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Hybrid systems consisting of multiple materials with distinct physical properties and tunable interactions provide a promising route for fulfilling transformative quantum innovations. Solid-state spin qubits and superconducting circuits stand out as leading candidates in this context due to their complementary device performance and quantum mechanical properties. Here, we report experimental integration of a single nitrogen-vacancy (NV) spin qubit and an on-chip superconducting resonator for realizing multimodal quantum applications. Specifically, we have observed superconductivity enhanced NV spin relaxation, which shows a similar Hebel-Slichter peak feature around the phase transition point. In the coherent interaction regime, we show that the superconducting resonator mode is capable of exciting NV Rabi oscillations. Taking advantage of scanning NV magnetometry, we further visualized microscopic electromagnetic behaviors of the superconducting resonator, revealing the formation and evolution of superconducting vortices at the nanoscale. Our results highlight the potential of harnessing NV centers and superconducting circuits for designing hybrid systems to advance the burgeoning quantum revolution. The current study will also open a new pathway to test and evaluate miniaturized superconducting electronics for their future design and performance improvements.

We consider the stray magnetic field noise outside a two-dimensional superconductor. Our considerations are motivated by recent experiments, which observed an enhancement in the magnetic field noise below the superconducting critical temperature based on the relaxation of diamond nitrogen-vacancy centers. Such enhancement is not captured by the standard two-fluid model for the superconducting state, recently proposed to explain such NV relaxometry experiments. Instead, we show that a microscopic BCS theory captures such an enhancement, and we compare with a similar theory and phenomenon, known as the Hebel-Schlicter peak (or coherence peak), observed in the relaxation of nuclear spins in the material. The primary difference is that the NV probes long-wavelength magnetic noise outside the sample, while the nuclear spin probes local hyperfine noise inside the sample. Accordingly, the noise probed by the NV depends on its height and can probe, in pristine samples, the superfluid coherence length. Finally, we discuss potential avenues for NVs to probe unconventional superconductivity via deviations from the above BCS theory., Comment: 6+8 pages, 4 figures

We present how entanglement between a spatially separated pair of color centers can be created by letting them weakly interact with the quantum fluctuations of a nonequilibrium magnetic environment. To this end, we consider two coupled ferromagnets, one in the ground state and one in an inverted state with respect to an applied magnetic field. The resulting energetic instability leads to a quantum spin current in the vacuum state that is sustained by the creation of magnon-antimagnon pairs at the interface. We show that these quantum fluctuations imprint a steady-state entanglement onto the two dipole-coupled color centers through nonlocal dissipation. We derive conditions for establishing a maximally entangled Bell state. This entanglement is absent in thermal equilibrium., Comment: 6 pages, 3 figures

We introduce a pro-cdh topology on formal schemes and prove that the $\infty$-topos of pro-cdh sheaves of spaces has an optimal bound of homotopy dimension. This remedies a defect for a pro-cdh topology on schemes introduced in [KS23]. As an application, we give a topos-theoretic interpretation of Weibel's vanishing of negative K-theory and motivic cohomology of Elmanto and Morrow.

We prove a `pro-cdh descent' result for suitably connective localizing invariants and the cotangent complex on arbitrary qcqs derived schemes. As an application, we deduce a generalised Weibel vanishing for negative $K$-groups of non-Noetherian schemes., Comment: 28 pages

These are expanded notes from a talk at the RIMS Workshop, Algebraic Number Theory and Related Topics, December 13th, 2023. We discussed Elmanto-Morrow's motivic complex, the procdh sheafification of the classical motivic complex, and their comparison. The procdh topology and the comparison is joint work with Shuji Saito. The comparison was obtained through joint discussion with Morrow, and its proof relies heavily on the main results of [EM23]., Comment: Comments (including complaints) welcome

