Detecting and quantifying entanglement on near-term quantum devices

Abstract

Quantum entanglement is a key resource in quantum technology, and its quantification is a vital task in the current Noisy Intermediate-Scale Quantum (NISQ) era. This paper combines hybrid quantum-classical computation and quasi-probability decomposition to propose two variational quantum algorithms, called Variational Entanglement Detection (VED) and Variational Logarithmic Negativity Estimation (VLNE), for detecting and quantifying entanglement on near-term quantum devices, respectively. VED makes use of the positive map criterion and works as follows. Firstly, it decomposes a positive map into a combination of quantum operations implementable on near-term quantum devices. It then variationally estimates the minimal eigenvalue of the final state, obtained by executing these implementable operations on the target state and averaging the output states. Deterministic and probabilistic methods are proposed to compute the average. At last, it asserts that the target state is entangled if the optimized minimal eigenvalue is negative. VLNE builds upon a linear decomposition of the transpose map into Pauli terms and the recently proposed trace distance estimation algorithm. It variationally estimates the well-known logarithmic negativity entanglement measure and could be applied to quantify entanglement on near-term quantum devices. Experimental and numerical results on the Bell state, isotropic states, and Breuer states show the validity of the proposed entanglement detection and quantification methods.

arXiv comment12 pages

References in corpus (51)

• Quantum entanglement
• Quantum Computing in the NISQ era and beyond
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• A variational eigenvalue solver on a quantum processor
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement detection
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Measurement-based quantum computation with cluster states
• Quantum Circuit Learning
• The logarithmic negativity: A full entanglement monotone that is not convex
• Error mitigation for short-depth quantum circuits
• Separability criterion and inseparable mixed states with positive partial transposition
• Quantum fingerprinting
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Extending the computational reach of a noisy superconducting quantum processor
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• On quantum Renyi entropies: a new generalization and some properties
• Hybrid quantum-classical algorithms and quantum error mitigation
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Quantum autoencoders for efficient compression of quantum data
• From Classical to Quantum Shannon Theory
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Entanglement Certification $-$ From Theory to Experiment
• Layerwise learning for quantum neural networks
• Further results on the cross norm criterion for separability
• Mixed-state entanglement from local randomized measurements
• Subspace-search variational quantum eigensolver for excited states
• Separable states are more disordered globally than locally
• Quantum generalisation of feedforward neural networks
• Effect of barren plateaus on gradient-free optimization
• Estimating outcome probabilities of quantum circuits using quasiprobabilities
• Optimal entanglement criterion for mixed quantum states
• Large gradients via correlation in random parameterized quantum circuits
• An Adaptive Optimizer for Measurement-Frugal Variational Algorithms
• Nonlinear entanglement witnesses
• Variational Quantum Fidelity Estimation
• When are correlations quantum? -- Verification and quantification of entanglement by simple measurements
• Single-copies estimation of entanglement negativity
• Efficiently computable bounds for magic state distillation
• Learning to learn with quantum neural networks via classical neural networks
• Optimal resource cost for error mitigation
• Cost of quantum entanglement simplified
• Noise-Assisted Quantum Autoencoder
• Improved Semidefinite Programming Upper Bound on Distillable Entanglement
• Physical Implementability of Linear Maps and Its Application in Error Mitigation
• Coherence and entanglement measures based on Rényi relative entropies
• Practical distributed quantum information processing with LOCCNet
• A comparison of old and new definitions of the geometric measure of entanglement

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