Quantum dynamics on curved spacetime has never been directly probed beyond the Newtonian limit. Although we can describe such dynamics theoretically, experiments would provide empirical evidence that quantum theory holds even in this extreme limit. The practical challenge is the minute spacetime curvature difference over the length scale of the typical extent of quantum effects. Here, we propose a quantum network of alkaline earth (like) atomic processors for constructing a distributed quantum state that is sensitive to the differential proper time between its constituent atomic processor nodes, implementing a quantum observable that is affected by post-Newtonian curved spacetime. Conceptually, we propose to delocalize one clock between three locations by encoding the presence or absence of a clock into the state of the local atoms. By separating three atomic nodes over approximately kilometer-scale elevation differences and distributing one clock between them via a $W$ state, we demonstrate that the curvature of spacetime is manifest in the interference of the three different proper times that give rise to three distinct beat notes in our nonlocal observable. We further demonstrate that $N$-atom entanglement within each node enhances the interrogation bandwidth by a factor of $N$. We discuss how our proposed system can probe new facets of fundamental physics, such as the linearity, unitarity, and probabilistic nature of quantum theory on curved spacetime. Our protocol combines several recent advances with neutral atom and trapped ions to realize a novel quantum probe of gravity uniquely enabled by quantum networks.

Echo-based spectroscopy of the superhyperfine interaction of an electronic spin with nuclear spins in its surroundings enables detailed insights into the microscopic magnetic environment of spins in solids. Still, it is an outstanding challenge to resolve individual nuclear spins in a dense bath, in which many of them exhibit a comparable coupling strength. This simultaneously requires a high spectral resolution and a large signal-to-noise ratio. However, when probing spin ensembles, dipolar interactions between the dopants can lead to a concentration-dependent trade-off between resolution and signal. Here, we fully eliminate this limitation of previous optical-echo-envelope-modulation spectroscopy experiments by integrating the emitters into a high-finesse resonator, which allows for strong optical echoes even at very low concentrations. To demonstrate its potential, the technique is applied to erbium dopants in yttrium orthosilicate ($\mathrm{Er}$:$\mathrm{YSO}$). Achieving an unprecedented spectral resolution enables precise measurements of the superhyperfine interaction with four of the Y nuclear spins densely surrounding each emitter. The achieved boost of the signal, enabled by the resonator, allows for extending the approach to the lowest concentration possible—to the level of single dopants, thereby providing a tool for detecting and studying individual nuclear spins. Thus, our technique paves the way for an improved understanding of dense nuclear-spin baths in solids.

As a waveguide circuit QED architecture, we investigate theoretically the single-photon pair emission of a Cooper pair splitter composed of two double quantum dots, each coupled to a microwave transmission line. We find that this system can generate frequency-entangled photon pairs in the left and right transmission lines, specifically a superposition of two photon wave packets at different frequencies. The frequency entanglement of the two photons arises from the particle-hole coherent superposition (i.e., Andreev bound states) involving the delocalized entangled spin singlet. We also estimate a lower bound for the efficiency of entangled photon-pair generation, accounting for the presence of nonradiative processes such as phonon emissions. Our proposal is realistic and achievable with state-of-the-art techniques in quantum microwave engineering with electostatically defined semiconducting quantum dots.

We present an optical tweezer array of  ${}^{87}\mathrm{Rb}$ atoms housed in an cryogenic environment that successfully combines a 4-K cryopumping surface, a <50-K cold box surrounding the atoms, and a room-temperature high-numerical-aperture objective lens. We demonstrate a 3000-s atom-trap lifetime, which enables us to optimize and measure losses at the ${10}^{-4}$ level that arise during imaging and cooling, which are important to array rearrangement. We perform both ground-state qubit manipulation with an integrated microwave antenna and two-photon coherent Rydberg control, with the local electric field tuned to zero via integrated electrodes. We anticipate that the reduced blackbody radiation at the atoms from the cryogenic environment, combined with future electrical shielding, should decrease the rate of undesired transitions to nearby strongly interacting Rydberg states, which cause many-body loss and impede Rydberg gates. This low-vibration, high-optical-access cryogenic platform can be used with a wide range of optically trapped atomic or molecular species for applications in quantum computing, simulation, and metrology.

