Many-body quantum state tomography with neural networks (1703.05334v2)

Abstract: The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing the full quantum state from simple measurements, and therefore provides a key tool to obtain reliable analytics. Brute-force approaches to QST, however, demand resources growing exponentially with the number of constituents, making it unfeasible except for small systems. Here we show that machine learning techniques can be efficiently used for QST of highly-entangled states, in both one and two dimensions. Remarkably, the resulting approach allows one to reconstruct traditionally challenging many-body quantities - such as the entanglement entropy - from simple, experimentally accessible measurements. This approach can benefit existing and future generations of devices ranging from quantum computers to ultra-cold atom quantum simulators.

• The paper introduces a novel quantum state tomography method that leverages neural networks and RBMs to efficiently reconstruct many-body quantum states.
• It achieves high-fidelity reconstructions of complex entanglement properties and dynamic state evolutions with significantly fewer measurements.
• The work paves the way for scalable experimental validations and improved quantum simulations by mitigating the exponential resource demands of traditional techniques.

Neural-Network Quantum State Tomography for Many-Body Systems

The paper "Neural-Network Quantum State Tomography for Many-Body Systems" authored by Giacomo Torlai et al. explores a novel methodology that leverages machine learning techniques for performing quantum state tomography (QST) on complex many-body quantum systems. Traditional quantum state tomography requires resources that scale exponentially with the system size, rendering it impractical for large and highly entangled systems. This paper introduces an approach utilizing artificial neural networks (ANN), particularly restricted Boltzmann machines (RBM), to efficiently reconstruct the quantum state from experimental data.

Key Contributions

The primary contribution of the paper is demonstrating that neural networks, known for their capability to handle and compress high-dimensional data, can be adapted to QST, thus facilitating the reconstruction of quantum states, even for highly entangled systems. The approach showcased in this paper addresses significant scalability issues faced by conventional methods, enabling the reconstruction of challenging many-body properties such as entanglement entropy from straightforward measurements.

The paper thoroughly examines several synthetic datasets, illustrating the potential of this method across various quantum systems and highlighting its applicability to both one-dimensional and two-dimensional states. One of the benchmarks includes reconstructing the W-state, an entangled state of qubits, achieving high fidelity with a significantly reduced number of measurements compared to traditional techniques.

The authors also extend the application of their neural-network approach to the dynamic case, exploring the unitary evolution of quantum states under certain Hamiltonians. This demonstration outlines the neural-network model's flexibility and capability in not only static analysis but also dynamic quantum system evaluations.

Methodology

The methodology relies on a sophisticated use of restricted Boltzmann machines to model the many-body wave functions. The RBM architecture serves as an efficient ansatz for the wave function, allowing the network to accommodate the complex correlation patterns of the system. The training involves optimizing the network parameters to maximize the likelihood of the observed data, which are presumed to follow the quantum statistics of the target system.

The critical step involves using the trained RBM to sample from the probability distribution corresponding to the squared amplitudes of the wave function, making it possible to deduce properties such as the entanglement entropy and various correlation functions. This is particularly beneficial as these quantities are not directly accessible through standard experimental procedures.

Implications and Future Work

This development holds significant implications for the future of quantum computing and quantum information sciences. By substantially reducing the resource burden associated with traditional QST, this method may accelerate experimental validations of quantum systems and enhance the efficiency of quantum simulators and computers.

Theoretical advancements facilitated by this method could include improved understanding of quantum phase transitions and dynamic quantum phenomena that remain challenging to probe with existing tools.

Future research could expand on exploring different neural network architectures, such as deep belief networks and other forms that may provide even more compact representations or faster convergence for larger and higher-dimensional systems. Additionally, real-world implementations in collaboration with experimental quantum hardware are anticipated to further test and refine these methods, potentially leading to the development of new quantum technologies.

In summary, the paper makes a substantial contribution to the domain of quantum physics and machine learning by providing a practical solution to the challenge of quantum state tomography in large and complex quantum systems through the application of neural networks. Its impact is expected to catalyze advancements in both theoretical insights and experimental practices in the field.