Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes
arXiv:2405.19293 · doi:10.22331/q-2026-01-16-1968
Abstract
We show in this paper that a strong and easy connection exists between quantum error correction and Lattice Gauge Theories (LGT) by using the Gauge symmetry to construct an efficient error-correcting code for Abelian LGTs. We identify the logical operations on this gauge covariant code and show that the corresponding Hamiltonian can be expressed in terms of these logical operations while preserving the locality of the interactions. Furthermore, we demonstrate that these substitutions actually give a new way of writing the LGT as an equivalent hardcore boson model. Finally we demonstrate a method to perform fault-tolerant time evolution of the Hamiltonian within the gauge covariant code using both product formulas and qubitization approaches. This opens up the possibility of inexpensive end to end dynamical simulations that save physical qubits by blurring the lines between simulation algorithms and quantum error correcting codes.
References in corpus (15)
- Simulating Lattice Gauge Theories within Quantum Technologies
- A Theory of Trotter Error
- Quantum Simulation for High Energy Physics
- Quantum Low-Density Parity-Check Codes
- Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
- Quantum Algorithms for Simulating the Lattice Schwinger Model
- Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
- Flag fault-tolerant error correction for any stabilizer code
- Hybridized Methods for Quantum Simulation in the Interaction Picture
- Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries
- Quantum phases of two-dimensional gauge theory coupled to single-component fermion matter
- Hierarchical Qubit Maps and Hierarchical Quantum Error Correction
- Error-correcting codes for fermionic quantum simulation
- Dynamical gauge fields with bosonic codes
- Robustness of Gauge Digitization to Quantum Noise