We introduce a family of local models of dynamics based on “word problems” from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random circuit or local Hamiltonian dynamics and include many familiar examples of constrained dynamics as special cases. The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must “work out” the other states in the sector to which they belong. When this problem has a high time complexity, relaxation is slow. In some of the cases we study, this problem also has high space complexity. When the space complexity is larger than the system size, an unconventional type of jamming transition can occur, whereby a system of a fixed size is not ergodic but can be made ergodic by appending a large reservoir of sites in a trivial product state. This finding manifests itself in a new type of Hilbert space fragmentation that we call fragile fragmentation. We present explicit examples where slow relaxation and jamming strongly modify the hydrodynamics of conserved densities. In one example, density modulations of wave vector $q$ exhibit almost no relaxation until times $O\mathbf{(}\exp (1/q)\mathbf{)}$, at which point they abruptly collapse. We also comment on extensions of our results to higher dimensions.

Programmable quantum devices are now able to probe wave functions at unprecedented levels. This is based on the ability to project the many-body state of atom and qubit arrays onto a measurement basis which produces snapshots of the system wave function. Extracting and processing information from such observations remains, however, an open quest. One often resorts to analyzing low-order correlation functions—that is, discarding most of the available information content. Here, we introduce wave-function networks—a mathematical framework to describe wave-function snapshots based on network theory. For many-body systems, these networks can become scale-free—a mathematical structure that has found tremendous success and applications in a broad set of fields, ranging from biology to epidemics to Internet science. We demonstrate the potential of applying these techniques to quantum science by introducing protocols to extract the Kolmogorov complexity corresponding to the output of a quantum simulator and implementing tools for fully scalable cross-platform certification based on similarity tests between networks. We demonstrate the emergence of scale-free networks analyzing experimental data obtained with a Rydberg quantum simulator manipulating up to 100 atoms. Our approach illustrates how, upon crossing a phase transition, the simulator complexity decreases while correlation length increases—a direct signature of buildup of universal behavior in data space. Comparing experiments with numerical simulations, we achieve cross-certification at the wave-function level up to timescales of $4\mathrm{\mu }\mathrm{s}$ with a confidence level of 90% and determine experimental calibration intervals with unprecedented accuracy. Our framework is generically applicable to the output of quantum computers and simulators with in situ access to the system wave function and requires probing accuracy and repetition rates accessible to most currently available platforms.

Coherence time and gate fidelities in Rydberg atom quantum simulators and computers are fundamentally limited by the Rydberg state lifetime. Circular Rydberg states are highly promising candidates to overcome this limitation by orders of magnitude, as they can be effectively protected from decay due to their maximum angular momentum. We report the first realization of alkaline-earth circular Rydberg atoms trapped in optical tweezers, which provide unique and novel control possibilities due to the optically active ionic core. Specifically, we demonstrate creation of very high-$n$ ($n=79$) circular states of ${}^{88}\mathrm{Sr}$. We measure lifetimes as long as 2.55 ms at room temperature, which are achieved via cavity-assisted suppression of black-body radiation. We show coherent control of a microwave qubit encoded in circular states of nearby manifolds, and characterize the qubit coherence time via Ramsey and spin-echo spectroscopy. Finally, circular-state tweezer trapping exploiting the ${\mathrm{Sr}}^{+}$ core polarizability is quantified via measurements of the trap-induced light shift on the qubit. Our work opens routes for quantum simulations with circular Rydberg states of divalent atoms, exploiting the emergent toolbox associated with the optically active core ion.

First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon ($e\text{−}\mathrm{ph}$) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For $e\text{−}\mathrm{ph}$ interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress $e\text{−}\mathrm{ph}$ interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to $e\text{−}\mathrm{ph}$ interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of $e\text{−}\mathrm{ph}$ interactions. Furthermore, they accelerate state-of-the-art first-principles $e\text{−}\mathrm{ph}$ calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of $e\text{−}\mathrm{ph}$ interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter.

