Nonunitary Operations for Ground-State Calculations in Near-Term Quantum Computers

Area of Science:

• Quantum Computing
• Computational Physics
• Quantum Chemistry

Background:

• Variational quantum algorithms often struggle with suboptimal performance due to heuristic Ansätze.
• Accurate energy estimation is crucial for understanding molecular and material properties.
• Short quantum circuits limit the expressiveness and accuracy of current quantum algorithms.

Purpose of the Study:

• To introduce a novel quantum Monte Carlo-inspired reweighting scheme.
• To accurately compute energies from optimally short quantum circuits.
• To enhance the performance of variational quantum algorithms for ground state energy calculations.

Main Methods:

• A hybrid quantum-classical approach combining short quantum circuits with classical reweighting.
• Utilizing a nonunitary operator, inspired by classical computation, to filter high-energy components.
• Numerical demonstrations on many-body lattice models and implementation on IBM quantum hardware.

Main Results:

• Accurate computation of energies for entangled ground states.
• Effective filtering of high-energy components from suboptimal variational quantum heuristic Ansätze.
• Successful practical implementation on an 8-qubit IBM quantum processor.

Conclusions:

• The proposed reweighting scheme accurately computes energies using short quantum circuits.
• This hybrid approach offers a practical improvement for variational quantum algorithms.
• The method shows promise for near-term quantum devices in solving complex quantum problems.