The ability to sense and control nuclear spins near solid-state defects might enable a range of quantum technologies. Dynamically decoupled radio-frequency (DDrf) control offers a high degree of design flexibility and long electron-spin coherence times. However, previous studies have considered simplified models and little is known about optimal gate design and fundamental limits. Here, we develop a generalized DDrf framework that has important implications for spin sensing and control. Our analytical model, which we corroborate by experiments on a single NV center in diamond, reveals the mechanisms that govern the selectivity of gates and their effective Rabi frequencies, and enables flexible detuned gate designs. We apply these insights to numerically show a $60\times$ sensitivity enhancement for detecting weakly coupled spins and study the optimization of quantum gates in multiqubit registers. These results advance the understanding for a broad class of gates and provide a toolbox for application-specific design, enabling improved quantum control and sensing.

The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard. Here, we present an efficient algorithm for learning states on $n$ fermion modes prepared by any number of Gaussian and at most $t$ non-Gaussian gates. By Jordan-Wigner mapping, this also includes $n$-qubit states prepared by nearest-neighbor matchgate circuits with at most $t$ swap gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of our algorithm is $\mathrm{poly}(n,2^t)$; thus if $t=\mathcal{O}(\log (n))$, it is efficient. We also show that, if $t$ scales slightly more than logarithmically, any learning algorithm to solve the same task must be inefficient, under common cryptographic assumptions. We also provide an efficient property-testing algorithm that, given access to copies of a state, determines whether such a state is far or close to the set of states for which our learning algorithm works. In addition to the outputs of quantum circuits, our tomography algorithm is efficient for some physical target states, such as those arising in time dynamics and low-energy physics of impurity models. Beyond tomography, our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity, enabling an efficient circuit-compilation method.

The classification and characterization of topological phases of matter is well understood for ground states of gapped Hamiltonians that are well isolated from the environment. However, decoherence due to interactions with the environment is inevitable—thus motivating the investigation of topological orders in the context of mixed states. Here, we take a step toward classifying mixed-state topological orders in two spatial dimensions by considering their (emergent) generalized symmetries. We argue that their 1-form symmetries and the associated anyon theories lead to a partial classification under two-way connectivity by quasilocal quantum channels. This allows us to establish mixed-state topological orders that are intrinsically mixed, i.e., that have no ground-state counterpart. We provide a wide range of examples based on topological subsystem codes, decohering $G$-graded string-net models, and “classically gauging” symmetry-enriched topological orders. One of our main examples is an Ising string-net model under the influence of dephasing noise. We study the resulting space of locally indistinguishable states and compute the modular transformations within a particular coherent space. Based on our examples, we identify two possible effects of quasilocal quantum channels on anyon theories: (1) anyons can be incoherently proliferated—thus reducing to a commutant of the proliferated anyons, or (2) the system can be “classically gauged,” resulting in the symmetrization of anyons and an extension by transparent bosons. Given these two mechanisms, we conjecture that mixed-state topological orders are classified by premodular anyon theories, i.e., those for which the braiding relations may be degenerate.

Decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. Here, we show that decoherence can also give rise to new types of topological order. Specifically, we construct concrete examples by proliferating fermionic anyons in the toric code via local quantum channels. The resulting mixed states retain long-range entanglement, which manifests in the nonzero topological entanglement negativity, though the topological quantum memory is destroyed by decoherence. By comparison with the gapless spin liquid in pure states, we show that the identified states represent a novel intrinsic mixed-state topological order, which has no counterpart in pure states. Through the lens of quantum anomalies of 1-form symmetries, we then provide general constructions of intrinsic mixed-state topological order and reveal the existence of nonbosonic deconfined anyons as another key feature of these novel phases. The extended meaning and characterization of deconfined excitations and their statistics in mixed states are clarified. Moreover, when these deconfined anyons have nontrivial braiding statistics, we prove that the mixed states cannot be prepared via finite-depth local quantum channels from any bipartite separable states. We further demonstrate our construction using the decohered Kitaev honeycomb model and the decohered double-semion model. In the latter case, a surprising scenario arises where decoherence gives rise to additional types of deconfined anyons.

