Unitary Dilation Strategy Towards Efficient and Exact Simulation of Non-Unitary Evolutions

The ability to accurately predict the dynamics of open quantum systems is key for understanding realistic processes, and quantum devices have the potential to allow for new methods of simulation. However, the cost of implementing non-unitary operators presents a substantial challenge in the number of qubits required in the dilation or in the number of required measurements. Here, we propose a general approach for simulating non-unitary dynamics using an analytical unitary decomposition of quantum operators, building on prior work based on an exact numerical unitary dilation strategy. Our approach provides an exact decomposition, requires minimal dilation, and has low measurement overhead, allowing us to simulate non-unitary dynamics with substantially less quantum resources. Our approach is promising for scalable simulations, and we highlight several applications which are amenable for near-term devices.