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A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
Mott physics - the interplay between itinerancy and localization of electrons - is undergoing a paradigm shift from the binary "bandwidth - filling" tuning framework to an intertwining of geometric, topological, and fractionalized degrees…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…
In the last three decades, several constructions of quantum error-correcting codes were presented in the literature. Among these codes, there are the asymmetric ones, i.e., quantum codes whose $Z$-distance $d_z$ is different from its…
Network structures are reconstructed from dynamical data by respectively naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. For TAP approximation, we use two methods to reconstruct the network: a) iteration method; b)…
The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…
Although classifying topological quantum phases have attracted great interests, the absence of local order parameter generically makes it challenging to detect a topological phase transition from experimental data. Recent advances in…
We present a new approach, the Topograph, which reconstructs underlying physics processes, including the intermediary particles, by leveraging underlying priors from the nature of particle physics decays and the flexibility of message…
Two-dimensional topological translationally-invariant (TTI) quantum codes, such as the toric code (TC) and bivariate bicycle (BB) codes, are promising candidates for fault-tolerant quantum computation. For such codes to be practically…
The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of…
Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…
Quantum Approximate Optimization Algorithm (QAOA) enables solving combinatorial optimization problems on quantum computers by optimizing variational parameters for quantum circuits. We investigate a simplified approach that combines linear…
Topological quantum computing has recently proven itself to be a powerful computational model when constructing viable architectures for large scale computation. The topological model is constructed from the foundation of a error correction…
Critical behavior of the Ising model is investigated at the center of large scale finite size systems, where the lattice is represented as the tiling of pentagons. The system is on the hyperbolic plane, and the recursive structure of the…
The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these…
We develop a supervised machine learning algorithm that is able to learn topological phases of finite condensed matter systems from bulk data in real lattice space. The algorithm employs diagonalization in real space together with any…
A significant challenge in quantum computing (QC) is developing learning models that truly align with quantum principles, as many current approaches are complex adaptations of classical frameworks. In this work, we introduce Quantum…
The Quantum Approximate Optimisation Algorithm (QAOA) is a hybrid quantum-classical algorithm for solving combinatorial optimisation problems. QAOA encodes solutions into the ground state of a Hamiltonian, approximated by a $p$-level…