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For over twenty years, ultra-cold atomic systems have formed an almost perfect arena for simulating different quantum many-body phenomena and exposing their non-obvious and very often counterintuitive features. Thanks to extremely precise…

Optimally-shaped electromagnetic fields have the capacity to coherently control the dynamics of quantum systems and thus offer a promising means for controlling molecular transformations relevant to chemical, biological, and materials…

Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here,…

A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…

Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…

Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…

Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…

The capacity to custom tailor the properties of quantum matter and materials is a central requirement for enlarging their range of possible functionalities. A particularly promising route is the use of driving protocols to engineer specific…

In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations…

Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…

Recent experimental progress in controlling neutral group-II atoms for optical clocks, and in the production of degenerate gases with group-II atoms has given rise to novel opportunities to address challenges in quantum computing and…

Adaptive quantum circuits, in which unitary operations, measurements, and feedback are used to steer quantum many-body systems, provide an exciting opportunity to generate new dynamical steady states. We introduce an adaptive quantum…

We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the…

Determining the physically accessible unitary dynamics of a quantum system under finite Hamiltonian resources is a central problem in quantum control and Hamiltonian engineering. Dynamical Lie algebras (DLAs) provide the fundamental link…

Response functions of resonant circuits create ringing artefacts if their input changes rapidly. When physical limits of electromagnetic spectroscopies are explored, this creates two types of problems. Firstly, simulation: the system must…

Simulating fermionic systems on a quantum computer requires representing fermionic states using qubits. The complexity of many simulation algorithms depends on the complexity of implementing rotations generated by fermionic…

The design and control of atomic-scale spin structures constitute major challenges for spin-based quantum technology platforms, including quantum dots, color centers, and molecular spins. Here, we showcase a strategy for designing the…

The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for…

The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…