Simulating 2D lattice gauge theories on a qudit quantum computer (2310.12110v3)

Abstract: Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. Here, we present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in $d$ different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Using a variational quantum eigensolver, we find the ground state of the model and observe the interplay between virtual pair creation and quantized magnetic field effects. The qudit approach further allows us to seamlessly observe the effect of different gauge field truncations by controlling the qudit dimension. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

Simulating 2D Lattice Gauge Theories on a Qudit Quantum Computer

This paper presents a detailed exploration into the quantum simulation of two-dimensional lattice gauge theories (LGTs) using a trapped-ion qudit quantum processor. The research primarily focuses on addressing two essential challenges in LGT quantum simulations: extending computations beyond one spatial dimension that incorporate both gauge fields and matter, and refining the discretization of gauge fields beyond the minimal representation.

The authors utilize quantum electrodynamics (QED) on a 2D lattice to simulate the basic building block of the lattice—a single plaquette—using qudits. Qudits, which encode quantum information in $d$ different states per ion, contrast with the traditional use of qubits, which are limited to two states per ion. This high-dimensional representation is particularly advantageous for describing gauge fields, leading to a significant reduction in register size and circuit complexity. The trapped-ion qudit platform allows for efficient mapping of lattice gauge theories, showing superior gate count scaling and resource optimization compared to qubit-based systems.

One of the notable strengths of qudits demonstrated in this paper is their ability to naturally map high-dimensional gauge fields, which are integral to LGTs. The experiment effectively employs variational quantum eigensolvers (VQEs) to prepare the ground state of the model, demonstrating how different gauge field discretizations influence quantum simulations. Using qutrits and ququints, the researchers showed the effect of these truncations on the plaquette expectation value, which relates directly to the fundamental feature of running coupling in gauge theories.

The authors argue that refining gauge field discretization encapsulates a significant advancement for hardware-efficient quantum simulations. The difference in circuit complexity and register size between qudit and qubit-based implementations underscores the potential of qudits in simplifying high-dimensional quantum simulations. Through effective use of trapped-ion systems with high-fidelity qudit entangling gates, the paper illustrates sizeable improvements in simulation accuracy, efficiency, and scaling potential.

Theoretical and experimental evidence indicates that qudit-based platforms offer marked advantages for LGT simulations, both in terms of depth of quantum circuits and accuracy. The experimental setup allowed exploring particle physics dynamics, running coupling, and plaquette operator calculations in models with periodic boundary conditions—key insights into real-time dynamics.

This paper has significant implications for future developments in quantum computing and particle physics. The findings pave the way for extending lattice gauge theory quantum simulations to practical applications in high-density physics and real-time evolutions. By combining efficient gauge field representation with advances in scalable quantum hardware, the paper sets a precedent for addressing previously intractable problems in particle physics using quantum computers.

Future research may focus on scaling these simulations to larger and more complex systems. This avenue would involve addressing computational challenges in 3D simulations and non-Abelian gauge theories. Nevertheless, the hardware-efficient qudit approach opens up exciting possibilities in quantum simulations of equilibrium and dynamical properties in high-energy physics models—a prospect until recently deemed unattainable with classical computing methods.