Overview
This research investigates the utility of Variational Quantum Eigensolver (VQE) for preparing initial states with significant overlap with true ground states, specifically for Quantum Phase Estimation (QPE) applied to Heisenberg spin-glass Hamiltonians. The study utilizes extensive classical numerical computations to analyze VQE's performance on systems up to 15 qubits.
Research Context
Quantum Phase Estimation (QPE) is identified as a quantum algorithmic method for computing ground state energies of quantum Hamiltonians. Ground state energy calculation of physical systems is framed as a promising application for quantum computing, potentially outperforming classical alternatives. This potential, however, depends on the availability of initial states for QPE that possess substantial overlap with the true ground state. VQE is considered a NISQ-era algorithm.
Approach
The study employed extensive numerical computations performed classically to assess VQE's effectiveness. The focus was on preparing high-overlap states for disordered fully-connected anisotropic Heisenberg spin-glass quantum Hamiltonians. The Hamiltonians studied encompassed systems of up to 15 qubits.
Findings
- VQE generally demonstrated an inability to efficiently converge to the ground state for the Hamiltonians under investigation. This finding is consistent with existing beliefs and is attributed to issues such as vanishing gradients and local minima inherent to VQE.
- Low energy states did not consistently correspond to large ground-state overlaps, though a correlation between these two measures was typically observed.
- Increasing the number of layers in the VQE ansatz beyond three did not lead to improvements in either the achieved ground-state overlap or the energies discovered.
- The scaling of the best-found overlap as a function of the Hamiltonian system size was not strongly exponentially decreasing. This particular observation suggests that VQE could potentially function as a heuristic state preparation algorithm for QPE.
Why This Matters
The availability of initial states with significant overlap with true ground states is crucial for the successful application of Quantum Phase Estimation (QPE) in computing ground state energies. This is a primary use case for quantum computing, with potential scientific and commercial value. The study's findings on VQE's limitations and its potential as a heuristic state preparation method directly address a foundational challenge for QPE's practical implementation.