Accelerated Variational Quantum Eigensolver.

Area of Science:

• Quantum computing
• Quantum algorithms
• Computational chemistry

Background:

• Finding the ground state energy of a Hamiltonian is crucial for quantum simulations.
• Current methods like Quantum Phase Estimation (QPE) and Variational Quantum Eigensolver (VQE) have distinct resource requirements.
• QPE offers high precision but requires deep circuits, while VQE uses shallower circuits but needs more samples.

Purpose of the Study:

• To develop a generalized VQE algorithm that interpolates between QPE and standard VQE.
• To offer a tunable trade-off between circuit depth and sample complexity for ground state energy estimation.
• To introduce a novel expectation estimation routine for resource-constrained quantum computations.

Main Methods:

• Proposal of a generalized VQE algorithm with a parameter α controlling the interpolation.
• Analysis of the algorithm's performance in terms of circuit depth and sample complexity.
• Development of a new expectation estimation subroutine for limited quantum resources.

Main Results:

• The generalized VQE algorithm achieves a tunable complexity of O(1/ε^{2(1-α)}) samples with circuit depth O(1/ε^{α}).
• This approach offers a flexible balance between the precision (ε) and the computational resources required.
• A new, efficient expectation estimation routine is presented.

Conclusions:

• The generalized VQE algorithm provides a more versatile approach to determining ground state energies on quantum computers.
• The tunable parameter α allows for optimization based on available quantum hardware and desired precision.
• The developed expectation estimation method has broader applicability in quantum algorithms.