Real-time dynamics of lattice gauge theories with a few-qubit quantum computer (1605.04570v1)

Abstract: Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories.

• The paper demonstrates a digital quantum simulation of the 1+1D Schwinger model by mapping gauge fields to spin interactions via a Jordan-Wigner transformation on a trapped-ion system.
• The paper shows that particle creation exhibits an initial growth followed by oscillations due to pair recombination, aligning with theoretical predictions across various masses and coupling strengths.
• The paper quantifies entanglement generation using logarithmic negativity, linking the dynamics of particle pair creation to vacuum decay and paving the way for simulating more complex gauge theories.

Overview of "Real-time dynamics of lattice gauge theories with a few-qubit quantum computer"

The paper presents an experimental demonstration of simulating the real-time dynamics of lattice gauge theories using a few-qubit quantum computer, specifically focusing on a trapped-ion platform. The research successfully realizes a digital quantum simulation of the 1+1-dimensional quantum electrodynamics, known as the Schwinger model, showcasing a pivotal step towards using quantum computation as a tool for studying complex high-energy physics problematic for classical computational methods.

Core Concepts and Methodology

The Schwinger model is a simplified quantum field theory that is extensively utilized as a testbed for lattice gauge theories, particularly valuable for its analogous properties to quantum chromodynamics such as confinement and chiral symmetry breaking. The paper leverages a discrete lattice formulation of gauge theories, which is inherently specified by gauge invariance and Gauss's laws — features characteristically difficult to accommodate in classical simulations due to their demand on computational resources.

The authors employ a trapped-ion quantum computer to perform the simulation. The simulation capitalizes on the Hamiltonian formulation of lattice gauge theories, where a crucial transformation is made by mapping gauge fields to long-range spin interactions using a Jordan-Wigner transformation. This strategy optimizes the few available qubits, facilitating their use to model both fermionic particles and the underlying gauge fields via spin interactions.

The experimental setup implements the digital simulation through a series of quantum gates applied to a string of $^{40}$Ca$^+$ ions held in a linear ion trap. This architecture supports universal quantum computation through high-fidelity entangling gates and local operations, allowing the researchers to encode the lattice gauge theory dynamics accurately.

Key Results and Interpretation

The primary objective of the paper is to simulate the Schwinger mechanism, which describes the spontaneous creation of electron-positron pairs from the vacuum due to quantum fluctuations. In this simulation, three pivotal observables are investigated:

1. Particle Creation: The research tracks the number density of particles over time, observing an initial growth phase followed by oscillations due to pair recombinations. Different masses and coupling strengths demonstrate varying dynamics, congruent with theoretical predictions.
2. Vacuum Decay: The evolution of the vacuum persistence amplitude, a central quantity describing vacuum decay in quantum field theories, corresponds well to theoretical expectations and offers insight into its behavior even under few-qubit conditions.
3. Entanglement Generation: The paper measures entanglement via the logarithmic negativity between different halves of the ion chain, reflecting the generation and spatial propagation of entangled pairs as a function of time. This relationship between particle pair creation and entanglement is novel and deepens understanding of dynamical processes in gauge theories.

Implications and Future Directions

The paper's demonstration of using a digital quantum simulation to explore lattice gauge theories marks a progression in quantum simulation's applicability to high-energy theoretical physics problems. The results suggest promising avenues for simulating more complex and non-Abelian gauge theories, perhaps in higher dimensions or with more particles, as the scaling challenges of quantum hardware are addressed.

This integration of quantum computing in simulating real-time dynamics signifies advancements that could circumvent limitations faced by classical approaches like Quantum Monte Carlo methods, which are restricted to equilibrium conditions. Thus, the work sets a foundation for broader investigations into real-time dynamics of field theories underlying fundamental physical interactions, holding potential to tackle problems intractable to current classical strategies.

In conclusion, this research represents a fundamental step towards exploiting quantum simulations in exploring intricate physical systems, potentially unveiling new insights and understanding of such systems as the capabilities and scale of quantum computers expand.