Variational Quantum Fidelity Estimation
Abstract
Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelityF(ρ,σ)based on the ``truncated fidelity''F(ρm,σ), which is evaluated for a stateρmobtained by projectingρonto itsm-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically withm. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalizeρ, (2) compute matrix elements ofσin the eigenbasis ofρ, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case whereσis arbitrary andρis low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 26, 2020
- Source ID
- 10.22331/q-2020-03-26-248
Entities
People
- Alexander Poremba
- M. Cerezo
- Patrick J. Coles
- Łukasz Cincio
Organizations
- California Institute of Technology
- Los Alamos National Laboratory