Evaluating Energy Differences on a Quantum Computer with Robust Phase Estimation.

Area of Science:

• Quantum Computing
• Quantum Chemistry
• Computational Physics

Background:

• Accurate calculation of molecular energies is crucial for understanding chemical reactions and material properties.
• Existing quantum algorithms for energy estimation often require significant qubit resources and complex gate operations.
• Robustness against noise is a key challenge for practical quantum computation.

Purpose of the Study:

• To adapt the robust phase estimation algorithm for efficient calculation of energy differences between molecular eigenstates.
• To develop a quantum algorithm that minimizes resource requirements, specifically avoiding controlled unitaries and auxiliary qubits.
• To quantify the algorithm's robustness against coherent errors in quantum state preparation and measurement.

Main Methods:

• Adaptation of the robust phase estimation algorithm for eigenvalue difference evaluation.
• Implementation of the algorithm on a cloud quantum computer.
• Proof-of-concept calculation of ground and low-lying electronic excitation energies for a hydrogen molecule in a minimal basis.

Main Results:

• Successfully calculated energy differences between eigenstates of a hydrogen molecule.
• Demonstrated a quantum approach that does not necessitate controlled unitaries or auxiliary qubits.
• Quantified the algorithm's robustness, showing high tolerance to coherent errors during state preparation and measurement.

Conclusions:

• The adapted robust phase estimation algorithm offers an efficient and resource-minimized approach for determining molecular energy differences.
• This method shows significant promise for practical quantum chemistry simulations, even in the presence of coherent noise.
• All quantum phase estimation algorithms fundamentally compute eigenvalue differences, providing a unified theoretical perspective.