Quantum Computing Explores Schwinger Model’s Phase Transition with Quantum Computer

A team of researchers from DESY Humboldt University, the Cyprus Institute, Deutsches Elektronen-Synchrotron (DESY), and IBM are using a quantum computer to explore the first-order phase transition in the lattice Schwinger model, a quantum field theory. The team is using the variational quantum eigensolver (VQE) algorithm to investigate two different fermion discretizations, Wilson and staggered fermions. They are also applying error-mitigation methods to obtain reliable data from the quantum hardware. The research aims to understand the fundamental laws of physics in various disciplines, including condensed matter and particle physics, and could offer a promising alternative to conventional numerical methods.

What is the First-Order Phase Transition of the Schwinger Model with a Quantum Computer?

The Schwinger model, a quantum field theory, is being explored using a quantum computer. The research team, including Takis Angelides from DESY Humboldt University, Pranay Naredi from the Cyprus Institute, Arianna Crippa from DESY Humboldt University, Karl Jansen and Stefan Kühn from Deutsches Elektronen-Synchrotron (DESY), Ivano Tavernelli from IBM Research Zurich, and Derek Wang from IBM, is investigating the first-order phase transition in the lattice Schwinger model. This model is in the presence of a topological θ-term, a mathematical function that plays a significant role in quantum field theory.

The team is using the variational quantum eigensolver (VQE), a quantum algorithm, to explore two different fermion discretizations, Wilson and staggered fermions. They are developing parametric ansatz circuits suitable for both discretizations and comparing their performance by simulating classically an ideal VQE optimization in the absence of noise. The states obtained by the classical simulation are then prepared on IBM’s superconducting quantum hardware.

How is Quantum Computing Applied in this Research?

The researchers are applying state-of-the-art error-mitigation methods to show that the electric field density and particle number observables, which reveal the phase structure of the model, can be reliably obtained from the quantum hardware. They are investigating the minimum system sizes required for a continuum extrapolation by studying the continuum limit using matrix product states and comparing their results to continuum mass perturbation theory.

The team demonstrates that taking the additive mass renormalization into account is vital for enhancing the precision that can be obtained with smaller system sizes. For the observables they investigate, they observe universality and both fermion discretizations produce the same continuum limit.

Why is the Phase Diagram of a Theory Important?

Exploring the phase diagram of a theory is central for understanding the fundamental laws of physics in many disciplines, ranging from condensed matter to particle physics. For instance, in the case of ferromagnetic materials, critical points and phase boundaries help to understand and design magnetic materials with various applications. Within superconductivity, phase diagrams allow for identifying the critical temperatures and magnetic fields required for materials to exhibit zero electrical resistance.

In particle physics, the phase diagram of Quantum Chromodynamics (QCD) elucidates the behavior of matter under extreme conditions relevant for the early universe and neutron stars. In high-energy physics, topological terms play an important role in the study of interesting phenomena such as the breaking of charge conjugation-parity symmetry in QCD and the occurrence of out-of-equilibrium dynamical effects involving axion fields.

What are the Challenges and Solutions in Exploring the Phase Structure of a Theory?

To explore the phase structure of a given theory, one often has to resort to numerical methods. A standard tool is Monte Carlo (MC) simulation, which has been successful for probing phase diagrams. However, the sign problem poses a barrier in certain parameter regimes, leaving relevant questions unanswered. Specifically for lattice QCD, large baryon chemical potentials or the presence of a topological θ-term would trigger this problem.

Thus, variations of the conventional MC approach have been proposed to tackle this obstacle, but so far only with limited success. Hence, there is great interest in alternative methods that bypass the issue, such as tensor networks and quantum computing. In particular, quantum computing offers a promising alternative route, with already a number of successful demonstrations.

How is the Schwinger Model Used in this Research?

The research team is focusing on exploring the possibility of studying the phase structure of the Schwinger model in the presence of a topological θ-term with near-term quantum devices. Despite its simplicity, the Schwinger model in the presence of a topological θ-term provides an example where conventional Monte Carlo methods would suffer from the sign problem. Moreover, it exhibits a rich phase structure with a first-order quantum phase transition for large enough masses at θ=π.

The Schwinger model serves as a benchmark system for developing and testing new methods. Regarding a quantum computing approach to the model in the presence of a topological θ-term, there are several open questions. First, the theory needs to be discretized on a lattice with a finite extent and there are various different ways for discretizing fermions on such a lattice. It is therefore a priori not clear which one will show the best performance for a given set of resources. Second, it is important to identify how large the system sizes should be in order to obtain a reliable continuum extrapolation in order to assess the applicability of near-term quantum devices.