Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. Here, we explore a surprising connection between mixed-state entanglement and ’t Hooft anomaly. More specifically, we consider lattice systems in $d$ space dimensions with anomalous symmetry $G$ where the anomaly is characterized by an invariant in the group cohomology $H^{d+2}[G,U(1)]$. We show that any mixed state $\rho$ that is strongly symmetric under $G$, in the sense that $G\rho \propto \rho$ is necessarily ($d+2$)-nonseparable, i.e., is not the mixture of tensor products of $d+2$ states in the Hilbert space. Furthermore, such states cannot be prepared from any ($d+2$)-separable states using finite-depth local quantum channels, so the nonseparability is long-ranged in nature. We provide proof of these results in $d\le 1$ and plausibility arguments in $d>1$. The anomaly-nonseparability connection, thus, allows us to generate simple examples of mixed states with nontrivial long-ranged multipartite entanglement. In particular, in $d=1$ we find an example of intrinsically mixed quantum phase, in the sense that states in this phase cannot be two-way connected to any pure state through finite-depth local quantum channels. We also analyze a mixed anomaly involving both strong and weak symmetries, including systems constrained by the Lieb-Schultz-Mattis type of anomaly. We find that, while strong-weak mixed anomaly, in general, does not constrain quantum entanglement, it does constrain long-range correlations of mixed states in nontrivial ways. Namely, such states are not symmetrically invertible and not gapped Markovian, generalizing familiar properties of anomalous pure states.

We find that the presence of strong non-Abelian symmetries can lead to highly entangled stationary states even for unital quantum channels. We derive exact expressions for the bipartite logarithmic negativity, Rényi negativities, and operator space entanglement for stationary states restricted to one symmetric subspace, with focus on the trivial subspace. We prove that these apply to open quantum evolutions whose commutants, characterizing all strongly conserved quantities, correspond to either the universal enveloping algebra of a Lie algebra or the Read-Saleur commutants. The latter provides an example of quantum fragmentation, whose dimension is exponentially large in system size. We find a general upper bound for all these quantities given by the logarithm of the dimension of the commutant on the smaller bipartition of the chain. As Abelian examples, we show that strong U(1) symmetries and classical fragmentation lead to separable stationary states in any symmetric subspace. In contrast, for non-Abelian $\mathrm{SU}(N)$ symmetries, both logarithmic and Rényi negativities scale logarithmically with system size. Finally, we prove that, while Rényi negativities with $n>2$ scale logarithmically with system size, the logarithmic negativity (as well as generalized Rényi negativities with $n<2$) exhibits a volume-law scaling for the Read-Saleur commutants. Our derivations rely on the commutant possessing a Hopf algebra structure in the limit of infinitely large systems and, hence, also apply to finite groups and quantum groups.

Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic level. We introduce a one-dimensional stabilizer Hamiltonian composed of group-based Pauli operators whose ground state is a $G\times \mathrm{Rep}(G)$-symmetric state: the $G$-cluster state introduced by Brell [New J. Phys. 17, 023029 (2015)]. We show that this state lies in a symmetry-protected topological (SPT) phase protected by $G\times \mathrm{Rep}(G)$ symmetry, distinct from the symmetric product state by a duality argument. We identify several signatures of SPT order, namely, protected edge modes, string order parameters, and topological response. We discuss how $G$-cluster states may be used as a universal resource for measurement-based quantum computation, explicitly working out the case where $G$ is a semidirect product of Abelian groups.

Floquet (periodically driven) systems can give rise to unique nonequilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: What other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasiperiodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasicrystals. Unlike conventional time crystals, time quasicrystals exhibit robust subharmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multifrequency nature of the quasiperiodic drive allows for the formation of diverse patterns associated with different discrete time quasicrystalline phases. Our findings demonstrate the existence of nonequilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems.

Multiplexed operations and extended coherent control over multiple trapping sites are fundamental requirements for a trapped-ion processor in a large-scale architecture. Here, we demonstrate these building blocks using a surface-electrode trap with integrated photonic components which are scalable to larger numbers of zones. We implement a Ramsey sequence using the integrated light in two zones, separated by $375\mathrm{\mu }\mathrm{m}$, performing transport of the ion from one zone to the other in $200\mathrm{\mu }\mathrm{s}$ between pulses. In order to achieve low motional excitation during transport, we develop techniques to measure and mitigate the effect of the exposed dielectric surfaces used to deliver the integrated light to the ion. We also demonstrate simultaneous control of two ions in separate zones with low optical crosstalk and use this to perform simultaneous spectroscopy to correlate field noise between the two sites. Our work demonstrates the first transport and coherent multizone operations in integrated photonic ion trap systems, forming the basis for further scaling in the trapped-ion quantum charge-coupled device architecture.

