the quantum-computational lattice-field-theory program; introduce the questions such a program is expected to address and the strategies it involves; report on recent progress; and end with a note on challenges and opportunities ahead.
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 early universe, astrophysical environments, and high-energy particle collisions. Developing and advancing a quantum-computing based lattice-gauge-theory program, therefore, is 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. 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 quantum-computing cost of quantum chromodynamics is presented in the end. Examples and exercises augment the material, and reinforce the concepts and methods introduced throughout.
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem. In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.