It is for the first time that quantum simulation for high-energy physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in quantum information sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This Roadmap is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.Received 26 July 2022Revised 18 January 2023Accepted 6 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.027001Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum simulationParticles & FieldsQuantum Information 

/pdf/quantum-simulation-for-high-energy-physics-3t3v3fgb.pdf

Quantum Simulation for High-Energy Physics

Abstract Advances in isolating, controlling and entangling quantum systems are transforming what was once a curious feature of quantum mechanics into a vehicle for disruptive scientific and technological progress. Pursuing the vision articulated by Feynman, a concerted effort across many areas of research and development is introducing prototypical digital quantum devices into the computing ecosystem available to domain scientists. Through interactions with these early quantum devices, the abstract vision of exploring classically-intractable quantum systems is evolving toward becoming a tangible reality. Beyond catalyzing these technological advances, entanglement is enabling parallel progress as a diagnostic for quantum correlations and as an organizational tool, both guiding improved understanding of quantum many-body systems and quantum field theories defining and emerging from the standard model. From the perspective of three domain science theorists, this article compiles thoughts about the interface on entanglement, complexity, and quantum simulation in an effort to contextualize recent NISQ-era progress with the scientific objectives of nuclear and high-energy physics. 

/pdf/standard-model-physics-and-the-digital-quantum-revolution-1wtbuhyn.pdf

Standard model physics and the digital quantum revolution: thoughts about the interface

Non-Abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. Here we take an approach where gauge fields, discretized in spacetime, are represented by qudits and are time evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as holonomic operations supported by a Rydberg blockade mechanism. We illustrate our proposal for a minimal digitization of SU(2) gauge fields, demonstrating a significant reduction in circuit depth and gate errors in comparison to a traditional qubit-based approach, which puts simulations of non-Abelian gauge theories within reach of NISQ devices. 

/pdf/hardware-efficient-quantum-simulation-of-non-abelian-gauge-1nhqmd5w.pdf

Hardware Efficient Quantum Simulation of Non-Abelian Gauge Theories with Qudits on Rydberg Platforms

Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects. Tensor network simulations of lattice gauge theories may overcome the limitations of the Monte Carlo approach, but results have been limited to 1+1 and 2+1 dimensions so far. Here, the authors report a tree-tensor-based numerical study of a 3+1d truncated U(1) lattice gauge theory with fermionic matter.

/pdf/lattice-quantum-electrodynamics-in-3-1-dimensions-at-finite-39rh0dp7uj.pdf

Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks.

In the near future, material and drug design may be aided by quantum computer assisted simulations. These have the potential to target chemical systems intractable by the most powerful classical computers. However, the resources offered by contemporary quantum computers are still limited, restricting the chemical simulations to very simple molecules. In order to rapidly scale up to more interesting molecular systems, we propose the embedding of the quantum electronic structure calculation into a classically computed environment obtained at the Hartree-Fock (HF) or Density Functional Theory (DFT) level of theory. We achieve this by constructing an effective Hamiltonian that incorporates a mean field potential describing the action of the inactive electrons on a selected Active Space (AS). The ground state of the AS Hamiltonian is determined by means of the Variational Quantum Eigensolver (VQE) algorithm. With the proposed iterative DFT embedding scheme we are able to obtain energy correction terms for a single pyridine molecule that outperform the Complete Active Space Self Consistent Field (CASSCF) results regardless of the chosen AS.

Quantum HF/DFT-Embedding Algorithms for Electronic Structure Calculations: Scaling up to Complex Molecular Systems

The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same calculation with a polynomial dependence on the number of degrees of freedom. A precise estimation is however particularly challenging for the simulation of lattice gauge theories in arbitrary dimensions, where gauge fields are dynamical variables, in addition to the particle fields. Moreover, there exist several choices for discretizing particles and gauge fields on a lattice, each of them coming at different prices in terms of qubit register size and circuit depth. Here we provide a resource counting for real-time evolution of $U(1)$ gauge theories, such as quantum electrodynamics, on arbitrary dimension using the Wilson fermion representation for the particles, and the quantum link model approach for the gauge fields. We study the phenomena of flux-string breaking up to a genuine bidimensional model using classical simulations of the quantum circuits and discuss the advantages of our discretization choice in simulation of more challenging $SU(N)$ gauge theories such as quantum chromodynamics.

Toward scalable simulations of lattice gauge theories on quantum computers

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage -- such as physical symmetries and chemical properties -- to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures:(1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

Protein design and directed evolution have separately contributed enormously to protein engineering. Without being mutually exclusive, the former relies on computation from first principles, while the latter is a combinatorial...

On synergy between ultrahigh throughput screening and machine learning in biocatalyst engineering

Pre-trained models have been successful in many protein engineering tasks. Most notably, sequence-based models have achieved state-of-the-art performance on protein fitness prediction while structure-based models have been used experimentally to develop proteins with enhanced functions. However, there is a research gap in comparing structure- and sequence-based methods for predicting protein variants that are better than the wildtype protein. This paper aims to address this gap by conducting a comparative study between the abilities of equivariant graph neural networks (EGNNs) and sequence-based approaches to identify promising amino-acid mutations. The results show that our proposed structural approach achieves a competitive performance to sequence-based methods while being trained on significantly fewer molecules. Additionally, we find that combining assay labelled data with structure pre-trained models yields similar trends as with sequence pre-trained models.

Predicting protein variants with equivariant graph neural networks

We introduce a software package that allows users to design and run simulations of thought experiments in quantum theory. In particular, it covers cases where several reasoning agents are modelled as quantum systems, such as Wigner’s friend experiment. Users can customize the protocol of the experiment, the inner workings of agents (includ-ing a quantum circuit that models their reasoning process), the abstract logical system used (which may or not allow agents to combine premises and make inferences about each other’s reasoning), and the interpretation of quantum theory used by diﬀerent agents. Our open-source software is written in a quantum programming language, ProjectQ, and runs on classical or quantum hardware. As an example, we model the Frauchiger-Renner extended Wigner’s friend thought experiment, where agents are allowed to measure each other’s physical memories, and make inferences about each other’s reasoning. Truth is a matter of the imagination. The Darkness Software available at https://github.com/jangnur/Quanundrum [1].

Thought experiments in a quantum computer

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