Formation of robust bound states of interacting microwave photons

Probing Site-Resolved Current in Strongly Interacting Superconducting Circuit Lattices

Transport measurements are fundamental for understanding condensed matter phenomena, from superconductivity to the fractional quantum Hall effect. Analogously, they can be powerful tools for probing synthetic quantum matter in quantum simulators. Here we demonstrate the measurement of in situ particle current in a superconducting circuit lattice and apply it to study transport in both coherent and bath-coupled lattices. Our method utilizes controlled tunneling in a double-well potential to map current to on-site density, revealing site-resolved current and current statistics. We prepare a strongly interacting Bose-Hubbard lattice at different lattice fillings, and observe the change in current statistics as the many-body states transition from superfluid to Mott insulator. Furthermore, we explore nonequilibrium current dynamics by coupling the lattice to engineered driven-dissipative baths that serve as tunable particle source and drain. We observe steady-state current in discrete conduction channels and interaction-assisted transport. These results establish a versatile platform to investigate microscopic quantum transport in superconducting circuits.

Strong Zero Modes in Integrable Quantum Circuits

It is a classic result that certain interacting integrable spin chains host robust edge modes known as strong zero modes (SZMs). In this Letter, we extend this result to the Floquet setting of local quantum circuits, focusing on a prototypical model providing an integrable Trotterization for the evolution of the XXZ Heisenberg spin chain. By exploiting the algebraic structures of integrability, we show that an exact SZM operator can be constructed for these integrable quantum circuits in certain regions of parameter space. Our construction, which recovers a well-known result by Paul Fendley in the continuous-time limit, relies on a set of commuting transfer matrices known from integrability, and allows us to easily prove important properties of the SZM, including normalizabilty. Our approach is different from previous methods and could be of independent interest even in the Hamiltonian setting. Our predictions, which are corroborated by numerical simulations of infinite-temperature autocorrelation functions, are potentially interesting for implementations of the XXZ quantum circuit on available quantum platforms.

Experimental observation of exceptional bound states in a classical circuit network

Exceptional bound (EB) states represent a unique new class of robust bound states protected by the defectiveness of non-Hermitian exceptional points. Conceptually distinct from the more well-known topological states and non-Hermitian skin states, they were recently discovered as a novel source of negative entanglement entropy in the quantum entanglement context. Yet, EB states have been physically elusive, being originally interpreted as negative probability eigenstates of the propagator of non-Hermitian Fermi gases. In this work, we show that EB states are in fact far more ubiquitous, also arising robustly in broad classes of systems whether classical or quantum. This hinges crucially on a newly-discovered spectral flow that rigorously justifies the EB nature of small candidate lattice systems. As a highlight, we present their first experimental realization through an electrical circuit, where they manifest as prominent stable resonant voltage profiles. Our work brings a hitherto elusive but fundamentally distinctive quantum phenomenon into the realm of classical metamaterials, and provides a novel pathway for the engineering of robust modes in otherwise sensitive systems..

Manybody interferometry of quantum fluids

Characterizing strongly correlated matter is an increasingly central challenge in quantum science, where structure is often obscured by massive entanglement. It is becoming clear that in the quantum regime, state preparation and characterization should not be treated separately-entangling the two processes provides a quantum advantage in information extraction. Here, we present an approach that we term "manybody Ramsey interferometry" that combines adiabatic state preparation and Ramsey spectroscopy: Leveraging our recently developed one-to-one mapping between computational-basis states and manybody eigenstates, we prepare a superposition of manybody eigenstates controlled by the state of an ancilla qubit, allow the superposition to evolve relative phase, and then reverse the preparation protocol to disentangle the ancilla while localizing phase information back into it. Ancilla tomography then extracts information about the manybody eigenstates, the associated excitation spectrum, and thermodynamic observables. This work illustrates the potential for using quantum computers to efficiently probe quantum matter.

