Cheaper and noise resilient ground state preparation using quantum eigenvector continuation

Ground state preparation is one of the major topics studied in many-body physics to understand the underlying nature of the real materials. While there are many quantum algorithms designed for this purpose, the task remains challenging due to various reasons such as scaling of required resources with lattice sizes, degeneracy in ground states at proximity to phase transitions, presence of level crossings and small energy gaps. For example, adiabatic time evolution cannot be implemented in the presence of level crossings and imaginary time evolution requires larger evolution times if energy gaps are small making these methods non-practical on today's and on early fault tolerant quantum hardware. Previous work has shown that eigenvector continuation (EC) - building a subspace out of eigenstates of the Hamiltonian for different parameters- is successful in improving the situation and enables the use of these techniques with reasonable cost. However, the small spectral gaps and protected level crossings remain an issue. In this work we extend the use of EC for the systems with these conditions by varying more than one parameter and choosing the subspace vectors from across different parameters. This enables us to implement adiabatic time evolution for models with level crossings (e.g. 1D XY model) and imaginary time evolution for the 2D Kagome XXZ model with small spectral gap at reduced cost. Given the noise inherent in the NISQ era quantum computers, we also investigate the effect of noise on EC, and show that the resulting errors can be mitigated via simple thresholding techniques. Our study demonstrates the practical scalability and noise resilience of eigenvector continuation.