論文

We classify the sign-problem-free relativistic fermion actions on the basis of the Majorana representation. In the Majorana representation, the sign-problem-free condition is given by the semi-positivity of a Pfaffian. We show that the known sign-problem-free actions of the Dirac fermions, which are usually understood from the semi-positivity of a determinant, e.g., the action of quantum chromodynamics with nonzero chiral chemical potential or nonzero isospin chemical potential, can also be understood from the semi-positivity of a Pfaffian. We also derive new classes of the sign-problem-free relativistic fermion actions with Majorana-type source terms.

Simulating nonequilibirum dynamics of a quantum many-body system is one of the promising applications of quantum computing. We simulate the time evolution of one-dimensional Z2 lattice gauge theory on IBM's superconducting 156-qubit device, ibm_fez. We consider the Floquet circuit made of the Trotter decomposition of Hamiltonian evolution and focus on its dynamics toward thermalization. Quantum simulation with the help of error mitigation is successful in running the Floquet circuit made of 38 and 116 qubits up to 10 Trotter steps in the best case. This is enough to reach the early stage of prethermalization. Our work would be a benchmark for the potential power of quantum computing for high-energy physics problems.