Related papers: Learning transitions of topological surface codes

Quantum probes that enable enhanced exploration and characterization of complex systems are central to modern science, spanning applications from biology to astrophysics and chemical design. In large many-body quantum systems, interactions…

Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error…

Qubit readout is commonly performed by thresholding a collection of analog detector signals to obtain a sequence of single-shot bit values. The intrinsic irreversibility of the mapping from analog to digital signals discards soft…

In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation. However, implementing these gates using methods like magic state distillation and code switching requires significant…

There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. ``Interpretability'' remains a concern: can we understand…

Quantum error correction protects quantum information against decoherence provided the noise strength remains below a critical threshold. This threshold marks the critical point for the decoding phase transition. Here we connect this…

We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…

In the canonical formalism of statistical physics, a signature of a first order phase transition for finite systems is the bimodal distribution of an order parameter. Previous thermodynamical studies of nuclear sources produced in heavy-ion…

The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…

Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…

The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…

The topology of a topological material can be encoded in its surface states. These surface states can only be removed by a bulk topological quantum phase transition into a trivial phase. Here we use photoemission spectroscopy to image the…

One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across…

Topological surface states are a class of novel electronic states that are of potential interest in quantum computing or spintronic applications. Unlike conventional two-dimensional electron states, these surface states are expected to be…

The success of modern deep learning hinges on the ability to train neural networks at scale. Through clever reuse of intermediate information, backpropagation facilitates training through gradient computation at a total cost roughly…

In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural…

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…

We begin with an introduction to topological order using Wegner's quantum $Z_2$ gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying $Z_2$ magnetic flux. The interplay between…

Recently, quantum convolutional neural networks (QCNNs) are proposed, harnessing the power of quantum computing for faster training compared to the classical counterparts. However, this framework for deep learning also relies on multiple…

The discovery of topological features of quantum states plays an important role in modern condensed matter physics and various artificial systems. Due to the absence of local order parameters, the detection of topological quantum phase…