In this work we investigate the conditions for quantum back action to result in a phase transition in the information dynamics of a monitored system. We introduce a framework that captures a wide range of experiments encompassing probes comprised of projective measurements and probes which more generally transfer quantum information from the system to a quantum computer. Our framework explicitly uses a model of unitary evolution which couples system, apparatus and environment. Information dynamics is investigated using the R\'enyi and von-Neumann entropies of the evolving state, and we construct a replica theory for them. We identify the possible replica symmetries an experiment can possess and discuss their spontaneous symmetry breaking. In particular, we identify a minimum subgroup whose spontaneous symmetry breaking results in an entanglement transition. This symmetry is only possible when the information in the apparatus is as informative about the dynamics of the system as the information transferred to the environment. We call this requirement the information exchange symmetry and quantify it by a relationship between the entropies. We then show how the entanglement transition can be understood as the spontaneously breaking of the information exchange symmetry and without referring to the replica theory. Information exchange symmetry breaking is then shown to generalize the phenomenology of the measurement-induced phase transition (MIPT). We apply this theory to the brickwork quantum-enhanced experiment introduced in an accompanying Letter [Phys. Rev. A 111, L010402 (2025) ] in the case where the unitaries are chosen from the Haar measure, and identify a distinct universality from the MIPT. This notion of information exchange symmetry breaking generalizes the MIPT, and provides a framework for understanding the dynamics of quantum information in quantum-enhanced experiments., Comment: 27 pages, 12 figures. Phys. Rev. A 111, L010402 (2025) is the accompanying Letter. arXiv admin note: substantial text overlap with arXiv:2310.03061

We study a random unitary circuit model of an impurity moving through a chaotic medium. The exchange of information between the medium and impurity is controlled by varying the velocity of the impurity, $v_d$, relative to the speed of information propagation within the medium, $v_B$. Above supersonic velocities, $v_d> v_B$, information cannot flow back to the impurity after it has moved into the medium, and the resulting dynamics are Markovian. Below supersonic velocities, $v_d< v_B$, the dynamics of the impurity and medium are non-Markovian, and information is able to flow back onto the impurity. We show the two regimes are separated by a continuous phase transition with exponents directly related to the diffusive spreading of operators in the medium. This is demonstrated by monitoring an out-of-time-order correlator (OTOC) in a scenario where the impurity is substituted at an intermediate time. During the Markovian phase, information from the medium cannot transfer onto the replaced impurity, manifesting in no significant operator development. Conversely, in the non-Markovian phase, we observe that operators acquire support on the newly introduced impurity. We also characterize the dynamics using the coherent information and provide two decoders which can efficiently probe the transition between Markovian and non-Markovian information flow. Our work demonstrates that Markovian and non-Markovian dynamics can be separated by a phase transition, and we propose an efficient protocol for observing this transition., Comment: 19+4 pages, 11+5 figures

We consider a class of non-reduced valuation rings, known in the literature as chain rings. We observe that the Grothendieck topology generated by the Zariski topology and smooth blowup squares is exactly the topology which has chain rings for its local rings, and that sheaves for this topology are \emph{not} characterised by excision for smooth blowup squares., Comment: 13 pages

In this article we propose a definition of a procdh topos. We show that it encodes procdh excision, has bounded homotopy dimension and therefore is hypercomplete and admits a conservative family of fibre functors. We also describe the local rings. As an application, we show that nonconnective $K$-theory is the procdh sheafification of connective $K$-theory, and that the motivic cohomology recently proposed by Elmanto and Morrow is the procdh sheafification of Voevodsky's motivic cohomology.

We present an entanglement transition in an array of qubits, induced by the transfer of quantum information from a system to a quantum computer. This quantum-data collection is an essential protocol in quantum machine learning algorithms that promise exponential advantage over their classical counterparts. In this and an accompanying work [Phys. Rev. A 111, 012425 (2025)], we identify sufficient conditions for an entanglement transition to occur in the late time state of the system and quantum computer. In this letter, we present an example entanglement transition occurring in a system comprised of a 1D chain of qubits evolving under a random brickwork circuit. After each layer, a fraction $p$ of sites undergo noisy quantum transduction in which quantum information is transferred to a quantum computer but at the cost of introducing noise from an environment. For an entanglement transition to occur, we argue that the environment must obtain the same amount of information as gained by the computer. Under this condition, the circuit shows a transition from volume law to area law entanglement as the rate $p$ is increased above a critical threshold. Our work delineates the prerequisites for quantum-data collection to induce entanglement transitions, thereby establishing a foundational framework for emergent entanglement phenomena in protocols relevant to quantum machine learning., Comment: 4 + 6 pages, 3 + 2 figures

