Suppressing nonperturbative gauge errors in the thermodynamic limit using local pseudogenerators

Abstract

With recent progress in quantum simulations of lattice-gauge theories, it is becoming a pressing question how to reliably protect the gauge symmetry that defines such models. In a recent work [J. C. Halimeh et al., arXiv:2108.02203], an experimentally feasible gauge-protection scheme has been proposed that is based on the concept of a local pseudogenerator, which is required to act identically to the full gauge-symmetry generator in the target gauge sector, but not necessarily outside of it. The scheme has been analytically and numerically shown to reliably stabilize lattice gauge theories in the presence of perturbative errors on finite-size analog quantum-simulation devices. In this work, through uniform matrix product state calculations, we demonstrate the efficacy of this scheme for nonperturbative errors in analog quantum simulators up to all accessible evolution times in the thermodynamic limit, where it is a priori neither established nor expected that this scheme will succeed. Our results indicate the presence of an emergent gauge symmetry in an adjusted gauge theory even in the thermodynamic limit, which is beyond our analytic predictions. Additionally, we show through quantum circuit model calculations that gauge protection with local pseudogenerators also successfully suppresses gauge violations on finite quantum computers that discretize time through Trotterization. Our results firm up the robustness and feasibility of the local pseudogenerator as a viable tool for enforcing gauge invariance in modern quantum simulators and NISQ devices.

Disorder-free localization with Stark gauge protection

“…The linear protection term then takes the form V ĤW = V j c j Ŵj − g tar j , and the conclusions from Ref. [74] apply the same way, with stabilization of gauge invariance having been numerically demonstrated up to all accessible times in finite systems [37] and also recently in the thermodynamic limit [83], even when c j is a noncompliant repeating sequence over two or four matter sites.…”

Quantum Simulation for High Energy Physics

“…Questions regarding the robustness of simulations to gauge-symmetry-breaking perturbations in the dynamics are starting to be explored in simpler gauge theories and quantum link models [146,147]. Furthermore, several proposals and algorithms are put forward in recent years for detecting and discarding Gauss's law violations [148,149], and for suppressing coherent gauge-symmetry-violating noise [119,[150][151][152][153][154][155][156][157][158][159][160][161][162], taking advantage of features like introduction of energy penalties, classical noise and Zeno effect, quantum control, dynamical decoupling, random rotations of the state throughout the evolution via unitaries generated by the symmetry (or pseudo symmetry) operator, and controlled operations in digital circuits. The value of these strategies and their limitations must be confirmed in realistic experiments [163] and in the context of each of the Hamiltonian formulations discussed above.…”

“…The second approach is an active protection of the symmetries as the system is evolved in the simulator. Examples include adding a penalty term to the Hamiltonian proportional to the (square of) Gauss's law operator to suppress the leakage to the unphysical Hilbert space [150][151][152][153][154], performing random rotations during evolution with the Gauss's law operator to average out the symmetry violation [155,156], adding to the Hamiltonian the Gauss's law operator with properly-chosen coefficients to separate out different Gauss's law sectors in the spectrum [157,158] or similar techniques [159,160], using classical noise proportional to the Gauss's law operator to suppress gauge-symmetry violation via a Zeno effect [161], a similar quantum approach in which quantum control is used to dynamically decouple unphysical sectors during the evolution [162], and in a more gate-based setting, using controlled operations to disallow unphysical transitions between basis states [119]. As a verification step, one could also use oracles in the quantum circuit to detect Gauss's law violations and discard the result [148,149].…”

Noise Improvements in Quantum Simulations of sQED using Qutrits

“…state and the other states. This is nearly identical to the problem in quantum simulation of gauge theories, where noise can move the simulation out of the physical Hilbert space[104][105][106][107][108]. There are ways to minimize these errors on noisy quantum computer using proceedures such…”