Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge (2207.01731v3)

Abstract: Tools necessary for quantum simulations of $1+1$ dimensional quantum chromodynamics are developed. When formulated in axial gauge and with two flavors of quarks, this system requires 12 qubits per spatial site with the gauge fields included via non-local interactions. Classical computations and D-Wave's quantum annealer Advantage are used to determine the hadronic spectrum, enabling a decomposition of the masses and a study of quark entanglement. Color edge states confined within a screening length of the end of the lattice are found. IBM's 7-qubit quantum computers, ibmq_jakarta and ibm_perth, are used to compute dynamics from the trivial vacuum in one-flavor QCD with one spatial site. More generally, the Hamiltonian and quantum circuits for time evolution of $1+1$ dimensional $SU(N_c)$ gauge theory with $N_f$ flavors of quarks are developed, and the resource requirements for large-scale quantum simulations are estimated.

• The paper introduces an axial gauge framework that maps one-dimensional QCD dynamics onto qubit registers using Jordan-Wigner transformations.
• It employs exact diagonalization and quantum annealing to compute spectra and reveal mass decompositions along with color edge-states.
• The study evaluates quantum circuit resource demands and highlights co-design prospects to mitigate challenges from non-local chromo-electric interactions.

An Overview of Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions

The paper "Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge" describes the development of tools necessary for simulating one-dimensional quantum chromodynamics (QCD) with quantum computers. The authors focus on employing the axial gauge formulation for the simulations, exploring systems with two flavors of quarks in a confining $SU(3)$ gauge theory. Their approach showcases the importance of mapping complex theoretical constructs onto operational quantum devices through careful consideration of quantum resource requirements.

Quantum Simulation Framework

The authors begin by removing gauge fields using axial gauge constraints via Gauss’s law, resulting in non-local interactions for color charges. Notably, each spatial site in the formulated system is associated with twelve qubits, providing an encoding for both flavor and color of quark states. They employ the Jordan-Wigner transformation to map fermionic quark and antiquark operators to qubits, revealing a Hamiltonian split into several components: kinetic terms, mass terms, chromo-electric energy, and chemical potentials for baryon number and isospin.

To simulate the dynamics of the QCD system, the authors introduce quantum circuits for Trotterized time evolution on qubit registers. These circuits are designed to implement the different contributions in the Hamiltonian efficiently, although the implementation is a non-trivial task given the non-local nature of interactions induced by the axial gauge formulation.

Exact and Hybrid Computational Results

The exploration employs various computational strategies to extract physical insights from the theoretical framework. Using exact diagonalization techniques, the authors compute the low-lying spectra of systems with small lattice sizes, revealing the mass decomposition of hadrons and suggesting the presence of color edge-states arising from the boundary conditions. Additionally, entanglement measures reveal the quark-antiquark entanglement as a parameter-dependent feature influencing state characteristics, providing potential insights into real-time dynamics often suppressed in classical methodologies.

Furthermore, they leverage D-Wave’s quantum annealers to determine ground and excited states, underscoring the device’s precision through iterative zooming methods for energy convergence. IBM’s quantum computers were used to verify implementations through experimental device runs, exploiting various error-mitigation strategies, including post-selection and dynamic decoupling, while highlighting the practical challenges within current quantum computational capabilities.

Resource Implications and Potential Co-design

The authors carefully delineate the quantum resource requirements, evaluating the depth of circuits in terms of CNOT gates necessary for Hamiltonian implementations, highlighting the scaling challenges posed by the contribution of non-local chromo-electric interactions. The resource calculations for one-dimensional QCD prompt discussions around potential co-design efforts, such as designing native many-body gates to alleviate computational costs induced by Trotter errors during digital simulation.

Implications and Future Directions

The paper provides a structured pathway toward understanding and simulating QCD using near-term quantum devices as part of broader moves towards computationally accessible quantum simulation. Understanding the one-dimensional QCD systems serves as a crucial stepping stone toward simulating higher-dimensional QCD, particularly within real-time out-of-equilibrium dynamics where exotic nuclear interactions and formation processes could be probed with unprecedented detail in future quantum experiments. Simulations of dense matter, multi-hadronic interactions, and nuclear medium modifications are anticipated outcomes that embody the union of theoretical rigor and experimental advancement as put forward in the paper's framework.

Despite the discursive challenges involved in a quantum framing of QCD dynamics, this work lays a valuable foundation for both theoretical exploration and experimental validation, enhancing the potential scalability of simulations in quantum regimes beyond traditional classical means. The implications are transformative for both quantum science and nuclear physics, hinting at the emergence of capabilities necessary to decode fine structures of nature's fundamental interactions.