Empirical Sample Complexity of Neural Network Mixed State Reconstruction

Abstract

Quantum state reconstruction using Neural Quantum States has been proposed as a viable tool to reduce quantum shot complexity in practical applications, and its advantage over competing techniques has been shown in numerical experiments focusing mainly on the noiseless case. In this work, we numerically investigate the performance of different quantum state reconstruction techniques for mixed states: the finite-temperature Ising model. We show how to systematically reduce the quantum resource requirement of the algorithms by applying variance reduction techniques. Then, we compare the two leading neural quantum state encodings of the state, namely, the Neural Density Operator and the positive operator-valued measurement representation, and illustrate their different performance as the mixedness of the target state varies. We find that certain encodings are more efficient in different regimes of mixedness and point out the need for designing more efficient encodings in terms of both classical and quantum resources.

7+4 pages, 5 figures

References in corpus (39)

• Quantum Computing in the NISQ era and beyond
• Quantum Cryptography
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Simulation
• The theory of variational hybrid quantum-classical algorithms
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Quantum Error Mitigation
• The randomized measurement toolbox
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Reconstructing quantum states with generative models
• Iterative maximum-likelihood reconstruction in quantum homodyne tomography
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Efficient tomography of a quantum many-body system
• Variational neural network ansatz for steady states in open quantum systems
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Latent Space Purification via Neural Density Operators
• Iterative algorithm for reconstruction of entangled states
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Models of quantum complexity growth
• Theoretical and Experimental Perspectives of Quantum Verification
• Efficient quantum state tomography with convolutional neural networks
• Neural network quantum state tomography in a two-qubit experiment
• Precise measurement of quantum observables with neural-network estimators
• Attention-based Quantum Tomography
• A Scalable Maximum Likelihood Method for Quantum State Tomography
• The learnability scaling of quantum states: restricted Boltzmann machines
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution
• Probabilistic Simulation of Quantum Circuits with the Transformer
• Eigenstate extraction with neural-network tomography
• Non-IID Quantum Federated Learning with One-shot Communication Complexity
• An Improved Sample Complexity Lower Bound for (Fidelity) Quantum State Tomography
• Neural network enhanced measurement efficiency for molecular groundstates

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• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Entanglement-induced provable and robust quantum learning advantages
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• Deep Neural Network-assisted improvement of quantum compressed sensing tomography