As a sequel of Part I, we consider a filtration of Hodge cohomology groups indexed by divisors "at infinity", and prove that they are represented in the category of motives with modulus. In particular, we obtain a realisation functor of the Hodge cohomology groups., Comment: 29 pages

We study thermalization dynamics in a fermion-phonon variant of the Sachdev-Ye-Kitaev model coupled to an external cold thermal bath of harmonic oscillators. We find that quantum critical fermions thermalize more efficiently than phonons, in sharp contrast to the behavior in the Fermi liquid regime. In addition, after a short prethermal stage, the system acquires a quasi-thermal distribution given by a time-dependent effective temperature, reminiscent of "hydrodynamic" relaxation. All physical observables relax at the same rate which scales with the final temperature through an exponent that depends universally on the low energy spectrum of the system and the bath. Such relaxation rate is derived using a hydrodynamic approximation in full agreement with the numerical solution of a set quantum kinetic equations derived from the Keldysh formalism for non-equilibrium Green's functions. Our results hint toward further research on the applicability of the hydrodynamic picture in the description of the late time dynamics of open quantum systems despite the absence of conserved quantities in regimes dominated by conserving collisions.

Topological defects have strong impact on both elastic and inelastic properties of materials. In this article, we investigate the possibility to controllably inject topological defects in quantum simulators of solid state lattice structures. We investigate the quench dynamics of a Frenkel-Kontorova chain, which is used to model discommensurations of particles in cold atoms and trapped ionic crystals. The interplay between an external periodic potential and the inter-particle interaction makes lattice discommensurations, the topological defects of the model, energetically favorable and can tune a commensurate-incommensurate structural transition. Our key finding is that a quench from the commensurate to incommensurate phase causes a controllable injection of topological defects at periodic time intervals. We employ this mechanism to generate quantum states which are a superposition of lattice structures with and without topological defects. We conclude by presenting concrete perspectives for the observation and control of topological defects in trapped ion experiments., Comment: 7 pages,4 figures

We study quantum information scrambling in a random unitary circuit that exchanges qubits with an environment at a rate $p$. As a result, initially localized quantum information not only spreads within the system, but also spills into the environment. Using the out-of-time-order correlator (OTOC) to characterize scrambling, we find a nonequilibrium phase transition in the directed percolation universality class at a critical swap rate $p_c$: for $p < p_c$ the ensemble-averaged OTOC exhibits ballistic growth with a tunable light cone velocity, while for $p > p_c$ the OTOC fails to percolate within the system and vanishes uniformly within a finite timescale, indicating that all local operators are rapidly swapped into the environment. To elucidate its information-theoretic consequences, we demonstrate that the transition in operator spreading coincides with a transition in an observer's ability to decode the system's initial quantum information from the swapped-out, or "radiated," qubits. We present a simple decoding scheme which recovers the system's initial information with perfect fidelity in the nonpercolating phase, and with continuously decreasing fidelity with decreasing swap rate in the percolating phase. Depending on the initial state of the swapped-in qubits, we further observe a corresponding entanglement transition in the coherent information from the system into the radiated qubits., Comment: 7+13 pages, 2+6 figures; v2: published version, improved clarity, modified references

Many-body cavity QED experiments are established platforms to tailor and control the collective responses of ensembles of atoms, interacting through one or more common photonic modes. The rich diversity of dynamical phases they can host, calls for a unified framework. Here we commence this program by showing that a cavity QED simulator assembled from $N$-levels bosonic atoms, can reproduce and extend the possible dynamical responses of collective observables occurring after a quench. Specifically, by initializing the atoms in classical or quantum states, or by leveraging intra-levels quantum correlations, we craft on demand the entire synchronization/desynchronization dynamical crossover of an exchange model for $SU(N)$ spins. We quantitatively predict the onset of different dynamical responses by combining the Liouville-Arnold theorem on classical integrability with an ansatz for reducing the collective evolution to an effective few-body dynamics. Among them, we discover a synchronized chaotic phase induced by quantum correlations and associated to a first order non-equilibrium transition in the Lyapunov exponent of collective atomic dynamics. Our outreach includes extensions to other spin-exchange quantum simulators and a universal conjecture for the dynamical reduction of non-integrable all-to-all interacting systems., Comment: 15+3 pages, 8+3 figures; close to published version; Editors' Suggestion

