Automated detection of symmetry-protected subspaces in quantum simulations

The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition Hilbert space into invariant subspaces of the time-evolution operator, each of which is demarcated according to its conserved quantity. We show that, starting from a chosen basis, any invariant, symmetry-protected subspaces which are diagonal in that basis are discoverable using transitive closure on graphs representing state-to-state transitions under $k$-local unitary operations. Importantly, the discovery of these subspaces relies neither upon the explicit identification of a symmetry operator or its eigenvalues nor upon the construction of matrices of the full Hilbert space dimension. We introduce two classical algorithms, which efficiently compute and elucidate features of these subspaces. The first algorithm explores the entire symmetry-protected subspace of an initial state in time complexity linear to the size of the subspace by closing local basis state-to-basis state transitions. The second algorithm determines, with bounded error, if a given measurement outcome of a dynamically-generated state is within the symmetry-protected subspace of the state in which the dynamical system is initialized. We demonstrate the applicability of these algorithms by performing post-selection on data generated from emulated noisy quantum simulations of three different dynamical systems: the Heisenberg-XXX model and the $T_6$ and $F_4$ quantum cellular automata. Due to their efficient computability and indifference to identifying the underlying symmetry, these algorithms lend themselves to the post-selection of quantum computer data, optimized classical simulation of quantum systems, and the discovery of previously hidden symmetries in quantum mechanical systems.Comment: 23 pages, 7 figures, 4 appendice

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma

Modern Approaches to Topological Quantum Error Correction

The construction of a large-scale fault-tolerant quantum computer is an outstanding scientific and technological goal. It holds the promise to allow us to solve a variety of complex problems such as factoring large numbers, quick database search, and the quantum simulation of many-body quantum systems in fields as diverse as condensed matter, quantum chemistry, and even high-energy physics. Sophisticated theoretical protocols for reliable quantum information processing under imperfect conditions have been de-veloped, when errors affect and corrupt the fragile quantum states during storage and computations. Arguably, the most realistic and promising ap-proach towards practical fault-tolerant quantum computation are topologi-cal quantum error-correcting codes, where quantum information is stored in interacting, topologically ordered 2D or 3D many-body quantum systems. This approach offers the highest known error thresholds, which are already today within reach of the experimental accuracy in state-of-the-art setups. A combination of theoretical and experimental research is needed to store, protect and process fragile quantum information in logical qubits effectively so that they can outperform their constituting physical qubits. Whereas small-scale quantum error correction codes have been implemented, one of the main theoretical challenges remains to develop new and improve existing efficient strategies (so-called decoders) to derive (near-)optimal error cor-rection operations in the presence of experimentally accessible measurement information and realistic noise sources. One main focus of this project is the development and numerical implementation of scalable, efficient decoders to operate topological color codes. Additionally, we study the feasibility of im-plementing quantum error-correcting codes fault-tolerantly in near-term ion traps. To this end, we use realistic modeling of the different noise sources, computer simulations, and most modern quantum information approaches to quantum circuitry and noise suppression techniques