Floquet engineering provides a toolbox for the realization of novel quantum phases without static counterparts, while conventionally the realization may rely on the manipulation of complex temporal evolution. Here, we propose a systematic and high-precision scheme to realize unconventional Floquet topological phases by engineering local band structures in particular momentum subspaces called band-inversion surfaces (BISs). This scheme is based on a new bulk-boundary correspondence that for a class of generic $d$-dimensional periodically driven systems, the local topological structure formed in each BIS uniquely determines the features of gapless boundary modes. By engineering the BIS configuration, we demonstrate a highly efficient approach to realize, manipulate, and detect novel Floquet topological phases. In particular, we predict a two-dimensional (2D) anomalous Floquet valley-Hall phase that carries trivial global bulk topological invariants but features protected counterpropagating edge states in each quasienergy gap. The unconventional nature of this novel 2D phase is further illustrated by the examination of edge-geometry dependence and its robustness to disorder scattering. Anomalous chiral topological phases with valley protection in higher dimensions are also predicted and studied. Our systematic and highly feasible scheme opens up a new route to realizing and engineering unconventional Floquet topological phases for ultracold atoms and other quantum simulators.

Quantum computers solve ever more complex tasks using steadily growing system sizes. Characterizing these quantum systems is vital, yet becoming increasingly challenging. The gold-standard method for this task is quantum state tomography (QST), capable of fully reconstructing a quantum state without prior knowledge. The measurement and classical computing costs, however, increase exponentially with the number of constituents (e.g., qubits)—a daunting bottleneck given the scale of existing and near-term quantum devices. Here, we demonstrate a scalable and practical QST approach that only uses a single measurement setting, namely symmetric informationally complete (SIC) positive operator-valued measures (POVMs). We implement these nonorthogonal measurements on an ion trap quantum processor by utilizing additional energy levels within each ion—without requiring ancillary ions to assist in measurements. More precisely, we locally map the SIC POVM to orthogonal states embedded in a higher-dimensional system, which we read out using repeated in-sequence detections, thereby providing full tomographic information in every shot. Combining this SIC tomography with the recently developed randomized measurement toolbox (“classical shadows”) proves to be a powerful combination. SIC tomography alleviates the need for choosing measurement settings at random (“derandomization”), while classical shadows enable the estimation of arbitrary polynomial functions of the density matrix orders of magnitudes faster than standard methods. The latter enables in-depth entanglement characterization, which we experimentally showcase on a five-qubit absolutely maximally entangled state. Moreover, the fact that the full tomography information is available in every shot enables online QST in real time (i.e., while the experiment is running). We demonstrate this on an eight-qubit entangled state (which has $2^8\cdot 2^8-1=65535$ degrees of freedom), as well as for fast state identification. All in all, these features single out SIC-based classical shadow estimation as a highly scalable and convenient tool for quantum state characterization.

We introduce a general setup for the analog quantum simulation of the dynamics of open quantum systems based on semiconductor quantum dots electrically connected to an array of quantum $RLC$ electronic circuits. The dots are chosen to be in the regime of spin-charge hybridization to enhance their sensitivity to the $RLC$ circuits while mitigating the detrimental effects of unwanted noise. In this context, we establish an experimentally realizable map between the hybrid system and a qubit coupled to thermal harmonic environments of arbitrary complexity that enables the analog quantum simulation of open quantum systems. We assess the utility of the simulator by numerically exact emulations that indicate that the experimental setup can faithfully mimic the intended target even in the presence of its natural inherent noise. We further provide a detailed analysis of the physical requirements on the quantum dots and the $RLC$ circuits needed to experimentally realize this proposal that indicates that the simulator can be created with existing technology. The approach can exactly capture the effects of highly structured non-Markovian quantum environments typical of photosynthesis and chemical dynamics and it offers clear potential advantages over conventional and even quantum computation. The proposal opens up a general path for effective quantum dynamics simulations based on semiconductor quantum dots.

Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of nontrivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states (MPSs). We compare counterdiabatic and leakage minimization approaches to the so-called local steering problem that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counterdiabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally, we apply our leakage minimization approach to construct quantum scars in the periodically driven nonintegrable Ising model.

We investigate topological order on fractal geometries embedded in $n$ dimensions. We consider the $n$-dimensional lattice with holes at all length scales the corresponding fractal (Hausdorff) dimension of which is $D_H=n-\delta$. In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a quantum error-correcting code with a macroscopic code distance or the presence of macroscopic systoles in systolic geometry. We first prove a no-go theorem that ${\mathbb{Z}}_N$ topological order cannot survive on any fractal embedded in two spatial dimensions and with $D_H=2-\delta$. For fractal-lattice models embedded in three dimensions (3D) or higher spatial dimensions, ${\mathbb{Z}}_N$ topological order survives if the boundaries on the holes condense only loop or, more generally, $k$-dimensional membrane excitations ($k\ge 2$), thus predicting the existence of fractal topological quantum memories (at zero temperature) or topological codes that are embeddable in 3D. Moreover, for a class of models that contain only loop or membrane excitations and are hence self-correcting on an $n$-dimensional manifold, we prove that ${\mathbb{Z}}_N$ topological order survives on a large class of fractal geometries independent of the type of hole boundary and is hence extremely robust. We further construct fault-tolerant logical gates in the ${\mathbb{Z}}_2$ version of these fractal models, which we term fractal surface codes, using their connection to global and higher-form topological symmetries equivalent to sweeping the corresponding gapped domain walls. In particular, we discover a logical controlled-controlled-Z (ccz) gate corresponding to a global symmetry in a class of fractal codes embedded in 3D with Hausdorff dimension asymptotically approaching $D_H=2+ϵ$ for arbitrarily small $ϵ$, which hence only requires a space overhead $\mathrm{\Omega }(d^{2+ϵ})$, where $d$ is the code distance. This in turn leads to the surprising discovery of certain exotic gapped boundaries that only condense the combination of loop excitations and certain gapped domain walls. We further obtain logical $C^{p}Z$ gates with $p\le n-1$ on fractal codes embedded in $n$ dimensions. In particular, for the logical $C^{n-1}Z$ in the $n\mathrm{th}$ level of the Clifford hierarchy, we can reduce the space overhead to $\mathrm{\Omega }(d^{n-1+ϵ})$. On the mathematical side, our findings in this paper also lead to the discovery of macroscopic relative systoles in a class of fractal geometries.

Quantum state-resolved spectroscopy was recently achieved for ${\mathrm{C}}_{60}$ molecules when cooled by buffer gas collisions and probed with a midinfrared frequency comb. This rovibrational quantum state resolution for the largest molecule on record is facilitated by the remarkable symmetry and rigidity of ${\mathrm{C}}_{60}$, which also present new opportunities and challenges to explore energy transfer between quantum states in this many-atom system. Here we combine state-specific optical pumping, buffer gas collisions, and ultrasensitive intracavity nonlinear spectroscopy to initiate and probe the rotation-vibration energy transfer and relaxation. This approach provides the first detailed characterization of ${\mathrm{C}}_{60}$ collisional energy transfer for a variety of collision partners, and determines the rotational and vibrational inelastic collision cross sections. These results compare well with our theoretical modeling of the collisions, and establish a route towards quantum state control of a new class of unprecedentedly large molecules.

Quantum metrology protocols exploiting ensembles of $N$ two-level systems and Ramsey-style measurements are ubiquitous. However, in many cases excess readout noise severely degrades the measurement sensitivity; in particular in sensors based on ensembles of solid-state defect spins. We present a dissipative “spin-amplification” protocol that allows us to dramatically improve the sensitivity of such schemes, even in the presence of realistic intrinsic dissipation and noise. Our method is based on exploiting collective (i.e., superradiant) spin decay, an effect that is usually seen as a nuisance because it limits spin-squeezing protocols. We show that our approach can allow a system with a highly imperfect spin readout to approach standard-quantum-limit-like scaling in $N$ within a factor of 2, without needing to change the actual readout mechanism. Our ideas are compatible with several state-of-the-art experimental platforms where an ensemble of solid-state spins ($\mathrm{NV}$ centers, $\mathrm{SiV}$ centers) is coupled to a common microwave or mechanical mode.

