Scalable quantum tomography with fidelity estimation

Wang, Jun; Han, Zhaoyu; Wang, Songbo; Li, Zeyang; Mu, Liang-Zhu; Fan, Heng; Wang, Lei

doi:10.1103/physreva.101.032321

Cited by 24 publications

(13 citation statements)

References 66 publications

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“…Several algorithms to overcome this severe complexity have been proposed over the last decade. Notable examples are compressed sensing tomography [167][168][169][170], permutationally invariant tomography [171,172] and tensor-network tomography [173][174][175][176], which rely respectively on the sparsity, translational invariance and lowentanglement of the target quantum state. More recently, a new framework built on neural networks and unsupervised learning has been put forward [52], based on the assumption that most physical states of interest typically contains some degree of structure (i.e.…”

Section: Quantum State Tomographymentioning

confidence: 99%

Neural networks in quantum many-body physics: a hands-on tutorial

Carrasquilla,

Torlai

2021

Preprint

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Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to mitigate the exponential complexity often encountered in quantum many-body physics, the study of properties of quantum systems built out of a large number of interacting particles. In this Article, we overview some applications of machine learning in condensed matter physics and quantum information, with particular emphasis on hands-on tutorials serving as a quick-start for a newcomer to the field. We present supervised machine learning with convolutional neural networks to learn a phase transition, unsupervised learning with restricted Boltzmann machines to perform quantum tomography, and variational Monte Carlo with recurrent neural-networks for approximating the ground state of a many-body Hamiltonian. We briefly review the key ingredients of each algorithm and their corresponding neural-network implementation, and show numerical experiments for a system of interacting Rydberg atoms in two dimensions.

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Section: Quantum State Tomographymentioning

confidence: 99%

Neural networks in quantum many-body physics: a hands-on tutorial

Carrasquilla,

Torlai

2021

Preprint

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“…The scheme has been proven to asymptotically reach the scaling limit imposed by quantum information theory in terms of number of measurements required, but globally entangling gates are necessary to enjoy less-than-exponential scaling for the task of fidelity estimation [16]. To tackle tasks like fidelity estimation, alternative recent tomography schemes employ classical generative machine learning (ML) tools like restricted Boltzmann machines (RBMs), recurrent neural networks (RNNs) and attention-based tomography (AQT) [19][20][21][22][23][24][25]. These ML approaches learn directly from raw data but generally require random measurements from an informationally complete (IC) set of positive operator valued measures (POVMs), which unfavorably scales as 4 N for an N -qubit system and is not required for general pure state reconstruction [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Learning Quantum Phases of Matter Using a Basis-Enhanced Born Machine

Gomez¹,

Yelin²,

Najafi³

2022

Preprint

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Rapid improvement in quantum hardware has opened the door to complex problems, but the precise characterization of quantum systems itself remains a challenge. To address this obstacle, novel tomography schemes have been developed that employ generative machine learning models, enabling quantum state reconstruction from limited classical data. In particular, quantum-inspired Born machines provide a natural way to encode measured data into a model of a quantum state. Born machines have shown great success in learning from classical data; however, the full potential of a Born machine in learning from quantum measurement has thus far been unrealized. To this end, we devise a complex-valued basis-enhanced Born machine and show that it can reconstruct pure quantum states using projective measurements from only two Pauli measurement bases. We implement the basis-enhanced Born machine to learn the ground states across the phase diagram of a 1D chain of Rydberg atoms, reconstructing quantum states deep in ordered phases and even at critical points with quantum fidelities surpassing 99%. The model accurately predicts quantum correlations and different observables, and system sizes as large as 37 qubits are considered. Quantum states across the phase diagram of a 1D XY spin chain are also successfully reconstructed using this scheme. Our method only requires simple Pauli measurements with a sample complexity that scales quadratically with system size, making it amenable to experimental implementation.

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“…However, such methods based on local density matrices are not easy to implement in practice since 1) exact tomography of a series of local density matrices may be already hard, and 2) we can only reconstruct an approximation of each local density matrix from tomography using a finite number of mea-surements, and the approximation errors could accumulate and affect the overall tomography performance of the entire state. Another method based on an MPS ansatz is proposed using an unsupervised machine learning algorithm in [21], where only global measurement data on a randomly prepared basis are required. Such method however only considers the reconstruction of pure states.…”

mentioning

confidence: 99%

Density matrix reconstruction using non-negative matrix product states

Han¹,

Guo²,

Wang³

2022

Preprint

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Quantum state tomography is a central technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best non-negative matrix product state approximation based on a set of measurement outcomes whose size does not necessarily grow exponentially. Compared to the tomography approach based on neural network states, our scheme utilizes a socalled tensor train representation that allows straightforward recovery of the unknown density matrix in matrix product state form. As applications, our algorithm is numerically demonstrated for the ground state of the XXZ spin chain under depolarization noise.

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Scalable quantum tomography with fidelity estimation

Cited by 24 publications

References 66 publications

Neural networks in quantum many-body physics: a hands-on tutorial

Neural networks in quantum many-body physics: a hands-on tutorial

Learning Quantum Phases of Matter Using a Basis-Enhanced Born Machine

Density matrix reconstruction using non-negative matrix product states

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