We propose a novel approach to generate, protect, and control Gottesman-Kitaev-Preskill (GKP) qubits. It employs a microwave frequency comb parametrically modulating a Josephson circuit to enforce a dissipative dynamics of a high-impedance circuit mode, autonomously stabilizing the finite-energy GKP code. The encoded GKP qubit is robustly protected against all dominant decoherence channels plaguing superconducting circuits but quasiparticle poisoning. In particular, noise from ancillary modes leveraged for dissipation engineering does not propagate at the logical level. In a state-of-the-art experimental setup, we estimate that the encoded qubit lifetime could extend 2 orders of magnitude beyond the break-even point, with substantial margin for improvement through progress in fabrication and control electronics. Qubit initialization, readout, and control via Clifford gates can be performed while maintaining the code stabilization, paving the way toward the assembly of GKP qubits in a fault-tolerant quantum computing architecture.

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of anti–de Sitter black holes. In this context, Brown and Susskind [Phys. Rev. D 97, 086015 (2018)] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly exponential times. In this work, we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behavior of chaotic quantum systems and could shed light on the physics of black-hole interiors. From a technical perspective, our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs.

Quantum Darwinism is a paradigm to understand how classically objective reality emerges from within a fundamentally quantum universe. Despite the growing attention that this field of research has been enjoying, it is currently not known what specific properties a given Hamiltonian describing a generic quantum system must have to allow the emergence of classicality. Therefore, in the present work, we consider a broadly applicable generic model of an arbitrary finite-dimensional system interacting with an environment formed from an arbitrary collection of finite-dimensional degrees of freedom via an unspecified, potentially time-dependent Hamiltonian containing at most two-body interaction terms. We show that such models support quantum Darwinism if the set of operators acting on the system which enter the Hamiltonian satisfy a set of commutation relations with a pointer observable and with one other. We demonstrate our results by analyzing a wide range of example systems: a qutrit interacting with a qubit environment, a qubit-qubit model with interactions alternating in time, and a series of collision models including a minimal model of a quantum Maxwell demon.

While data qubits with a long coherence time are essential for the storage of quantum information, ancilla qubits are pivotal in quantum error correction (QEC) for fault-tolerant quantum computing. The recent development of optical tweezer arrays, such as the preparation of large-scale qubit arrays and high-fidelity gate operations, offers the potential for realizing QEC protocols, and one of the important next challenges is to control and detect ancilla qubits while minimizing atom loss and crosstalk. Here, we present the realization of a hybrid system consisting of a dual-isotope ytterbium (Yb) atom array, in which we can utilize a nuclear spin qubit of fermionic ${}^{171}\mathrm{Yb}$ as a data qubit and an optical clock qubit of bosonic ${}^{174}\mathrm{Yb}$ as an ancilla qubit with a capacity of nondestructive qubit readout. We evaluate the crosstalk between qubits regarding the impact on the coherence of the nuclear spin qubits from the imaging light for ${}^{174}\mathrm{Yb}$. For the Hahn-echo sequence with a 399 nm probe and 556 nm cooling beams for ${}^{174}\mathrm{Yb}$, we observe 99.1(1.8)% coherence retained under 20 ms exposure, yielding a discrimination fidelity of 0.9992 and a survival probability of 0.988. The Ramsey sequence with a 556 nm probe beam shows negligible influence on the coherence, suggesting the potential future improvement of low crosstalk measurements. This result highlights the potential of the hybrid-Yb atom array for midcircuit measurements for ancilla-qubit-based QEC protocols.

Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum ergodicity for closed systems with time-dependent Hamiltonians, defined as statistical randomness exhibited in their longtime dynamics. Concretely, we consider the temporal ensemble of quantum states (time-evolution operators) generated by the evolution, and investigate the conditions necessary for them to be statistically indistinguishable from uniformly random states (operators) in the Hilbert space (space of unitaries). We find that the number of driving frequencies underlying the Hamiltonian needs to be sufficiently large for this to occur. Conversely, we show that statistical pseudo-randomness—indistinguishability up to some large but finite moment—can already be achieved by a quantum system driven with a single frequency, i.e., a Floquet system, as long as the driving period is sufficiently long. Our work relates the complexity of a time-dependent Hamiltonian and that of the resulting quantum dynamics, and offers a fresh perspective to the established topics of quantum ergodicity and chaos from the lens of quantum information.