Quantum Information Spreading in Generalized Dual-Unitary Circuits

We study the spreading of quantum information in a recently introduced family of brickwork quantum circuits that generalizes the dual-unitary class. These circuits are unitary in time, while their spatial dynamics is unitary only in a restricted subspace. First, we show that local operators spread at the speed of light as in dual-unitary circuits, i.e., the butterfly velocity takes the maximal value allowed by the geometry of the circuit. Then, we prove that the entanglement spreading can still be characterized exactly for a family of compatible initial states (in fact, for an extension of the compatible family of dual-unitary circuits) and that the asymptotic entanglement slope is again independent on the Rényi index. Remarkably, however, we find that the entanglement velocity is generically smaller than 1. We use these properties to find a closed-form expression for the entanglement-membrane line tension.

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain's center, [Formula: see text]. The first two moments of [Formula: see text] show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.

Squeezed Ensembles and Anomalous Dynamic Roughening in Interacting Integrable Chains

It is widely accepted that local subsystems in isolated integrable quantum systems equilibrate to generalized Gibbs ensembles. Here, we identify a particular class of initial states in interacting integrable models that evade canonical generalized thermalization. Particularly, we demonstrate that in the easy-axis regime of the quantum XXZ chain, pure nonequilibrium initial states that lack magnetic fluctuations instead locally relax to squeezed generalized Gibbs ensembles governed by nonlocal equilibrium Hamiltonians, representing exotic equilibrium states with subextensive charge fluctuations that violate the self-affine scaling. At the isotropic point, we find exceptional behavior and explicit dependence on the initial state. Particularly, we find that relaxation from the Néel state is governed by extensive fluctuations and a superdiffusive dynamical exponent compatible with the Kardar-Parisi-Zhang universality. On the other hand, there are other nonfluctuating initial states that display diffusive scaling, e.g., a product state of spin singlets. Our predictions provide examples of anomalous quantum transport and fluctuations in strictly quantum states which can be directly tested in state-of-the-art cold atomic experimental settings.

Stable quantum-correlated many-body states through engineered dissipation

Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.

Exact Quench Dynamics of the Floquet Quantum East Model at the Deterministic Point

We study the nonequilibrium dynamics of the Floquet quantum East model (a Trotterized version of the kinetically constrained quantum East spin chain) at its "deterministic point," where evolution is defined in terms of CNOT permutation gates. We solve exactly the thermalization dynamics for a broad class of initial product states by means of "space evolution." We prove: (i) the entanglement of a block of spins grows at most at one-half the maximal speed allowed by locality (i.e., half the speed of dual-unitary circuits); (ii) if the block of spins is initially prepared in a classical configuration, speed of entanglement is a quarter of the maximum; (iii) thermalization to the infinite temperature state is reached exactly in a time that scales with the size of the block.

Nonlinear Fluctuating Hydrodynamics for Kardar-Parisi-Zhang Scaling in Isotropic Spin Chains

Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ (Kardar-Parisi-Zhang) or stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a nonlinear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.

Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions

The Trotter-Suzuki decomposition is a promising avenue for digital quantum simulation (DQS), approximating continuous-time dynamics by discrete Trotter steps of duration τ. Recent work suggested that DQS is typically characterized by a sharp Trotter transition: when τ is increased beyond a threshold value, approximation errors become uncontrolled at large times due to the onset of quantum chaos. Here, we contrast this picture with the case of integrable DQS. We focus on a simple quench from a spin-wave state in the prototypical XXZ Heisenberg spin chain, and study its integrable Trotterized evolution as a function of τ. Because of its exact local conservation laws, the system does not heat up to infinite temperature and the late-time properties of the dynamics are captured by a discrete generalized Gibbs ensemble (dGGE). By means of exact calculations we find that, for small τ, the dGGE depends analytically on the Trotter step, implying that discretization errors remain bounded even at infinite times. Conversely, the dGGE changes abruptly at a threshold value τ_{th}, signaling a novel type of Trotter transition. We show that the latter can be detected locally, as it is associated with the appearance of a nonzero staggered magnetization with a subtle dependence on τ. We highlight the differences between continuous and discrete GGEs, suggesting the latter as novel interesting nonequilibrium states exclusive to digital platforms.