Efficient Quantum State Sample Tomography with Basis-dependent Neural-networks

Abstract

We use a meta-learning neural-network approach to analyse data from a measured quantum state. Once our neural network has been trained it can be used to efficiently sample measurements of the state in measurement bases not contained in the training data. These samples can be used calculate expectation values and other useful quantities. We refer to this process as "state sample tomography". We encode the state's measurement outcome distributions using an efficiently parameterized generative neural network. This allows each stage in the tomography process to be performed efficiently even for large systems. Our scheme is demonstrated on recent IBM Quantum devices, producing a model for a 6-qubit state's measurement outcomes with a predictive accuracy (classical fidelity) > 95% for all test cases using only 100 random measurement settings as opposed to the 729 settings required for standard full tomography using local measurements. This reduction in the required number of measurements scales favourably, with training data in 200 measurement settings yielding a predictive accuracy > 92% for a 10 qubit state where 59,049 settings are typically required for full local measurement-based quantum state tomography. A reduction in number of measurements by a factor, in this case, of almost 600 could allow for estimations of expectation values and state fidelities in practicable times on current quantum devices.

References in corpus (22)

• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• On the Measurement of Qubits
• Reconciling modern machine learning practice and the bias-variance trade-off
• Many-body quantum state tomography with neural networks
• Matrix product states represent ground states faithfully
• Efficient quantum state tomography
• Quantum state estimation
• Variational Quantum Computation of Excited States
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Quantum Entanglement in Neural Network States
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Reconstructing quantum states with generative models
• Machine Learning Topological States
• Efficient tomography of a quantum many-body system
• Cross-Platform Verification of Intermediate Scale Quantum Devices
• Latent Space Purification via Neural Density Operators
• Quantum Neural Network States: A Brief Review of Methods and Applications
• Entanglement in mutually unbiased bases
• Symmetric Informationally Complete Measurements of Arbitrary Rank
• Scalable on-chip quantum state tomography
• The Learnability of Quantum States

Cited by in corpus (14)

• Efficient quantum state tomography with convolutional neural networks
• Flexible learning of quantum states with generative query neural networks
• Neural network-based prediction of the secret-key rate of quantum key distribution
• Gradient-descent quantum process tomography by learning Kraus operators
• Certification of quantum states with hidden structure of their bitstrings
• Transformer neural networks and quantum simulators: a hybrid approach for simulating strongly correlated systems
• Quantum Similarity Testing with Convolutional Neural Networks
• High-dimentional Multipartite Entanglement Structure Detection with Low Cost
• On the connection between least squares, regularization, and classical shadows
• Digital Quantum Simulation of Scalar Yukawa Coupling
• Reinforcement learning to learn quantum states for Heisenberg scaling accuracy
• Deep Neural Network-assisted improvement of quantum compressed sensing tomography
• Neural quantum states for entanglement depth certification from randomized Pauli measurements
• Quantum Machine Learning for State Tomography Using Classical Data