The coherent superposition of quantum states is an important resource for quantum information processing which distinguishes quantum dynamics and information from their classical counterparts. In this article we determine the coherence requirements to communicate quantum information in a broad setting encompassing monitored quantum dynamics and quantum error correction codes. We determine these requirements by considering hybrid circuits that are generated by a quantum information game played between two opponents, Alice and Eve, who compete by applying unitaries and measurements on a fixed number of qubits. Alice applies unitaries in an attempt to maintain quantum channel capacity, while Eve applies measurements in an attempt to destroy it. By limiting the coherence generating or destroying operations available to each opponent, we determine Alice's coherence requirements. When Alice plays a random strategy aimed at mimicking generic monitored quantum dynamics, we discover a coherence-tuned phase transitions in entanglement and quantum channel capacity. We then derive a theorem giving the minimum coherence required by Alice in any successful strategy, and conclude by proving that coherence sets an upper bound on the code distance in any stabelizer quantum error correction codes. Such bounds provide a rigorous quantification of the coherence resource requirements for quantum communication and error correction., Comment: 19+11 pages, 12+3 figures

Cavity QED experiments are natural hosts for non-equilibrium phases of matter supported by photon-mediated interactions. In this work, we consider a cavity QED simulation of the BCS model of superfluidity, by studying regimes where the cavity photons act as dynamical degrees of freedom instead of mere mediators of the interaction via virtual processes. We find an enhancement of long time coherence following a quench whenever the cavity frequency is tuned into resonance with the atoms. We discuss how this is equivalent to enhancement of non-equilibrium superfluidity and highlight similarities to an analogous phenomena recently studied in solid state quantum optics. We also discuss the conditions for observing this enhanced resonant pairing in experiments by including the effect of photon losses and inhomogeneous coupling in our analysis., Comment: 5 pages, 3 figures, Supplemental Material

We study a fully connected quantum spin model resonantly coupled to a small environment of non-interacting spins, and investigate how initial state properties are remembered at long times. We find memory of initial state properties, in addition to the total energy, that are not conserved by the dynamics. This memory occurs in the middle of the spectrum where an eigenstate quantum phase transition (ESQPT) occurs as a function of energy. The memory effect at that energy in the spectrum is robust to system-environment coupling until the coupling changes the energy of the ESQPT. This work demonstrates the effect of ESQPT memory as independent of integrability and suggests a wider generality of this mechanism for preventing thermalization at ESQPTs., Comment: 8 pages, 8 Figures

We generalise Kahn, Miyazaki, Saito, Yamazaki's theory of modulus pairs to pairs $(X, D)$ consisting of a qcqs scheme $X$ equipped with an effective Cartier divisor $D$ representing a ramification bound. We develop theories of sheaves on such pairs for modulus versions of the Zariski, Nisnevich, \'etale, fppf, and qfh-topologies. We extend the Suslin-Voevodsky theory of correspondances to modulus pairs, under the assumption that the interior $U = X \setminus D$ is Noetherian. The resulting point of view highlights connections to (Raynaud-style) rigid geometry, and potentially provides a setting where wild ramification can be compared with irregular singularities. This framework leads to a homotopy theory of modulus pairs $\underline{M}H(X,D)$ and a theory of motives with modulus $\underline{M}DM^{eff}(X,D)$ over a general base $(X, D)$. For example, the case where $X$ is the spectrum of a rank one valuation ring (of mixed or equal characteristic) equipped with a choice $D$ of pseudo-uniformiser is allowed., Comment: 123 pages, 2 figures

