Variational quantum thermalizers based on weakly-symmetric nonunitary multi-qubit operations

We propose incorporating multi-qubit nonunitary operations in Variational Quantum Thermalizers (VQTs). VQTs are hybrid quantum-classical algorithms that generate the thermal (Gibbs) state of a given Hamiltonian, with applications in quantum algorithms and simulations. However, current algorithms struggle at intermediate temperatures, where the target state is nonpure but exhibits entanglement. We devise multi-qubit nonunitary operations that harness weak symmetries and thereby improve the performance of the algorithm. Utilizing dissipation engineering, we create these nonunitary multi-qubit operations without the need for measurements or additional qubits. To train the ansatz, we develop and benchmark novel methods for entropy estimation of quantum states, expanding the toolbox for quantum state characterization. We demonstrate that our approach can prepare thermal states of paradigmatic spin models at all temperatures. Our work thus creates new opportunities for simulating open quantum many-body systems.