arXiv:2206.01273

Reconstructing Quantum States Using Basis-Enhanced Born Machines

Abigail McClain Gomez, Susanne F. Yelin, Najafi, Khadijeh

Published Jun 2, 2022• 2 citations

Abstract

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.

DOI: 10.48550/arxiv.2206.01273

Related papers

Quantum machine learning for state tomography using classical data

S. Jabeen, Dmytro Kurdydyk, Aadi Palnitkar +3 more

Reconstructing quantum states from measurement data represents a formidable challenge in quantum information science, especially as system sizes grow beyond the reach of traditional tomography methods. While recent studies have explored quantum machine learning (QML) for quantum state tomography (QST), nearly all rely on idealized assumptions, such as direct access to the unknown quantum state as quantum data input, which are incompatible with current hardware constraints. In this work, we present a QML-based tomography protocol that operates entirely on classical measurement data and is fully executable on noisy intermediate-scale quantum (NISQ) devices. Our approach employs a variational quantum circuit trained to reconstruct quantum states based solely on measurement outcomes. We test the method in simulation, achieving high-fidelity reconstructions of diverse quantum states, including GHZ states, spin chain ground states, and states generated by random circuits. The protocol is then validated on quantum hardware from IBM and IonQ. Additionally, we demonstrate accurate tomography is possible using incomplete measurement bases, a crucial step towards scaling up our protocol. Our results in various scenarios illustrate successful state reconstruction with fidelity reaching 90% or higher. To our knowledge, this is the first QML-based tomography scheme that has been implemented on real quantum processors using exclusively classical measurements. This work establishes the feasibility of QML-based tomography on current quantum platforms and offers a scalable pathway for practical quantum state reconstruction.

arXiv:2507.01246Quantum Machine IntelligenceApr 2, 20260 citations

Adaptive Quantum State Tomography with Active Learning

Hannah Lange, Matjaž Kebrič, Maximilian Buser +3 more

Recently, tremendous progress has been made in the field of quantum science and technologies: different platforms for quantum simulation as well as quantum computing, ranging from superconducting qubits to neutral atoms, are starting to reach unprecedentedly large systems. In order to benchmark these systems and gain physical insights, the need for efficient tools to characterize quantum states arises. The exponential growth of the Hilbert space with system size renders a full reconstruction of the quantum state prohibitively demanding in terms of the number of necessary measurements. Here we propose and implement an efficient scheme for quantum state tomography using active learning. Based on a few initial measurements, the active learning protocol proposes the next measurement basis, designed to yield the maximum information gain. We apply the active learning quantum state tomography scheme to reconstruct different multi-qubit states with varying degree of entanglement as well as to ground states of the XXZ model in 1D and a kinetically constrained spin chain. In all cases, we obtain a significantly improved reconstruction as compared to a reconstruction based on the exact same number of measurements and measurement configurations, but with randomly chosen basis configurations. Our scheme is highly relevant to gain physical insights in quantum many-body systems as well as for benchmarking and characterizing quantum devices, e.g. for quantum simulation, and paves the way for scalable adaptive protocols to probe, prepare, and manipulate quantum systems.

arXiv:2203.15719QuantumOct 9, 202323 citations

Machine learning assisted quantum state estimation

Sanjaya Lohani, Brian T Kirby, Michael Brodsky +2 more

Abstract We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate via simulations that our method produces functionally equivalent reconstructed states to that of traditional methods with the added benefit that expensive computations are front-loaded with our system. Further, by training our system with measurement results that include simulated noise sources we are able to demonstrate a significantly enhanced average fidelity when compared to typical reconstruction methods. These enhancements in average fidelity are also shown to persist when we consider state reconstruction from partial tomography data where several measurements are missing. We anticipate that the present results combining the fields of machine intelligence and quantum state estimation will greatly improve and speed up tomography-based quantum experiments.

arXiv:2003.03441Machine Learning Science and TechnologyJun 5, 2020101 citations

Reconstructing Quantum States from Sparse Measurements

Yufan Xie, Chu Guo, Zhihui Peng

Quantum state tomography (QST) is a central technique to fully characterize an unknown quantum state. However, standard QST requires an exponentially growing number of quantum measurements against the system size, which limits its application to smaller systems. Here, we explore the sparsity of underlying quantum state and propose a QST scheme that combines the matrix product states’ representation of the quantum state with a supervised machine learning algorithm. Our method could reconstruct the unknown sparse quantum states with very high precision using only a portion of the measurement data in a randomly selected basis set. In particular, we demonstrate that the Wolfgang states could be faithfully reconstructed using around 25% of the whole basis, and that the randomly generated quantum states, which could be efficiently represented as matrix product states, could be faithfully reconstructed using a number of bases that scales sub-exponentially against the system size.

ElectronicsFeb 22, 20231 citation

Reconstructing Complex States of a 20 -Qubit Quantum Simulator

Murali Krishna Kurmapu, V. V. Tiunova, Egor Tiunov +6 more

A prerequisite to the successful development of quantum computers and simulators is precise understanding of the physical processes occurring therein, which can be achieved by measuring the quantum states that they produce.However, the resources required for traditional quantum state estimation scale exponentially with the system size, highlighting the need for alternative approaches.Here, we demonstrate an efficient method for reconstruction of significantly entangled multiqubit quantum states.Using a variational version of the matrix-product-state ansatz, we perform the tomography (in the pure-state approximation) of quantum states produced in a 20-qubit trapped-ion Ising-type quantum simulator, using the data acquired in only 27 bases, with 1000 measurements in each basis.We observe superior statereconstruction quality and faster convergence compared to the methods based on neural-network quantum state representations: restricted Boltzmann machines and feed-forward neural networks with autoregressive architecture.Our results pave the way toward efficient experimental characterization of complex states produced by the quench dynamics of many-body quantum systems.

arXiv:2208.04862PRX QuantumDec 18, 202324 citations

Predicting Properties of Quantum Systems with Conditional Generative Models

Haoxiang Wang, Maurice Weber, Josh Izaac +1 more

Machine learning has emerged recently as a powerful tool for predicting properties of quantum many-body systems. For many ground states of gapped Hamiltonians, generative models can learn from measurements of a single quantum state to reconstruct the state accurately enough to predict local observables. Alternatively, classification and regression models can predict local observables by learning from measurements on different but related states. In this work, we combine the benefits of both approaches and propose the use of conditional generative models to simultaneously represent a family of states, learning shared structures of different quantum states from measurements. The trained model enables us to predict arbitrary local properties of ground states, even for states not included in the training data, without necessitating further training for new observables. We first numerically validate our approach on 2D random Heisenberg models using simulations of up to 45 qubits. Furthermore, we conduct quantum simulations on a neutral-atom quantum computer and demonstrate that our method can accurately predict the quantum phases of square lattices of 13$\times$13 Rydberg atoms.

arXiv:2211.16943Nov 30, 20223 citations