Cat qubits, for which logical $|0⟩$ and $|1⟩$ are coherent states $|\pm \alpha ⟩$ of a harmonic mode, offer a promising route towards quantum error correction. Using dissipation to our advantage so that photon pairs of the harmonic mode are exchanged with single photons of its environment, it is possible to stabilize the logical states and exponentially increase the bit-flip time of the cat qubit with the photon number $|\alpha {|}^2$. A large two-photon dissipation rate ${\kappa }_2$ ensures fast qubit manipulation and short error-correction cycles, which are instrumental to correct the remaining phase-flip errors in a repetition code of cat qubits. Here, we introduce and operate an autoparametric superconducting circuit that couples a mode containing the cat qubit to a lossy mode whose frequency is set at twice that of the cat mode. This passive coupling does not require a parametric pump, and it reaches a rate ${\kappa }_2/2\pi \approx 2\mathrm{MHz}$. With such a strong two-photon dissipation, bit-flip errors of the autoparametric cat qubit are prevented for a characteristic time up to 0.3 s with only a mild impact on phase-flip errors. In addition, we illustrate how the phase of a quantum superposition between $|\alpha ⟩$ and $|-\alpha ⟩$ can be arbitrarily changed by driving the harmonic mode while keeping the engineered dissipation active.

A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different species of quasiparticles, which can get stuck at high enough density, realizing the quantum analog of jamming. We identify a family of interactions satisfying simple kinetic constraints and consider generic translationally invariant models built up from them. We study dynamics following a local unjamming perturbation in a jammed state. We show that they can be mapped into dynamics of ordinary unconstrained systems, but the nonlocality of the mapping changes the scales at which the phenomena manifest themselves. Scattering of quasiparticles, formation of bound states, and eigenstate localization become all visible at macroscopic scales. Depending on whether a symmetry is present or not, the microscopic details of the jammed state turn out to have either a marginal or a strong effect. In the former case or when the initial state is almost homogeneous, we show that even a product state is turned into a macroscopic quantum state.

We propose multilayer moiré structures in strong external magnetic fields as a novel platform for realizing highly tunable, frustrated Hubbard physics with topological order. Identifying the layer degree of freedom as a pseudospin allows us to retain SU(2) symmetry while controlling ring-exchange processes and concurrently quenching the kinetic energy by large external magnetic fields. This way, a broad class of interacting Hubbard-Hofstadter states and their transitions can be studied. Remarkably, in the limit of strong interactions the system becomes Mott insulating and we find chiral pseudospin-liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable toward relevant perturbations. We discuss how layer pseudospin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moiré systems, our approach provides a promising route toward the experimental realization and control of topologically ordered phases of matter.

The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to investigate non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. Our theory provides a general framework for studying non-Hermitian bands beyond one dimension. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.

Cooling the motion of trapped ions to near the quantum ground state is crucial for many applications in quantum information processing and quantum metrology. However, certain motional modes of trapped-ion crystals can be difficult to cool due to weak or zero interaction between the modes and the cooling radiation, typically laser beams. We overcome this challenge by coupling a mode that interacts weakly with cooling radiation to one that interacts strongly with cooling radiation using parametric modulation of the trapping potential, thereby enabling indirect cooling of the weakly interacting mode. In this way, we demonstrate near-ground-state cooling of motional modes with weak or zero cooling radiation interaction in multi-ion crystals of the same and mixed ion species, specifically ${}^9{\mathrm{Be}}^{+}\text{−}{}^9{\mathrm{Be}}^{+}$, ${}^9{\mathrm{Be}}^{+}\text{−}{}^{25}{\mathrm{Mg}}^{+}$, and ${}^9{\mathrm{Be}}^{+}\text{−}{}^{25}{\mathrm{Mg}}^{+}\text{−}{}^9{\mathrm{Be}}^{+}$ crystals. This approach can be generally applied to any Coulomb crystal where certain motional modes cannot be directly cooled efficiently, including crystals containing molecular ions, highly charged ions, charged fundamental particles, or charged macroscopic objects.

Coupled cluster theory is one of the most popular post-Hartree-Fock methods for ab initio molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating systems has been observed to satisfy the inverse volume scaling, even in the absence of any correction schemes. This is surprising, as simpler theories that utilize only a subset of the coupled cluster diagrams exhibit much slower decay of the finite-size error, which scales inversely with the length of the system. In this study, we review the current understanding of finite-size error in quantum chemistry methods for periodic systems. We introduce new tools that elucidate the mechanisms behind this phenomenon in the context of coupled cluster doubles calculations. This reconciles some seemingly paradoxical statements related to finite-size scaling. Our findings also show that singularity subtraction can be a powerful method to effectively reduce finite-size errors in practical quantum chemistry calculations for periodic systems.

