## Error suppression in quantum simulation by symmetry protection: Two wrongs make a right

We propose a technique to suppress error in simulating physics on a quantum computer. Our technique works by manipulating the errors from different steps of the simulation such that they interfere destructively and thus cancel out each other.

Simulating quantum systems is an important application of quantum computers. While the dynamics of a quantum system to be simulated are continuous, their approximation on a quantum computer is often made by breaking up the simulation into small, finite time steps. Then, in each time step, a discrete series of elementary quantum gates realizes an approximate version of the evolution. This discreteness introduces undesirable errors to the simulation. In contrast to dephasing and other sources of incoherent noise, this type of 'coherent' error does not represent any measurement or other information flow from the simulator to the environment, which in principle can be removed by a variety of correction techniques. Here, we propose a technique that uses the symmetries of the target system to suppress this simulation error and thus significantly reduce the gate count of the simulation.

Specifically, we insert unitary transformations generated by the symmetries of the target system in between the discrete time steps of the simulation. While these transformations do not affect the true evolution, they induce destructive interference between the coherent errors from different steps of the simulation, resulting in a smaller total error, fewer quantum gates, and hence a faster quantum simulation.

We prove rigorous bounds on the total error of the simulation under this symmetry protection technique. By applying our technique to the simulations of several quantum systems, including spin chains and lattice quantum field theories, we demonstrate significant error reduction due to the symmetry protection, sometimes by several orders of magnitude. The technique is applicable to a wide range of quantum simulation algorithms, including the Suzuki-Trotter product formulas and more advanced algorithms based on linear combinations of unitaries.

This work has been accepted for publication on PRX Quantum.