Relaxational Quantum Eigensolver: Optimization and Tuning

In the last several years the Variational Quantum Eigensolver (VQE) has garnered significant interest due to its ability to efficiently prepare approximate ground states of quantum problems. However, current implementations of VQE must race against proliferating gate error, which limits its usefulness for problems requiring high circuit depths. Our work draws on ideas from bath engineering, open quantum systems, and variational algorithms to develop an algorithm exhibiting continuous, approximate error correction, which we call the Relaxational Quantum Eigensolver (RQE). In RQE we instantiate a second register of auxiliary "shadow" qubits and weakly couple them to the primary system in Trotterized evolution, allowing us to engineer an approximate zero-temperature bath by periodically resetting them during the algorithm's runtime. Balancing the infinite temperature bath of random gate error, RQE returns distributions with an average energy equal to a constant fraction of the ground state, even at infinite circuit depth. Using extensive simulations, we have demonstrated that RQE is able to successfully find approximate near-ground steady states in the face of proliferating error, for circuits with over 450 layers and 24 total qubits. This talk focuses on optimizing and fine tuning the algorithm's parameters in order to improve overall performance and reduce the impact of error on the ground state approximation.