Electrostrictive Brillouin scattering provides a ubiquitous mechanism to optically excite high-frequency ($>10\mathrm{GHz}$), bulk acoustic phonons that are robust to surface-induced losses. Resonantly enhancing such photon-phonon interactions in high-$Q$ microresonators has spawned diverse applications spanning microwave to optical domains. However, tuning both the pump and scattered waves into resonance usually comes with the cost of photon confinement or modal overlap, leading to limited optomechanical coupling. Here, we introduce Bragg scattering to realize strong bulk optomechanical coupling in the same spatial modes of a micron-sized supermode microresonator. A single-photon optomechanical coupling rate up to 12.5 kHz is demonstrated, showing more than 10 times improvement than other devices. Low-threshold phonon lasing and optomechanical strong coupling are also observed for the 10.2-GHz mechanical mode. Our work establishes a compact and efficient paradigm to optically control bulk acoustic phonons, paving the way toward optomechanical coupling at the single-photon level and providing a powerful engine for large-scale integration of quantum networks in which quantum states are massively transferred and stored.

Bosonic encoding is an approach for quantum information processing, promising lower hardware overhead by encoding in the many levels of a harmonic-oscillator mode. Scaling to multiple modes requires weak interaction for independent control, yet strong interaction for fast control. Applying fast and efficient universal control on multiple modes remains an open problem. Surprisingly, we find that displacements conditioned on the state of a single-qubit ancilla coupled to multiple harmonic oscillators are sufficient for universal control. We present the conditional-no operation concept, which can be used to reduce the duration of entangling gates. Within this guiding concept, we develop the conditional-not displacement control method which enables fast generation and control of bosonic states in multimode systems weakly coupled to a single-ancilla qubit. Our method is fast despite the weak ancilla coupling. The weak coupling in turn allows for excellent separability and thus independent control. We demonstrate our control on a superconducting transmon qubit weakly coupled to a multimode superconducting cavity. We create both entangled and separable cat states in different modes of the multimode cavity, showing entangling operations at low crosstalk while maintaining independent control of the different modes. We show that the operation time is not limited by the inverse of the coupling rate, which is the typical timescale, and we exceed it by almost 2 orders of magnitude. We verify our results with an efficient method for measurement of the multimode characteristic function which employs our conditional-not displacement. Our results inspire a new approach toward general entangling operations and allow for fast and efficient multimode bosonic encoding and measurement.

Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a “dual-rail qubit” consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon $T_1$ errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability $p_{\text{erasure}}=2.19(2)\times {10}^{-3}$ per gate while the residual errors are $\sim 40$ times lower. We further demonstrate midcircuit detection of erasure errors while introducing $<0.1\%$ dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction.

Quantum simulators built from ultracold atoms promise to study quantum phenomena in interacting many-body systems. However, it remains a challenge to experimentally prepare strongly correlated continuous systems such that the properties are dominated by quantum fluctuations. Here, we show how to enhance the quantum correlations in a one-dimensional multimode bosonic Josephson junction, which is a quantum simulator of the sine-Gordon field theory. Our approach is based on the ability to track the nonequilibrium dynamics of quantum properties. After creating a bosonic Josephson junction at the stable fixed point of the classical phase space, we observe squeezing oscillations in the two conjugate variables. We show that the squeezing oscillation frequency can be tuned by more than one order of magnitude, and we are able to achieve a spin squeezing close to 10 dB by utilizing these oscillatory dynamics. The impact of improved spin squeezing is directly revealed by detecting enhanced spatial phase correlations between decoupled condensates. Our work provides new ways for engineering correlations and entanglement in the external degree of freedom of interacting many-body systems.

Quantum systems with engineered Hamiltonians can be used to study many-body physics problems to provide insights beyond the capabilities of classical computers. Semiconductor gate-defined quantum dot arrays have emerged as a versatile platform for realizing generalized Fermi-Hubbard physics, one of the richest playgrounds in condensed matter physics. In this work, we employ a germanium $4\times 2$ quantum dot array and show that the naturally occurring long-range Coulomb interaction can lead to exciton formation and transport. We tune the quantum dot ladder into two capacitively coupled channels and exploit Coulomb drag to probe the binding of electrons and holes. Specifically, we shuttle an electron through one leg of the ladder and observe that a hole is dragged along in the second leg under the right conditions. This corresponds to a transition from single-electron transport in one leg to exciton transport along the ladder. Our work paves the way for the study of excitonic states of matter in quantum dot arrays.

Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term—equivalently, the adiabatic gauge potential—is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term.

