Efficient particle-conserving symmetric quantum circuits
Babatunde M. Ayeni
The variational quantum simulation technique on gate-based quantum processors can be made more efficient if symmetries of the Hamiltonian system of interest are factored into the design construction of the underlying parameterized quantum circuits (PQC) needed by the technique. In the first part of this work, we present an easy and practical approach that can be used to construct symmetric quantum circuits. The method we present can directly be adapted for any symmetry, though in the present work we focus explicitly on the examples of Z 2 , Z 3 , and particle number conservation. We show how to construct symmetric gates that respects the aforementioned symmetries. In the second part, we focus on numerical analysis of parameterized particle-conserving gates. In variational quantum simulation, for example, the variational quantum eigensolver (VQE), the symmetric gates of the PQC are parameterized. Since there are often many possible inequivalent parametrizations, it is often not immediately obvious which gate parametrization would be most efficient in general for a wide range of Hamiltonians that respect the symmetry. We streamline our analysis to particle-conserving circuits and Hamiltonians. We numerically analyze the efficiency of different particle-conserving gate parametrizations by studying two examples, namely, a physics problem of learning the ground state of Heisenberg spin chains, and an artificial problem of learning the random arbitary states sampled within the particle number conserved subspace.
arXiv:2406.12130•Physical Review A•Feb 25, 2025•1 citation