Florian Marquardt

In fault-tolerant quantum computation, the preparation of logical states is a ubiquitous subroutine, yet significant challenges persist even for the simplest states required. In the present work, we present a unitary, scalable, distance-preserving encoding scheme for preparing Pauli eigenstates in surface codes. Unlike previous unitary approaches whose fault-distance remains constant with increasing code distance, our scheme ensures that the protection offered by the code is preserved during state preparation. Building on strategies discovered by reinforcement learning for the surface-17 code, we generalize the construction to arbitrary code distances and both rotated and unrotated surface codes. The proposed encoding relies only on geometrically local gates, and is therefore fully compatible with planar 2D qubit connectivity, and it achieves circuit depth scaling as $\mathcal{O}(d)$, consistent with fundamental entanglement-generation bounds. We design explicit stabilizer-expanding circuits with and without ancilla-mediated connectivity and analyze their error-propagation behavior. Numerical simulations under depolarizing noise show that our unitary encoding without ancillas outperforms standard stabilizer-measurement-based schemes, reducing logical error rates by up to an order of magnitude. These results make the scheme particularly relevant for platforms such as trapped ions and neutral atoms, where measurements are costly relative to gates and idling noise is considerably weaker than gate noise. Our work bridges the gap between measurement-based and unitary encodings of surface-code states and opens new directions for distance-preserving state preparation in fault-tolerant quantum computation.

The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient control, calibration and validation of quantum states and their dynamics. Although the full simulation of large-scale quantum systems may only be possible on a quantum computer, classical characterization and optimization methods still play an important role. Here, we review different approaches that use classical post-processing techniques, possibly combined with adaptive optimization, to learn quantum systems, their correlation properties, dynamics and interaction with the environment. We discuss theoretical proposals and successful implementations across different multiple-qubit architectures such as spin qubits, trapped ions, photonic and atomic systems, and superconducting circuits. This Review provides a brief background of key concepts recurring across many of these approaches with special emphasis on the Bayesian formalism and neural networks.

How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this work, we analyse and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-$1/2$ particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions even for the long-time non-integrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.

Superconducting circuits are among the leading contenders for quantum information processing. This promising avenue has been strengthened with the advent of circuit quantum electrodynamics, underlined by recent experiments coupling on-chip microwave resonators to superconducting qubits. However, moving towards more qubits will require suitable novel architectures. Here, we propose a scalable setup for quantum computing where such resonators are arranged in a two-dimensional grid with a qubit at each intersection. Its versatility allows any two qubits on the grid to be coupled at a swapping overhead independent of their distance and yields an optimal balance between reducing qubit transition frequency spread and spurious cavity-induced couplings. These features make this setup unique and distinct from existing proposals in ion traps, optical lattices, or semiconductor spins. We demonstrate that this approach encompasses the fundamental elements of a scalable fault-tolerant quantum computing architecture.