Practical variational tomography for critical 1D systems

Abstract

We improve upon a recently introduced efficient quantum state reconstruction procedure targeted to states well-approximated by the multi-scale entanglement renormalization ansatz (MERA), e.g., ground states of critical models. We show how to numerically select a subset of experimentally accessible measurements which maximizes information extraction about renormalized particles, thus dramatically reducing the required number of physical measurements. We numerically estimate the number of measurements required to characterize the ground state of the critical 1D Ising (resp. XX) model and find that MERA tomography on 16-qubit (resp. 24-qubit) systems requires the same experimental effort than brute-force tomography on 8 qubits. We derive a bound computable from experimental data which certifies the distance between the experimental and reconstructed states.

References in corpus (21)

• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Scalable multi-particle entanglement of trapped ions
• Entanglement renormalization
• 14-qubit entanglement: creation and coherence
• An Area Law for One Dimensional Quantum Systems
• A class of quantum many-body states that can be efficiently simulated
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Matrix product states represent ground states faithfully
• Efficient quantum state tomography
• Direct Fidelity Estimation from Few Pauli Measurements
• Optimal, reliable estimation of quantum states
• Algorithms for entanglement renormalization
• Practical characterization of quantum devices without tomography
• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Reliable Quantum State Tomography
• Scalable reconstruction of density matrices
• Practical learning method for multi-scale entangled states

Cited by in corpus (4)

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