Synthesis of Energy-Conserving Quantum Circuits with XY interaction

Understand

We study quantum circuits constructed from $\sqrt{iSWAP}$ gates and, more generally, from the entangling gates that can be realized with the XX+YY interaction alone.

• Such gates preserve the Hamming weight of states in the computational basis, which means they respect the global U(1) symmetry corresponding to rotations around the z axis.
• Equivalently, assuming that the intrinsic Hamiltonian of each qubit in the system is the Pauli Z operator, they conserve the total energy of the system.
• We develop efficient methods for synthesizing circuits realizing any desired energy-conserving unitary using XX+YY interaction with or without single-qubit rotations around the z-axis.