Synthesizing efficient circuits for Hamiltonian simulation

Abstract We provide an approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford non-Clifford operations can reduce the number of operations. The total gates, especially CNOT, many cases. show it is possible implement exponentiated sum commuting Paulis with at most m (controlled)-rotation where distinct non-zero eigenvalues (ignoring sign). Thus we collect mutually Hamiltonian terms into groups satisfying one several symmetries identified this work. This allows inexpensive entire group terms. further cost some cases be reduced by partially allocating a polynomial time classical algorithm greedily allocate appropriate groupings.