Decoherence in qubits, caused by their interaction with a noisy environment, poses a significant challenge to the development of reliable quantum processors. A prominent source of errors arises from noise in coupled ancillas, which can quickly spread to qubits. By actively monitoring these noisy ancillas, it is possible to not only identify qubit decoherence events but also to correct these errors in real time. This approach is particularly beneficial for bosonic qubits, where the interaction with ancillas is a dominant source of decoherence. In this work, we uncover the intricate dynamics of decoherence in a superconducting cavity qubit due to its interaction with a noisy transmon ancilla. By tracking the noisy ancilla trajectory and using real-time feedback, we successfully recover the lost coherence of the cavity qubit, achieving a fivefold increase in its pure dephasing time. Additionally, by detecting ancilla errors and converting them into erasures, we improve the pure dephasing time by more than an order of magnitude. These advances are essential for realizing long-lived cavity qubits with high-fidelity gates, and they pave the way for more efficient bosonic quantum error-correction codes.

When an ensemble of quantum emitters couples to a common radiation field, their polarizations can synchronize and a collective emission termed superfluorescence can occur. Entering this regime in a free-space setting requires a large number of emitters with a high spatial density as well as coherent optical transitions with small inhomogeneity. Here, we show that, by coupling nitrogen-vacancy centers in a diamond membrane to a high-finesse microcavity, also few, incoherent, inhomogeneous, and spatially separated emitters—as are typical for solid state systems—can enter the regime of collective emission. We observe a superlinear power dependence of the emission rate as a hallmark of collective emission. Furthermore, we find simultaneous photon bunching and antibunching on different timescales in the second-order autocorrelation function, revealing cavity-induced interference in the quantized emission from about 15 emitters. We develop theoretical models for mesoscopic emitter numbers to analyze the behavior in the Dicke state basis and find that the population of collective states together with cavity enhancement and filtering can explain the observations. Such a system has prospects for the generation of multiphoton quantum states, the preparation of entanglement in few-emitter systems, and enhancement of signals in quantum sensing.

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools.

Striving for higher gate fidelity is crucial not only for enhancing existing noisy intermediate-scale quantum devices, but also for unleashing the potential of fault-tolerant quantum computation through quantum error correction. A recently proposed theoretical scheme, the double-transmon coupler (DTC), aims to achieve both suppressed residual interaction and a fast high-fidelity two-qubit gate simultaneously, particularly for highly detuned qubits. Harnessing the state-of-the-art fabrication techniques and a model-free pulse-optimization process based on reinforcement learning, we translate the theoretical DTC scheme into reality, attaining fidelities of 99.90% for a controlled-$Z$ gate and 99.98% for single-qubit gates. The performance of the DTC scheme demonstrates its potential as a competitive building block for superconducting quantum processors.

The Kerr-cat qubit is a bosonic qubit in which multiphoton Schrödinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By integrating an effective band-block filter on chip, we overcome this trade-off and realize a Kerr-cat qubit in a scalable 2D superconducting circuit with high coherence. This filter provides 30 dB of isolation at the qubit frequency with negligible attenuation at the frequencies required for stabilization and readout. We experimentally demonstrate quantum nondemolition readout fidelity of 99.6% for a cat with eight photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the $X(\pi /2)$ gate through phase modulation of the stabilization drive. Finally, the lifetime in this architecture is examined as a function of the cat size of up to ten photons in the oscillator, achieving a bit-flip time higher than 1 ms and only a linear increase in the phase-flip rate, in good agreement with the theoretical analysis of the circuit. Our qubit shows promise as a building block for fault-tolerant quantum processors with a small footprint.

In recent demonstrations of the quantum charge-coupled device computer architecture, circuit times are dominated by cooling. Some motional modes of multi-ion crystals take orders of magnitude longer to cool than others because of low coolant ion participation. Here we demonstrate a new technique, that solves this issue by coherently exchanging the thermal populations of selected modes on timescales short compared to direct cooling. Using this method, which we call “phonon rapid adiabatic passage,” we can achieve subquanta temperatures from initial states with occupations as high as $\overline{n}\sim 200$ quanta. Analogous to adiabatic rapid passage, we quasistatically couple these slow-cooling modes with fast-cooling modes using dc electric fields. When the crystal is then adiabatically ramped through the resultant avoided crossing, nearly complete phonon population exchange results. We demonstrate this on two-ion crystals, and show the indirect ground-state cooling of all radial modes—achieving an order of magnitude speedup compared to direct cooling. We also show the technique’s insensitivity to trap potential and control field fluctuations, and find that it still achieves subquanta temperatures starting as high as $\overline{n}\sim 200$.

