Table 2 Comparison of QPE and VQE algorithms
| Â | QPE | VQE |
|---|---|---|
Solution Accuracy | Exact eigenstate with controllable error | Limited by ansatz |Ψ(θ)〉 with uncontrollable error |
Cost | O(#terms/ε) | O((#terms/ε)2)×optimization steps |
Ansatz fidelity requirement | non-negligible | 99.9% |
Small non-trivial demonstrations | H2 on NISQ | H10, H2O on NISQ |
Industrial scale demonstrations | Requires logical qubits 1011 Toffoli gate operations (von Burg et al. 2021) | Requires logical qubits 105 gates for state prep (Kühn et al. 2019) 1011 measurement for energy evaluation (Wecker et al. 2015) 103 gradient descent |