We use a noisy signal with finite correlation time to drive a spin (dissipative impurity) in the quantum XY spin chain and calculate the dynamics of entanglement entropy of a bipartition of spins, for a stochastic quantum trajectory. We compute the noise averaged entanglement entropy of a bipartition of spins and observe that its speed of spreading decreases at strong dissipation, as a result of the Zeno effect. We recover the Zeno crossover and show that noise averaged entanglement entropy can be used as a proxy for the heating and Zeno regimes. Upon increasing the correlation time of the noise, the location of the Zeno crossover shifts at stronger dissipation, extending the heating regime., Comment: 14 pages, 5 figures

We study the far-from-equilibrium dynamical regimes of a many-body spin boson model with disordered couplings relevant for cavity QED and trapped ions experiments, using the discrete truncated Wigner approximation (DTWA). We focus on the dynamics of spin observables upon varying the disorder strength and the frequency of the photons, finding that the latter can considerably alter the structure of the system's dynamical responses. When the photons evolve at a similar rate as the spins, they can induce qualitatively distinct frustrated dynamics characterized by either logarithmic or algebraically slow relaxation. The latter illustrates resilience of glassy-like dynamics in the presence of active photonic degrees of freedom, suggesting that disordered quantum many body systems with resonant photons or phonons can display a rich diagram of non-equilibrium responses, with near future applications for quantum information science., Comment: 5 Pages 3 Figures

We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time crystals, but they are understood via two intertwined stroboscopic effects similar to the aliasing resulting from video taping a single fast rotating helicopter blade. The first effect is similar to a single blade appearing as multiple blades due to a frame rate that is in resonance with the frequency of the helicopter blades' rotation; the second is akin to the optical appearance of the helicopter blades moving in reverse direction. Analogously to other dynamically stabilized states in interacting quantum many-body systems, this stroboscopic aliasing is robust to detuning and excursions from a chosen set of driving parameters, and it offers a novel route for engineering dynamical $n$-tuplets in long-range quantum simulators, with potential applications to spin squeezing generation and entangled state preparation., Comment: 5 pages, 4 figures

We prove that the $\infty$-category of motivic spectra satisfies Milnor excision: if $A\to B$ is a morphism of commutative rings sending an ideal $I\subset A$ isomorphically onto an ideal of $B$, then a motivic spectrum over $A$ is equivalent to a pair of motivic spectra over $B$ and $A/I$ that are identified over $B/IB$. Consequently, any cohomology theory represented by a motivic spectrum satisfies Milnor excision. We also prove Milnor excision for Ayoub's \'etale motives over schemes of finite virtual cohomological dimension., Comment: 11 pages. Final version, to appear in J. reine angew. Math

We give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh infinity-topos of a quasi-compact quasi-separated scheme of finite valuative dimension is hypercomplete, extending a theorem of Voevodsky to nonnoetherian schemes. As an application, we show that if E is a motivic spectrum over a field k which is n-torsion for some n invertible in k, then the cohomology theory on k-schemes defined by E satisfies Milnor excision., Comment: 28 pages. v3: final version, to appear in Mathematische Annalen; v2: new title and minor corrections

By developing a semi-classical analysis based on the Eigenstate Thermalization Hypothesis, we determine the long time behavior of a large spin evolving with a nonlinear Hamiltonian. Despite integrable classical dynamics, we find the Eigenstate Thermalization Hypothesis for the diagonal matrix elements of observables is satisfied in the majority of eigenstates, and thermalization of long time averaged observables is generic. The exception is a novel mechanism for the breakdown of thermalization based on an unstable fixed point in the classical dynamics. Using the semi-classical analysis we derive how the equilibrium values of observables encode properties of the initial state. This analysis shows an unusual memory effect in which the remembered initial state property is not conserved in the integrable classical dynamics. We conclude with a discussion of relevant experiments and the potential generality of this mechanism for long time memory and the breakdown of thermalization., Comment: 10 pages

In this self-contained paper we prove that Voevodsky's smooth blowup triangle of motives generalises to a smooth blowup triangle of motives with modulus.