RQS Seminar

Suppressing errors is the central challenge for quantum computers to become practically relevant. The paradigmatic approach to this is quantum error correction, which uses quantum codes—redundantly encoded ‘logical qubits’—in combination with repeated rounds of error detection and correction. In this work, we report the realization of a quantum processor whose fundamental processing units are such logical qubits. The processor is based on reconfigurable arrays of neutral atoms in optical tweezers.

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics.

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems.

A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. In this talk, I will introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call “hyperbolic Floquet codes.” These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature.

In this talk, Dr Bermúdez will start by reviewing the recent progress of analog quantum simulators based on crystals of trapped atomic ions. He will discuss recent experiments that exploit both the electronic and vibrational degrees of freedom to simulate spin models and bosonic lattice models.

Circuit QED enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e., oscillator) operations are realizable only through optimal control theory (OCT) which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter and Baker–Campbell–Hausdorff product formulas.

Hamiltonian simulation is one of the most promising applications of quantum computing. Recent experimental results suggest that continuous-time analog quantum simulation would be advantageous over gate-based digital quantum simulation in the Noisy Intermediate-Size Quantum (NISQ) machine era. However, programming such analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software, and the only few known examples are all hardware-specific.

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Trapped-ion quantum computers provide a pristine one-dimensional spin system, featuring high isolation from the environment, high-fidelity measurement and preparation of individual spins, and fully connected spin-spin interactions.

Trapped atomic ions are a highly versatile platform for quantum simulation and computation. In this talk, I will provide a brief description of the quantum control that enables both analog and digital modes of quantum simulation on this platform before reporting on two recent results: a digital quantum simulation that measured the first out-of-time-order correlators in a thermal system, and an analog simulation of particles with exotic statistics.

Abstract: The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum information and thermodynamics.