Optical metasurfaces of subwavelength pillars have provided new capabilities for the versatile definition of the amplitude, phase, and polarization of light. In this work, we demonstrate that an efficient dielectric metasurface lens can be used to trap and image single neutral atoms with a long working distance from the lens of 3 mm. We characterize the high-numerical-aperture optical tweezers using the trapped atoms and compare with numerical computations of the metasurface-lens performance. We predict that future metasurfaces for atom trapping will be able to leverage multiple ongoing developments in metasurface design and enable multifunctional control in complex quantum information experiments with neutral-atom arrays.

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction of replicas, which requires an effort exponential in the number of replicas and which is costly in terms of memory. In contrast, our method requires the stochastic sampling of matrix elements of the classically represented reduced states with respect to random states drawn from simple product probability measures constituting frames. Even though not corresponding to physical operations, such matrix elements are straightforward to calculate for tensor network states, and their moments provide the Rényi entropies and negativities as well as their symmetry-resolved components. We test our method on the one-dimensional critical XX chain and the two-dimensional toric code in a checkerboard geometry. Although the cost is exponential in the subsystem size, it is sufficiently moderate so that—in contrast with other approaches—accurate results can be obtained on a personal computer for relatively large subsystem sizes.

Hosting nonclassical states of light in three-dimensional microwave cavities has emerged as a promising paradigm for continuous-variable quantum information processing. Here we experimentally demonstrate high-fidelity generation of a range of Wigner-negative states useful for quantum computation, such as Schrödinger-cat states, binomial states, Gottesman-Kitaev-Preskill states, as well as cubic phase states. The latter states have been long sought after in quantum optics and have never been achieved experimentally before. We use a sequence of interleaved selective number-dependent arbitrary phase (SNAP) gates and displacements. We optimize the state preparation in two steps. First we use a gradient-descent algorithm to optimize the parameters of the SNAP and displacement gates. Then we optimize the envelope of the pulses implementing the SNAP gates. Our results show that this way of creating highly nonclassical states in a harmonic oscillator is robust to fluctuations of the system parameters such as the qubit frequency and the dispersive shift.

The ability to perform high-precision optical measurements is paramount in science and engineering. Laser interferometry enables interaction-free sensing with a precision ultimately limited by shot noise. Quantum optical sensors can surpass this limit but single- or multiphoton schemes are challenged by low experimental sampling rates, while squeezed-light approaches require complex optical setups and sophisticated time gating. Here, we introduce a simple method that infers optical phase shifts through standard intensity measurements while still maintaining the quantum advantage in the measurement precision. Capitalizing on the robustness and high sampling rates of our device, we implement a quantum optical microphone in the audio band. Its performance is benchmarked against a classical laser microphone in a standardized medically approved speech-recognition test on 45 subjects. We find that quantum-recorded words improve the speech-recognition threshold by $-0.57{\mathrm{dB}}_{\mathrm{SPL}}$, thus making the quantum advantage audible. Not only do these results open the door toward applications in quantum nonlinear interferometry but they also show that quantum phenomena can be experienced by humans.

Current superconducting quantum processors require strategies for coping with material defects and imperfect parameter targeting in order to scale up while maintaining high performance. To that end, in situ control of qubit frequencies with magnetic flux can be used to avoid spurious resonances. However, increased dephasing due to $1/f$ flux noise limits performance at all of these operating points except for noise-protected sweet spots, which are sparse under dc flux bias and monochromatic flux modulation. Here we experimentally demonstrate that two-tone flux modulation can be used to create a continuum of dynamical sweet spots, greatly expanding the range of qubit frequencies achievable while first-order insensitive to slow flux noise. To illustrate some advantages of this flexibility, we use bichromatic flux control to reduce the error rates and gate times of parametric entangling operations between transmons. Independent of the gate scheme, the ability to use flux control to freely select qubit frequencies while maintaining qubit coherence represents an important step forward in the robustness and scalability of near-term superconducting qubit devices.

Tensor processing units (TPUs) are specialized hardware accelerators developed by Google to support large-scale machine-learning tasks but they can also be leveraged to accelerate and scale other linear-algebra-intensive computations. In this paper, we demonstrate the usage of TPUs for massively parallel classical simulations of quantum many-body dynamics on long time scales. We apply our methods to study the phenomenon of Floquet prethermalization, i.e., exponentially slow heating in quantum spin chains subject to high-frequency periodic driving. We simulate the dynamics of $L=34$ qubits for over ${10}^5$ Floquet periods, corresponding to circuits with $4\times {10}^6$ nearest-neighbor two-qubit gates. The circuits simulated have no additional symmetries and represent a pure-state evolution in the full $2^L$-dimensional Hilbert space. This is achieved by distributing the computation over 128 TPU cores. On that size TPU cluster, we find speed-ups in wall-clock run time of 230 times and 15 times when compared to reference CPU and single-graphics-processing-unit (GPU) simulations, respectively, for shorter-time 30-qubit simulations that can be handled by all three platforms. We study the computational cost of the simulations, as a function of both the number of qubits and the number of TPU cores used, up to our maximum capacity of $L=40$ qubits, which requires a “full pod” of 2048 TPU cores with tens of terabytes of memory in total. For these simulations, an eight-TPU-core machine is comparable to a single A100 GPU and thus the full TPU pod is comparable to a machine with hundreds of top-of-the-line GPUs. However, the TPU pod is more energy and cost efficient and readily accessible (via Google Cloud), unlike such large many-GPU configurations. We also study the accumulation of numerical error as a function of circuit depth in very deep circuits. Our work demonstrates that TPUs can offer significant advantages for state-of-the-art simulations of quantum many-body dynamics.

Scalable local control over gate operations is an outstanding challenge in the field of quantum computing and programmable quantum simulation with Rydberg-atom arrays. One approach is to use a global field to excite atoms to the Rydberg state and tune individual atoms in and out of resonance via local light shifts. In this work, we point out that photon-scattering errors from light shifts can be significantly reduced if the light shift is applied to the Rydberg state instead of the ground state, which can be realized in Rydberg states of alkaline-earth atoms using optical transitions in the ion core. As a proof of concept, we experimentally demonstrate global control of Rydberg excitations in an $\mathrm{Yb}$ optical-tweezer array via light shifts induced by a laser tuned near the $\mathrm{Yb}$${}^{+}6s\to 6p_{1/2}$ transition. We also perform detailed spectroscopy of the induced light shift and scattering rates of the $6sns{}^3{\mathrm{S}}_1$ Rydberg states and reveal the existence of satellite lines where losses from autoionization are strongly suppressed. This work can be readily extended to implement local gate operations in Rydberg-atom arrays.

We use the resonant dipole-dipole interaction between Rydberg atoms and a periodic external microwave field to engineer $XXZ$ spin Hamiltonians with tunable anisotropies. The atoms are placed in one-dimensional (1D) and two-dimensional (2D) arrays of optical tweezers. As illustrations, we apply this engineering to two iconic situations in spin physics: the Heisenberg model in square arrays and spin transport in 1D. We first benchmark the Hamiltonian engineering for two atoms and then demonstrate the freezing of the magnetization on an initially magnetized 2D array. Finally, we explore the dynamics of 1D domain-wall systems with both periodic and open boundary conditions. We systematically compare our data with numerical simulations and assess the residual limitations of the technique as well as routes for improvement. The geometrical versatility of the platform, combined with the flexibility of the simulated Hamiltonians, opens up exciting prospects in the fields of quantum simulation, quantum information processing, and quantum sensing.