Attosecond physics enables the study of ultrafast coherent electron dynamics in matter upon photoexcitation and photoionization, revealing spectacular effects such as hole migration and coherent Auger dynamics in molecules. In the photoionization scenario, there has been a strong focus on probing the physical manifestations of internal quantum coherence within the individual parent ion and photoelectron systems. However, quantum correlations between these two subsystems emerging from attosecond photoionization events have thus far remained much more elusive. In this work, we design theoretically and model numerically a direct probe of quantum entanglement in attosecond photoionization in the form of a Bell test. We simulate from first principles a Bell test protocol for the case of noble gas atoms photoionized by ultrashort, circularly polarized infrared laser pulses in the strong-field regime predicting robust violation of the Bell inequality. This theoretical result paves the way for the direct observation of entanglement in the context of ultrafast photoionization of many-electron systems. Our work provides a novel perspective on attosecond physics directed toward the detection of quantum correlations between systems born during attosecond photoionization and unraveling the signatures of entanglement in ultrafast coherent molecular dynamics, including in the chemical decomposition pathways of molecular ions.

We show that the path integral of conformal field theories in $D$ dimensions (${\mathrm{CFT}}_D$) can be constructed by solving for eigenstates of a renormalization group (RG) operator following from the Turaev-Viro formulation of a topological field theory (topological quantum field theory) (TQFT) in $D+1$ dimensions (${\mathrm{TQFT}}_{D+1}$), explicitly realizing the holographic sandwich relation between a symmetric theory and a TQFT. Generically, exact eigenstates corresponding to symmetric ${\mathrm{TQFT}}_D$ follow from Frobenius algebra in ${\mathrm{TQFT}}_{D+1}$. For $D=2$, we construct eigenstates that produce 2D rational CFT path integrals exactly, which curiously connect a continuous-field theoretic path integral with the Turaev-Viro state sum. We also devise and illustrate numerical methods for $D=2$, 3 to search for ${\mathrm{CFT}}_D$ as phase transition points between symmetric ${\mathrm{TQFT}}_D$. Finally, since the RG operator is in fact an exact analytic holographic tensor network, we compute “bulk-boundary” correlators and compare them with the AdS/CFT dictionary at $D=2$. Promisingly, they are numerically compatible given our accuracy, although further works will be needed to explore the precise connection to the AdS/CFT correspondence.

Following recent progress in the experimental application of electro-optic sampling to the detection of the quantum fluctuations of the electromagnetic-field ground state and ultrabroadband squeezed states on a subcycle scale, we propose an approach to elevate broadband electro-optic sampling from a spectroscopic method to a full quantum tomography scheme, able to reconstruct a free-space quantum state directly in the time domain. By combining two recently developed methods to theoretically describe quantum electro-optic sampling, we analytically relate the photon-count probability distribution of the electro-optic signal to a transformed phase-space quasiprobability distribution of the sampled quantum state as a function of the time delay between the sampled midinfrared pulsed state and an ultrabroadband near-infrared probe pulse. We catalog and analyze sources of noise and show that in quantum electro-optic sampling with an ultrabroadband probe pulse one can expect to observe thermalization due to entanglement breaking. Mitigation of the thermalization noise enables a tomographic reconstruction of broadband quantum states while granting access to its dynamics on a subcycle scale.

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors of the non-Hermitian operators that generate the dynamics, i.e., quantum channels (Markov chains). However, since these operators are non-Hermitian, their spectra are an unreliable guide to dynamical relaxation timescales or to stability against perturbations. We propose an alternative dynamical criterion for a steady state to be in a stable phase, which we name uniformity: Informally, our criterion amounts to requiring that, under sufficiently small local perturbations of the dynamics, the unperturbed and perturbed steady states are related to one another by a finite-time dissipative evolution. We show that this criterion implies many of the properties one would want from any reasonable definition of a phase. We prove that uniformity is satisfied in a canonical classical cellular automaton, and we provide numerical evidence that the gap determines the relaxation rate between nearby steady states in the same phase, a situation we conjecture holds generically whenever uniformity is satisfied. We further conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability.