Enhancing the Accuracy and Efficiency of Sample-Based Quantum Diagonalization with Phaseless Auxiliary-Field Quantum...

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Quantum Selected Configuration Interaction (QSCI) and Sample-based Quantum Diagonalization (SQD) are promising quantum algorithms for solving the electronic Schrödinger equation.
• These methods utilize noisy quantum computers by preparing quantum circuits and measuring configurations to form a subspace for classical Hamiltonian diagonalization.

Purpose of the Study:

• To investigate a hybrid quantum-classical approach combining SQD trial wave functions from quantum hardware with phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC).
• To assess the efficiency of this hybrid method in recovering correlation energy for molecular dissociation problems.

Main Methods:

• Employed QSCI/SQD protocols on quantum hardware to generate trial wave functions.
• Utilized a nonperturbative stochastic approach, ph-AFQMC, with truncated SQD trial wave functions.
• Applied the method to the dissociation of N₂ and a [2Fe - 2S] cluster model.

Main Results:

• The hybrid quantum-classical approach successfully recovered a substantial amount of correlation energy (O(100) mHa) for the studied molecular systems.
• Demonstrated that using SQD trial wave functions from quantum hardware with ph-AFQMC significantly reduces the sampling burden compared to pure QSCI/SQD.

Conclusions:

• This hybrid quantum-classical combination offers a compelling alternative to existing methods, potentially reducing reliance on quantum state tomography.
• The approach shows promise for efficiently solving complex electronic structure problems on near-term quantum devices.