Variational quantum algorithms to estimate rank, quantum entropies, fidelity and Fisher information via purity minimization

Abstract

Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition, variations of these VQAs are also adapted to perform other useful functions such as quantum state learning and approximate fractional inverses. The common theme shared by the proposed algorithms is that their cost functions are all based on minimizing the quantum purity of a quantum state. Strategies to mitigate or avoid the problem of exponentially vanishing cost function gradients are also discussed.

arXiv comment10 pages, 4 figures

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Cited by in corpus (16)

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• Estimating distinguishability measures on quantum computers
• New Quantum Algorithms for Computing Quantum Entropies and Distances
• Fast Quantum Algorithms for Trace Distance Estimation
• Estimating Quantum Mutual Information Through a Quantum Neural Network
• QuEst: Graph Transformer for Quantum Circuit Reliability Estimation
• Optimal Trace Distance and Fidelity Estimations for Pure Quantum States
• Ancilla-free continuous-variable SWAP test
• Unified multivariate trace estimation and quantum error mitigation
• A quantum information theoretic analysis of reinforcement learning-assisted quantum architecture search
• The topology of data hides in quantum thermal states
• Variational-toolbox-based separability detection of multiqubit states
• Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information
• Performance Guarantees for Quantum Neural Estimation of Entropies
• Prime Number Identification Demonstrated with Quantum Processors Using a New Rescaling-Based Noise Mitigation Technique