We propose a hardware architecture and protocol for connecting many local quantum processors contained within an optical cavity. The scheme is compatible with trapped ions or Rydberg arrays, and realizes teleported gates between any two qubits by distributing entanglement via single-photon transfers through a cavity. Heralding enables high-fidelity entanglement even for a cavity of moderate quality. For processors composed of trapped ions in a linear chain, a single cavity with realistic parameters successfully transfers photons every few $\mu \mathrm{s}$, increasing the interchain entanglement rate over 2 orders of magnitude beyond current methods and eliminating a major bottleneck for scaling trapped-ion systems. For one realistic scenario, we outline how to achieve the any-to-any entanglement of 20 ion chains containing a total of 500 qubits in $200\mu \mathrm{s}$, with both fidelities and rates limited only by local operations and ion readout. For processors composed of Rydberg atoms, our method fully connects a large array of thousands of neutral atoms. The connectivity afforded by our architecture is extendable to tens of thousands of qubits using multiple overlapping cavities, expanding capabilities for noisy intermediate-scale quantum era algorithms and Hamiltonian simulations, as well as enabling more robust high-dimensional error-correcting schemes.

A clock is, from an information-theoretic perspective, a system that emits information about time. One may therefore ask whether the theory of information imposes any constraints on the maximum precision of clocks. Here we show a quantum-over-classical advantage for clocks or, more precisely, the task of generating information about what time it is. The argument is based on information-theoretic considerations: we analyze how the accuracy of a clock scales with its size, measured in terms of the number of bits that could be stored in it. We find that a quantum clock can achieve a quadratically improved accuracy compared to a purely classical one of the same size.

An ensemble of noble-gas nuclear spins is a unique quantum system that could maintain coherence for many hours at room temperature and above, owing to exceptional isolation from the environment. This isolation, however, is a mixed blessing, limiting the ability of these ensembles to interface with other quantum systems coherently. Here we show that spin-exchange collisions with alkali-metal atoms render a quantum interface for noble-gas spins without impeding their long coherence times. We formulate the many-body theory of the hybrid system and reveal a collective mechanism that strongly couples the macroscopic quantum states of the two spin ensembles. Despite their stochastic and random nature, weak collisions enable entanglement and reversible exchange of nonclassical excitations in an efficient, controllable, and deterministic process. With recent experiments now entering the strong-coupling regime, this interface paves the way toward realizing hour-long quantum memories and entanglement at room temperature.

The controlled preparation of the excited state in a quantum emitter is a prerequisite for its usage as a single-photon source—a key building block for quantum technologies. In this paper, we propose a coherent excitation scheme using off-resonant pulses. In the usual Rabi scheme, these pulses would not lead to a significant occupation. This is overcome by using a frequency-modulated pulse to swing up the excited-state population. The same effect can be obtained using two pulses with different strong detunings of the same sign. We theoretically analyze the applicability of the scheme to a semiconductor quantum dot. In this case, the excitation is several millielectronvolts below the band gap, i.e., far away from the detection frequency, allowing for easy spectral filtering, and does not rely on any auxiliary particles such as phonons. Our scheme has the potential to lead to the generation of close-to-ideal photons.

We present a method for mitigating measurement errors on quantum computing platforms that does not form the full assignment matrix, or its inverse, and works in a subspace defined by the noisy input bit strings. This method accommodates both uncorrelated and correlated errors and allows for the computation of accurate error bounds. Additionally, we detail a matrix-free preconditioned iterative-solution method that converges in $\mathcal{O}(1)$ steps that is performant and uses orders of magnitude less memory than direct factorization. We demonstrate the validity of our method and mitigate errors in a few seconds on numbers of qubits that would otherwise be impractical.