# Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge

**Authors:** Roland C. Farrell, Ivan A. Chernyshev, Sarah J. M. Powell, Nikita A. Zemlevskiy, Marc Illa, Martin J. Savage  
**arXiv:** [2207.01731](https://arxiv.org/abs/2207.01731)  
**Date:** 2022-07-04  
**Summary page:** https://www.summarizepaper.com/en/paper/2207.01731v1/

## Key points

- Development of tools for quantum simulations of $1+1$ dimensional QCD
- System formulated in axial gauge with two flavors of quarks
- Simulation requires 12 qubits per spatial site, including gauge fields
- Utilization of classical computations and D-Wave's quantum annealer Advantage
- Discovery of confined color edge states within a screening length
- Use of IBM's 7-qubit quantum computers for dynamics computation in one-flavor QCD
- Development of Hamiltonian and quantum circuits for time evolution in $1+1$ dimensional $SU(N_c)$ gauge theory with $N_f$ flavors of quarks
- Estimation of resource requirements for large-scale quantum simulations
- Advancement in simulating QCD in lower dimensions using classical and quantum computing technologies

## Summary

In this study, the authors focus on the development of tools necessary for quantum simulations of $1+1$ dimensional quantum chromodynamics (QCD). Specifically, they consider the system formulated in axial gauge with two flavors of quarks. The simulation of this system requires 12 qubits per spatial site, taking into account the inclusion of gauge fields through non-local interactions. To determine the hadronic spectrum and gain insights into the masses and quark entanglement, classical computations and D-Wave's quantum annealer Advantage are utilized. The researchers find color edge states that are confined within a screening length at the end of the lattice. Furthermore, IBM's 7-qubit quantum computers, namely ibmq_jakarta and ibm_perth, are employed to compute dynamics starting from the trivial vacuum in one-flavor QCD with one spatial site. This allows for an exploration of dynamics in a simplified setting. The study also extends its scope by developing Hamiltonian and quantum circuits for time evolution in $1+1$ dimensional $SU(N_c)$ gauge theory with $N_f$ flavors of quarks. Additionally, the authors estimate resource requirements for large-scale quantum simulations. Overall, this research contributes to advancing our understanding and capabilities in simulating quantum chromodynamics in lower dimensions using both classical computations and state-of-the-art quantum computing technologies.