Dynamical quantum phase transitions in a noisy lattice gauge theory

Dynamical Quantum Phase Transitions of the Schwinger Model: Real-Time Dynamics on IBM Quantum

“…The latter determines the gauge connection , characterized by the generalized canonical commutation relation . The lattice model Hamiltonian for a finite lattice with N sites reads [ 4 , 31 , 32 , 33 , 49 ] where periodic boundary conditions [ 50 , 51 ] require the identification . The model involves staggered (Kogut–Susskind) fermions [ 61 ], described by single-component spinors , with negative-mass components encoded in odd- x sites.…”

“…The physical subspace is spanned by states satisfying the Gauss law constraint at all sites x , where, for a gauge group, The electric field was simulated in the following through a discretization of U [ 31 , 32 , 33 , 49 , 52 , 53 ] with . Unlike in the quantum link models [ 50 , 51 ], where the electric field is replaced by a spin operator, the model is based on replacing gauge connections with permutation matrices [ 49 ]. In the case of , the electric field in each link can have two eigenstates, which will be labeled as , with while the gauge connections act as [ 31 , 32 , 33 ] An immediate implication of the model is the irrelevance in the Hamiltonian ( 1 ) of the electric field energy, which becomes a constant.…”

“…We aimed at studying the non-equilibrium dynamics of the described lattice Schwinger model following a quantum quench [ 50 , 51 , 57 ]. Generally, in this protocol, one considers a family of Hamiltonians that depends on a tunable parameter and prepares an initial state coinciding with the ground state of .…”

“…This paper aimed at testing the superconducting qubit systems available in the IBM Quantum platform [ 1 ] in a simple lattice gauge theory application. We implemented digital evolutions generated by the QED Hamiltonian in dimensions, consisting of non-commuting local contributions [ 4 , 31 , 32 , 33 , 37 , 41 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 ] and displaying the occurrence of dynamical quantum phase transitions (DQPTs) [ 57 , 58 , 59 ] in specific cases of quantum quenches. A discretization of the electromagnetic field is required to implement gauge degrees of freedom in the quantum simulator: accomplishing such a task by replacing the continuous gauge group with one of the cyclic groups guarantees a unitary implementation of the gauge connections [ 49 ]; another possible choice is represented by the family of quantum link models [ 60 ].…”

“…The ground state preparation required by the chosen quench protocol was specifically designed in order to minimize errors and characterize the first stage’s output statistics. Then, we characterized the effectiveness of time evolution, choosing to analyze the system in proximity of a DQPT, where the dynamics is particularly sensitive to noise [ 51 ], thus framing the simulation in most unsafe conditions. A concluding estimation of the amount of error probability reduction required for a partial observation of the targeted DQPT was made by analyzing the statistics of the collected results.…”