Mitigating Errors in Analog Quantum Simulation by Hamiltonian Reshaping or Hamiltonian Rescaling

Simulating quantum many-body systems is crucial for advancing physics but poses substantial challenges for classical computers. Quantum simulations overcome these limitations, with analog simulators offering unique advantages over digital methods, such as lower systematic errors and reduced circuit depth, making them efficient for studying complex quantum phenomena. However, unlike their digital counterparts, analog quantum simulations face significant limitations due to the absence of effective error mitigation techniques. This work introduces two novel error mitigation strategies -- Hamiltonian reshaping and Hamiltonian rescaling -- in analog quantum simulation for tasks like eigen-energy evaluation. Hamiltonian reshaping uses random unitary transformations to generate new Hamiltonians with identical eigenvalues but varied eigenstates, allowing error reduction through averaging. Hamiltonian rescaling mitigates errors by comparing eigenvalue estimates from energy-scaled Hamiltonians. Numerical calculations validate both methods, demonstrating their significant practical effectiveness in enhancing the accuracy and reliability of analog quantum simulators.