Optimizing unitary coupled cluster wave functions on quantum hardware: Error bound and resource-efficient optimizer.

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Many-body systems require accurate ground state calculations.
• Variational Quantum Eigensolver (VQE) is a common hybrid approach.
• Projective Quantum Eigensolver (PQE) offers an alternative optimization strategy.

Purpose of the Study:

• To mathematically analyze the Projective Quantum Eigensolver (PQE) algorithm.
• To derive bounds for PQE's energy error and wavefunction overlap.
• To develop and validate a novel residue-based optimizer for PQE.

Main Methods:

• Mathematical derivation of bounds relating Hamiltonian residues to energy error and overlap.
• Analysis of classical optimization convergence for PQE.
• Development of a new residue-based optimizer.

Main Results:

• Formal guarantees for PQE derived from bounds on off-diagonal Hamiltonian coefficients (residues).
• A new convergence criterion for residue-based optimizers.
• Numerical evidence showing the proposed optimizer outperforms existing methods for H4, H6, BeH2, and LiH dissociation curves.

Conclusions:

• PQE provides a robust framework for ground state computation.
• The derived bounds offer theoretical support and practical convergence criteria for PQE.
• The new residue-based optimizer demonstrates superior performance in benchmark chemical systems.