Neural-Shadow Quantum State Tomography

Abstract

Quantum state tomography (QST) is the art of reconstructing an unknown quantum state through measurements. It is a key primitive for developing quantum technologies. Neural network quantum state tomography (NNQST), which aims to reconstruct the quantum state via a neural network ansatz, is often implemented via a basis-dependent cross-entropy loss function. State-of-the-art implementations of NNQST are often restricted to characterizing a particular subclass of states, to avoid an exponential growth in the number of required measurement settings. To provide a more broadly applicable method for efficient state reconstruction, we present "neural-shadow quantum state tomography" (NSQST)-an alternative neural network-based QST protocol that uses infidelity as the loss function. The infidelity is estimated using the classical shadows of the target state. Infidelity is a natural choice for training loss, benefiting from the proven measurement sample efficiency of the classical shadow formalism. Furthermore, NSQST is robust against various types of noise without any error mitigation. We numerically demonstrate the advantage of NSQST over NNQST at learning the relative phases of three target quantum states of practical interest, as well as the advantage over direct shadow estimation. NSQST greatly extends the practical reach of NNQST and provides a novel route to effective quantum state tomography.

20 pages, 14 figures. New subsection added and several other changes. Final version published in Physical Review Research

References in corpus (8)

• Randomized Benchmarking of Quantum Gates
• Efficient quantum state tomography
• The randomized measurement toolbox
• Theoretical and Experimental Perspectives of Quantum Verification
• Experimental single-setting quantum state tomography
• Only n-Qubit Greenberger-Horne-Zeilinger States are Undetermined by their Reduced Density Matrices
• Investigating Topological Order using Recurrent Neural Networks
• Local Manipulation and Measurement of Nonlocal Many-Body Operators in Lattice Gauge Theory Quantum Simulators

Cited by in corpus (5)

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits
• Observing Schrödinger's Cat with Artificial Intelligence: Emergent Classicality from Information Bottleneck
• Learning topological states from randomized measurements using variational tensor network tomography
• Neural quantum states for entanglement depth certification from randomized Pauli measurements
• Quantum Machine Learning for State Tomography Using Classical Data