We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed state can display intrinsically mixed-state topological order (imTO)—topological order that is not expected to occur in the ground state of 2D local gapped Hamiltonians. Specifically, we show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, is more naturally phrased as, and provides a physical mechanism for, “gauging out” anyons in the original Hilbert space. We find that gauging out anyons generically results in imTO, with the decohered mixed state strongly symmetric under certain anomalous 1-form symmetries. This framework lays bare a striking connection between the decohered density matrix and topological subsystem codes, which can appear as anomalous surface states of three-dimensional topological orders. Through a series of examples, we show that the decohered state can display a classical memory, encode logical qubits (i.e., exhibit a quantum memory), and even host chiral or nonmodular topological order. We argue that a partial classification of imTO is given in terms of nonmodular braided-fusion categories.

Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes that affects code performance and ease of physical realization. For device architectures restricted to two-dimensional (2D) local gates, naively implementing the high-rate codes suitable for low-overhead fault-tolerant quantum computing incurs prohibitive overhead. In this work, we present an error-correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates by measuring some generators less frequently than others. We investigate the family of bivariate-bicycle qLDPC codes and show that they are well suited for a parallel syndrome-measurement scheme using fast routing with local operations and classical communication (LOCC). Through circuit-level simulations, we find that in some parameter regimes, bivariate-bicycle codes implemented with this protocol have logical error rates comparable to the surface code while using fewer physical qubits.

The simulation of high-temperature superconducting materials by implementing strongly correlated fermionic models in optical lattices is one of the major objectives in the field of analog quantum simulation. Here we show that local control and optical bilayer capabilities combined with spatially resolved measurements create a versatile toolbox to study fundamental properties of both nickelate and cuprate high-temperature superconductors. On the one hand, we present a scheme to implement a mixed-dimensional (mixD) bilayer model that has been proposed to capture the essential pairing physics of pressurized bilayer nickelates. This allows for the long-sought realization of a state with long-range superconducting order in current lattice quantum simulation machines. In particular, we show how coherent pairing correlations can be accessed in a partially particle-hole transformed and rotated basis. On the other hand, we demonstrate that control of local gates enables the observation of $d$-wave pairing order in the two-dimensional (single-layer) repulsive Fermi-Hubbard model through the simulation of a system with attractive interactions. Lastly, we introduce a scheme to measure momentum-resolved dopant densities, providing access to observables complementary to solid-state experiments—which is of particular interest for future studies of the enigmatic pseudogap phase appearing in cuprates.

Cavity quantum electrodynamics offers the possibility of observing and controlling the motion of a few or individual atoms, enabling the realization of various quantum technological tasks such as quantum enhanced metrology or quantum simulation of strongly correlated matter. A core limitation of these experiments lies in the mode structure of the cavity field, which is hard coded in the shape and geometry of the mirrors. As a result, most applications of cavity QED trade spatial resolution for enhanced sensitivity. Here, we propose and demonstrate a cavity-microscope device capable of controlling in space and time the coupling between atoms and light in a single-mode high-finesse cavity, reaching a spatial resolution an order of magnitude lower than the cavity-mode waist. This is achieved through local Floquet engineering of the atomic level structure, imprinting a corresponding atom-field coupling. We illustrate this capability by engineering micrometer-scale coupling, using cavity-assisted atomic measurements and optimization. Our system forms an optical device with a single optical axis, has the same footprint and complexity as a standard Fabry-Perot cavity or confocal lens pair, and can be used for any atomic species. This technique opens a wide range of perspectives, from ultrafast cavity-enhanced midcircuit readout to the quantum simulation of fully connected models of quantum matter such as the Sachdev-Ye-Kitaev model.

Naturally occurring background radiation is a potential source of correlated decoherence events in superconducting qubits that will challenge error-correction schemes. In order to characterize the radiation environment in an unshielded laboratory representative of superconducting qubits’ environments, we performed broadband, spectroscopic measurements of background radiation events inside a millikelvin refrigerator. The spectrometer was designed to mimic the size and composition of a quantum circuit. Specifically, we measured the background radiation spectra in silicon substrates of two thicknesses, 500 and 1500 µm, and one area, 25 ${\mathrm{mm}}^2$. The observed spectra span energies from a few kilo-electron-volts up to nearly 10 MeV, are nearly featureless, and decrease in intensity by a factor of 40 000 between 100 keV and 3 MeV for the 500-µm substrate. We integrate the spectra to obtain the average event rates and deposited power levels. These quantities correspond to a rate of 0.023 events per second and a power of 4.9 keV ${\mathrm{s}}^{-1}$, when counting events that deposit at least 40 keV for the 500-µm-thick substrate. We find that the cryogenic measurements are in good agreement with predictions based on simple measurements of the terrestrial gamma-ray flux outside the refrigerator, published models of cosmic-ray fluxes, a crude model of the cryostat, and radiation-transport simulations. This model requires no free parameters to predict the background radiation spectra in the silicon substrates. The agreement between measurements and predictions demonstrates that the model we present can be used to assess the relative contributions of terrestrial and cosmic-ray sources to background radiation interactions in silicon substrates of varying thickness. These spectroscopic measurements are performed with a novel combination of superconducting microresonators located on micromachined silicon islands that define the interaction volume with background radiation. The resonators transduce deposited energy to a readily detectable electrical signal. Microresonator readout closely resembles dispersive superconducting qubit readout, so similar devices—with or without micromachined islands—are suitable for integration with superconducting quantum circuits as detectors for background radiation events. For our specific laboratory conditions, we find that gamma-ray emissions from radioisotopes are responsible for the majority of events that deposit $E<1\mathrm{Me}\mathrm{V}$. We present results demonstrating that the background radiation spectrum contains relevant contributions from cosmic-ray particles other than muons, particularly a tail of multi-mega-electron-volt events due to protons and neutrons. These observations suggest several paths to reducing the impact of background radiation on quantum circuits, supported by an empirically validated model for generating reliable predictions of radiation interactions with silicon substrates.

Quantum processors require a signal-delivery architecture with high addressability (low crosstalk) to ensure high performance already at the scale of dozens of qubits. Signal crosstalk causes inadvertent driving of quantum gates, which will adversely affect quantum gate fidelities in scaled-up devices. Here, we demonstrate packaged flip-chip superconducting quantum processors with signal-crosstalk performance competitive with those reported in other platforms. For capacitively coupled qubit-drive lines, we find on-resonant crosstalk better than $-27$ dB (average $-37$ dB). For inductively coupled magnetic-flux-drive lines, we find less than 0.13% direct-current flux crosstalk (average 0.05%). These observed crosstalk levels are adequately small and indicate a decreasing trend with increasing distance, which is promising for further scaling up to larger numbers of qubits. We discuss the implications of our results for the design of a low-crosstalk on-chip signal-delivery architecture, including the influence of a shielding tunnel structure, potential sources of crosstalk, and estimation of crosstalk-induced qubit-gate error in scaled-up quantum processors.

Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it has been shown that the Affleck-Kennedy-Lieb-Tasaki state—a paradigmatic example of an MPS—can be exactly prepared with an adaptive quantum circuit of constant depth, an impossible feat with local unitary gates alone due to its nonzero correlation length [Smith et al., PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states.

The distribution of high-fidelity high-rate entanglement over telecommunication infrastructure is one of the main paths toward large-scale quantum networks, enabling applications such as quantum encryption and network protection, blind quantum computing, distributed quantum computing, and distributed quantum sensing. However, the fragile nature of entangled photons operating in real-world fiber infrastructure has historically limited continuous operation of such networks. Here, we present a fully automated system capable of distributing polarization-entangled photons over a 34-km deployed fiber in New York City, achieving high rates of nearly $5\times {10}^5$ pairs/s. Separately, we demonstrate a high fidelity of approximately $99\mathrm{\%}$ for rates up to $2\times {10}^4$ pairs/s. Lastly, we achieve 15 days of continuous distribution, with a network up-time of $99.84\mathrm{\%}$. Our work paves the way for practical deployment of always-on entanglement-based networks with rates and fidelity adequate for many current and future use cases.

Assembling and maintaining large arrays of individually addressable atoms is a key requirement for continued scaling of neutral-atom-based quantum computers and simulators. In this work, we demonstrate a new paradigm for assembly of atomic arrays, based on a synergistic combination of optical tweezers and cavity-enhanced optical lattices, and the incremental filling of a target array from a repetitively filled reservoir. In this protocol, the tweezers provide microscopic rearrangement of atoms, while the cavity-enhanced lattices enable the creation of large numbers of optical traps with sufficient depth for rapid low-loss imaging of atoms. We apply this protocol to demonstrate near-deterministic filling (99% per-site occupancy) of 1225-site arrays of optical traps. Because the reservoir is repeatedly filled with fresh atoms, the array can be maintained in a filled state indefinitely. We anticipate that this protocol will be compatible with mid-circuit reloading of atoms into a quantum processor, which will be a key capability for running large-scale error-corrected quantum computations whose durations exceed the lifetime of a single atom in the system.

Quantum gases of doubly polar molecules represent appealing frameworks for a variety of cross-disciplinary applications, encompassing quantum simulation and computation, controlled quantum chemistry, and precision measurements. Through a joint experimental and theoretical study, here we explore a novel class of ultracold paramagnetic polar molecules combining lithium alkali and chromium transition metal elements. Focusing on the specific bosonic isotopologue ${}^6{\mathrm{Li}}^{53}\mathrm{Cr}$, leveraging on the Fermi statistics of the parent atomic mixture and on suitable Feshbach resonances recently discovered, we produce up to $50\times {10}^3$ ultracold $\mathrm{Li}\mathrm{Cr}$ molecules at peak phase-space densities exceeding 0.1, prepared within the least bound rotationless level of the $\mathrm{Li}\mathrm{Cr}$ electronic sextet ground state $X{}^6{\mathrm{\Sigma }}^{+}$. By also developing new probing methods, we thoroughly characterize the molecular gas, demonstrating the paramagnetic nature of $\mathrm{Li}\mathrm{Cr}$ dimers and the precise control of their quantum state. We investigate their stability against inelastic processes and identify a parameter region where pure $\mathrm{Li}\mathrm{Cr}$ samples exhibit lifetimes exceeding 0.2 s. Parallel to this, we employ state-of-the-art quantum chemical calculations to accurately predict the properties of $\mathrm{Li}\mathrm{Cr}$ ground and excited electronic states. This ab initio model, able to reproduce the experimental $\mathrm{Li}$-$\mathrm{Cr}$ high-spin, octet scattering length, allows us to identify both efficient paths to coherently transfer weakly bound $\mathrm{Li}\mathrm{Cr}$ dimers to their absolute ground state, and suitable transitions for their subsequent optical manipulation. Our studies establish $\mathrm{Li}$-$\mathrm{Cr}$ as a prime candidate to realize ultracold gases of doubly polar molecules with significant electric (3.3 D) and magnetic ($5{\mu }_B$) dipole moments.

Polar molecules are a quantum resource with rich internal structure that can be coherently controlled. The structure, however, also makes the state preparation and measurement (SPAM) of molecules challenging. We advance the SPAM of individual molecules assembled from constituent atoms trapped in optical-tweezer arrays. Sites without $\mathrm{Na}\mathrm{Cs}$ molecules are eliminated using high-fidelity $\mathrm{Cs}$ atom detection, increasing the peak molecule filling fraction of the array threefold. We site-selectively initialize the array in a rotational qubit subspace that is insensitive to differential ac Stark shifts from the optical tweezer. Lastly, we detect multiple rotational states per experimental cycle by imaging atoms after sequential state-selective dissociations. These demonstrations extend the SPAM capabilities of molecules for quantum information, simulation, and metrology.

Control over the quantum states of individual molecules is crucial in the quest to harness their rich internal structure and dipolar interactions for applications in quantum science. In this paper, we develop a toolbox of techniques for the control and readout of individually trapped polar molecules in an array of optical tweezers. Starting with arrays of up to eight Rb and eight Cs atoms, we assemble arrays of RbCs molecules in their rovibrational and hyperfine ground state with an overall efficiency of 48(2)%. We demonstrate global microwave control of multiple rotational states of the molecules and use an auxiliary tweezer array to implement site-resolved addressing and state control. We show how the rotational state of the molecule can be mapped onto the position of Rb atoms and use this capability to readout multiple rotational states in a single experimental run. Further, using a scheme for the midsequence detection of molecule formation errors, we perform rearrangement of assembled molecules to prepare small defect-free arrays. Finally, we discuss a feasible route to scaling to larger arrays of molecules.