We study two-dimensional (2D) droplets of noninteracting electrons in a strong magnetic field, placed in a confining potential with arbitrary shape. Using semiclassical methods adapted to the lowest Landau level, we obtain near-Gaussian energy eigenstates that are localized on level curves of the potential and have a position-dependent height. This one-particle insight allows us to deduce explicit formulas for expectation values of local many-body observables, such as density and current, in the thermodynamic limit. In particular, correlations along the edge are long-ranged and inhomogeneous. As we show, this is consistent with the system’s universal low-energy description as a free 1D chiral conformal field theory of edge modes, known from earlier works in simple geometries. A delicate interplay between radial and angular dependencies of eigenfunctions ultimately ensures that the theory is homogeneous in terms of the canonical angle variable of the potential, despite its apparent inhomogeneity in terms of more naïve angular coordinates. Finally, we propose a scheme to measure the anisotropy by subjecting the droplet to microwave radiation; we compute the corresponding absorption rate and show that it depends on the droplet’s shape and the waves’ polarization. These results, both local and global, are likely to be observable in solid-state systems or quantum simulators of 2D electron gases with a high degree of control on the confining potential.

We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass. A close connection between open quantum dynamics and replica symmetry breaking is established, in which individual quantum trajectories are the replicas. We observe that entanglement plays an important role in the emergence of replica symmetry breaking in a fully connected, frustrated spin network of up to 15 spin-$1/2$ particles. Quantum trajectories of entangled spins reach steady-state spin configurations of lower energy than that of semiclassical trajectories. Cavity emission allows monitoring of the continuous stochastic evolution of spin configurations, while backaction from this projects entangled states into states of broken Ising and replica symmetry. The emergence of spin glass order manifests itself through the simultaneous absence of magnetization and the presence of nontrivial spin overlap density distributions among replicas. Moreover, these overlaps reveal incipient ultrametric order, in line with the Parisi replica symmetry breaking solution for the Sherrington-Kirkpatrick model. A nonthermal Parisi order parameter distribution, however, highlights the driven-dissipative nature of this quantum optical spin glass. This practicable system could serve as a test bed for exploring how quantum effects enrich the physics of spin glasses.

High-precision atomic spectroscopy provides an invaluable and sensitive tool for exploring a wide range of physical questions. Here, we investigate the forbidden optical transition of the $6s6p{{}^{3}P}_0-4f^{13}5d6s^2$ ($J=2$) in ${}^{171}\mathrm{Y}\mathrm{b}$ atoms at the wavelength of 1695 nm, which exhibits the highest sensitivity to the variation of the fine-structure constant $\alpha$ compared to the current neutral optical clock. We obtain high-resolution transition spectroscopy in a one-dimensional optical lattice, and the measurement of its absolute frequency achieves kHz-level accuracy. Meanwhile, several essential atomic constants are also determined, including the electric-dipole ($E1$) magic wavelengths, as well as the hyperpolarizabilities and tensor polarizabilities around the $E1$ magic wavelengths. Additionally, we derive the hyperfine constant for the $J=2$ state from the measured absolute frequencies $1123252.3\pm 2.0\mathrm{kHz}$, providing a sixfold enhancement in the uncertainty reduction compared to the recent result. We anticipate that this work will prompt further investigation of the additional clock transition at 1695 nm in ${}^{171}\mathrm{Y}\mathrm{b}$ atoms. Together with the well-established ${}^1{S}_0\text{−}{}^3{P}_0$ transition, many fundamental and new physics research, such as the time variation of $\alpha$, ultralight dark-matter searches, Lorentz violation, etc., will enable new bounds and measurements with unprecedented precision.

We experimentally investigate the collective radiative decay of a fully inverted ensemble of two-level atoms for a chiral, i.e., propagation direction-dependent light-matter coupling. Despite a fundamentally different interaction Hamiltonian which has a reduced symmetry compared to the standard Dicke case of superradiance, we do observe a superradiant burst of light. The burst occurs above a threshold number of atoms, and its peak power scales faster with the number of atoms than in the case of free-space Dicke superradiance. We measure the first-order coherence of the burst and experimentally distinguish two regimes, one dominated by the coherence induced during the excitation process and the other governed by vacuum fluctuations. Our results shed light on the collective radiative dynamics of cascaded quantum many-body systems, i.e., systems in which each quantum emitter is only driven by light radiated by emitters that are upstream in the cascade. Our findings may turn out useful for generating multiphoton Fock states as a resource for quantum technologies.