A team of researchers from the University of Iowa and Syracuse University have conducted a study into the use of quantum computers in simulating field theories. The study focused on Trotter evolution in the Gross-Neveu and hyperbolic Ising models in two spacetime dimensions. The team identified various sources of errors in quantum processing units and discussed the challenges in scaling up the size of the computation. They also presented benchmark results obtained on a variety of platforms and employed a range of error mitigation techniques to address coherent and incoherent noise.
Quantum Computing and Field Theories
A study conducted by Muhammad Asaduzzaman, Simon Catterall, Yannick Meurice, and Goksu Can Toga from the University of Iowa and Syracuse University investigates the use of quantum computers in simulating field theories. The researchers focused on Trotter evolution in the Gross-Neveu and hyperbolic Ising models in two spacetime dimensions. They identified various sources of errors in quantum processing units and discussed the challenges in scaling up the size of the computation.
Quantum Computing Platforms and Error Mitigation Techniques
The team presented benchmark results obtained on a variety of platforms and employed a range of error mitigation techniques to address coherent and incoherent noise. They compared these mitigated outcomes with exact diagonalization results and density matrix renormalization group calculations to assess the effectiveness of their approaches. They also demonstrated the implementation of an out-of-time-ordered correlator (OTOC) protocol using IBM’s quantum computers.
Quantum Information Science Technologies
The researchers noted the impressive advances in quantum information science (QIS) technologies over the last decade. These advancements have sparked interest among high-energy physicists to explore different physics problems where a quantum advantage might be realized. The focus is on identifying problems that may benefit from the use of quantum computers, developing efficient quantum algorithms to gain quantum advantage, and characterizing present-day quantum devices to identify technological limitations.
Quantum Field Theory Models
The study discussed two different models that have importance in the field of high-energy physics. The first is the Gross-Neveu model, a multi-flavor interacting fermionic model. The researchers discussed the qubitization of the model and demonstrated the real-time evolution of the system with quantum computers. The second model discussed is the Ising model on hyperbolic space. The researchers computed the out-of-time ordered correlators (OTOC), which measure information spreading in a quantum system.
Steps to Analyze a Quantum Field Theory Model
The researchers outlined the steps to compute the real-time evolution of the expectation values of a quantum field theory (QFT) model with quantum devices. These steps include deriving a lattice description of the continuum Hamiltonian, converting the fields into qubit operators, preparing the vacuum and the initial state, developing a time evolution circuit, and adding a measurement circuit after the time-evolution circuit.
Error Mitigation Techniques
The study emphasized the importance of applying different error mitigation techniques to improve the scope of quantum simulation with current NISQ-era devices. These techniques include readout error correction, incoherent noise mitigation, and coherent noise mitigation. The researchers noted that the implementation of these techniques may introduce classical and quantum overheads.
Gross-Neveu Model
The Gross-Neveu model, a field theory of interacting Dirac fermions in 1+1 dimensions, was used in the study to demonstrate the steps to compute real-time evolution. The researchers wrote down the lattice Hamiltonian for spatial sites and flavors of fermion in terms of reduced staggered fields. They then converted the fermionic fields to bosonic Pauli operators for investigation with quantum computers.
An article titled “Simulating Field Theories with Quantum Computers” was published on January 3, 2024. The authors of this paper are Muhammad Asaduzzaman, Simon Catterall, Yannick Meurice, and Goksu Can Toga. The paper was published on arXiv, a repository of electronic preprints approved for publication after moderation, hosted by Cornell University. The paper can be accessed through its DOI reference: https://doi.org/10.48550/arxiv.2401.01962.
