Circuit Optimization for Simulations of Quantum Systems

Simulating the time evolution of a quantum mechanical system is one of the most promising near-term applications of quantum computing, potentially offering an exponential advantage compared to classical simulation. However, as the desired accuracy of these calculations increases, the required quantum resources do not scale favorably. The quantum evolution circuits are represented by tensor products of Pauli matrices obtained from the second quantization form using transformation methods such as Jordan-Wigner or Bravyi-Kitaev. The required number of quantum gates scales as O(N⁴), thus leading to the accumulation of error due to the presence of physical gate errors. In addition, algorithmic errors due to Trotterization are also present. Prior work focused on reducing either of these error types in isolation. We demonstrate a new technique that simultaneously reduces (i) Trotterization errors by reordering terms in the Hamiltonian, and (ii) gate error accumulation by achieving gate cancellation. We map the problem to a graph-theoretic formulation and use the clique cover and traveling salesperson heuristics to optimize the order of the terms. Our simulations demonstrate at least 5% overall fidelity improvement.