Related papers: SU(d)-Symmetric Random Unitaries: Quantum Scrambli…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes that obey (are covariant with respect to) continuous symmetries in a certain sense cannot…
The efficiency of locally generating unitary designs, which capture statistical notions of quantum pseudorandomness, lies at the heart of wide-ranging areas in physics and quantum information technologies. While there are extensive potent…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes covariant with respect to continuous symmetries cannot correct erasure errors perfectly…
Local symmetric quantum circuits provide a simple framework to study the dynamics and phases of complex quantum systems with conserved charges. However, some of their basic properties have not yet been understood. Recently, it has been…
The generation of $k$-designs (pseudorandom distributions that emulate the Haar measure up to $k$ moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive…
The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
Dynamical decoupling is a long-established and effective way to suppress unwanted interactions in qubit systems, enabling advances in fields ranging from quantum metrology to quantum computing. For general qudit systems, however, comparable…
Deep learning was recently successfully used in deriving symmetry transformations that preserve important physics quantities. Being completely agnostic, these techniques postpone the identification of the discovered symmetries to a later…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
Symmetric extensions are essential in quantum mechanics, providing a lens to investigate the correlations of entangled quantum systems and to address challenges like the quantum marginal problem. Though semi-definite programming (SDP) is a…
Symmetry underlies many of the most effective classical and quantum learning algorithms, yet whether quantum learners can gain a fundamental advantage under symmetry-imposed structures remains an open question. Based on evidence that…
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…
This work investigates variational compilation methods for simulating quantum systems with internal SU(2) symmetry. The central component of the research is the application of the Dynamic Mode Decomposition (DMD) method to extrapolate…
Conservation of symmetries plays a crucial role in both classical and quantum simulations of many-body systems, enabling the tracking of states with specific symmetry properties and leading to substantial reductions in the number of…
The notion of symmetry is shown to be at the heart of all error correction/avoidance strategies for preserving quantum coherence of an open quantum system S e.g., a quantum computer. The existence of a non-trivial group of symmetries of the…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU$(d)$ symmetries. It allows us to enhance a natural model of quantum…
We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum…