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

The resource requirements for quantum simulations of 1+1 dimensional quantum chromodynamics are estimated. When formulated in axial gauge and with two flavors of quarks, this system requires 12 qubits per spatial site once Gauss’s law has been enforced to uniquely constrain the gauge fields. 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. We identify color “edge” states, resulting from open boundary conditions, that are confined within a screening length to the end of the lattice. Quantum circuits for the time evolution of SU(Nc) gauge theory with Nf flavors of quarks are developed and used to determine the resources required for large-scale quantum simulations. IBM’s 7-qubit quantum computers ibmq_jakarta and ibm_perth were used to compute the trivial vacuum-to-vacuum and trivial vacuum-to-qr qr bar probabilities in Nf=1 QCD with one spatial site from one Trotter step of the time-evolution operator.