Quantum communication is needed to build powerful quantum computers and establish reliable quantum networks. At its basis lies the ability to generate and distribute entanglement to separate quantum systems, which can be used to run remote quantum operations on them or teleport quantum states from one system to another with the help of classical channels. To this end, it is useful to harness the resource of continuous-variable (CV) entanglement, since it can be efficiently and unconditionally produced by squeezing light in a nonlinear medium and can be easily manipulated, distributed, and measured using standard components. While various aspects of CV-based quantum communication have been successfully demonstrated in the optical domain, some key capabilities, such as entanglement swapping, have been lacking in the microwave domain. Here, we demonstrate three key elements of CV-based microwave quantum communication: (i) a Josephson mixer operating as a nondegenerate two-mode entangler with maximum measured logarithmic negativity $E_N=1.5$, (ii) a quantum teleportation apparatus, capable of teleporting vacuum and coherent states with a maximum fidelity of 73%, which exceeds the 50% classical limit and is mainly limited by intermediate losses in the setup, and (iii) an entanglement-swapping system which generates entanglement between two remote noninteracting modes via entanglement-swapping operations applied to input vacuum and coherent states with maximum measured logarithmic negativity $E_N=0.53$. Such hardware-efficient CV entanglement building blocks that are based on nondegenerate Josephson mixers could enable wide-ranging applications in modular quantum computation, quantum cryptography, and quantum communication.

We initiate the study of state complexity for continuous-variable quantum systems. Concretely, we consider a setup with bosonic modes and auxiliary qubits, where available operations include Gaussian one- and two-mode operations and single- and two-qubit operations as well as qubit-controlled phase-space displacements. We define the (approximate) complexity of a bosonic state by the minimum size of a circuit that prepares an approximation to the state in trace distance. We propose a new circuit which prepares an approximate Gottesman-Kitaev-Preskill (GKP) state $|{\mathsf{G}\mathsf{K}\mathsf{P}}_{\kappa ,\mathrm{\Delta }}⟩$. Here, ${\kappa }^{-2}$ is the variance of the envelope, and ${\mathrm{\Delta }}^2$ is the variance of the individual peaks. We show that the circuit accepts with constant probability and—conditioned on acceptance—the output state is polynomially close in $(\kappa ,\mathrm{\Delta })$ to the state $|{\mathsf{G}\mathsf{K}\mathsf{P}}_{\kappa ,\mathrm{\Delta }}⟩$. The size of our circuit is linear in $(\log 1/\kappa ,\log 1/\mathrm{\Delta })$. To our knowledge, this is the first protocol for GKP-state preparation with fidelity guarantees for the prepared state. We also show converse bounds, establishing that the linear circuit-size dependence of our construction is optimal. This fully characterizes the complexity of GKP states.

Anticoncentration describes how an ensemble of quantum states spreads over the allowed Hilbert space, leading to statistically uniform output probability distributions. In this work, we investigate the anticoncentration of random Clifford circuits toward the overlap distribution of random stabilizer states. Using exact analytical techniques and extensive numerical simulations based on Clifford replica tensor networks, we demonstrate that random Clifford circuits fully anticoncentrate in logarithmic circuit depth; namely, higher-order moments of the overlap distribution converge to those of random stabilizer states. Moreover, we investigate the effect of introducing a controlled number of non-Clifford (magic) resources into Clifford circuits. We show that inserting a polylogarithmic in qudit number of $T$ states is sufficient to drive the overlap distribution toward the Porter-Thomas statistics, effectively recovering full quantum randomness. In short, this fact presents doped tensor networks and shallow Clifford circuits as pseudomagic quantum states. Our results clarify the interplay between Clifford dynamics, magic-state injection, and quantum complexity, with implications for quantum circuit sampling, many-body quantum physics, and the benchmarking of quantum computational advantage.

Thermodynamic principles governing energy and information are important tools for a deeper understanding and better control of quantum systems. In this work, we experimentally investigate the interplay of the thermodynamic costs and information flow in a quantum system undergoing iterative quantum measurement and feedback. Our study employs a state stabilization protocol involving repeated measurement and feedback on an electronic spin qubit associated with a silicon-vacancy center in diamond, which is strongly coupled to a diamond nanocavity. This setup allows us to verify the fundamental laws of nonequilibrium quantum thermodynamics, including the second law and the fluctuation theorem, both of which incorporate measures of quantum information flow induced by iterative measurement and feedback. We further assess the reducible entropy based on the feedback’s causal structure and quantitatively demonstrate the thermodynamic advantages of non-Markovian feedback over Markovian feedback. For that purpose, we extend the theoretical framework of quantum thermodynamics to include the causal structure of the applied feedback protocol. Our work lays the foundation for investigating the entropic and energetic costs of real-time quantum control in various quantum systems.

We consider a generic one-dimensional spin system of length $L$, arbitrarily large, with strictly local interactions, for example, nearest neighbor, and prove that the dynamical $\alpha$-Rényi entropies, $0<\alpha \le 1$, of an initial product state grow at most linearly in time. This result arises from a general relation among dynamical $\alpha$-Rényi entropies and Lieb-Robinson bounds. We extend our bound on the dynamical generation of entropy to systems with exponential decay of interactions, for values of $\alpha$ close enough to 1, and, moreover, to initial pure states with low entanglement, of the order of $\log L$, that are typically represented by critical states. We establish that low entanglement states have an efficient matrix product state representation that persists at least up to times of the order of $\log L$. The main technical tools are the Lieb-Robinson bounds, to locally approximate the dynamics of the spin chain, a strict upper bound of Audenaert on $\alpha$-Rényi entropies, and a bound on their concavity. Such a bound, that we provide in an appendix, can be of independent interest.

Semiconductor spin qubits have emerged as a promising platform for quantum computing, following a significant improvement in their control fidelities over recent years. Increasing the qubit count remains challenging, beginning with the fabrication of small features and complex fan-outs. A particular challenge has been formed by the need for individual barrier gates to control the exchange interaction between adjacent spin qubits. Here, we propose a method to vary two-qubit interactions without applying pulses on individual barrier gates while also remaining insensitive to detuning noise in first order. Experimentally we find that changing plunger gate voltages over 300 mV can tune the exchange energy $J$ from 100 kHz to 60 MHz. This allows us to perform two-qubit operations without changing the barrier gate voltage. Based on these findings we conceptualize a spin qubit architecture without individual barrier gates, simplifying the fabrication while maintaining the control necessary for universal quantum computation.

It was conjectured 30 years ago that gravity could arise from the entropic rearrangement of information. We offer a set of microscopic quantum models which realize this idea in detail. In particular, we suggest a simple mechanism by which Newton’s law of gravity arises from extremization of the free energy of a collection of qubits or oscillators, rather than from the exchange of virtual quanta of a fundamental field. We give both a local and a nonlocal version of the construction and show how to distinguish a range of these entropic models from ordinary perturbative quantum gravity using existing observations and near-term experiments.

We derive Floquet theory from quantum geometry. We identify quasienergy folding as a consequence of a broken gauge group of the adiabatic gauge potential $\mathrm{U}(1)\mapsto \mathbb{Z}$. Fixing instead the gauge freedom using the parallel-transport gauge uniquely decomposes Floquet dynamics into a purely geometric and a purely dynamical evolution. The dynamical average-energy operator provides an unambiguous sorting of the quasienergy spectrum, identifying a Floquet ground state and suggesting a way to define the filling of Floquet-Bloch bands. We exemplify the features of geometric Floquet theory using an exactly solvable $XY$ model and a nonintegrable kicked Ising chain. We elucidate the geometric origin of inherently nonequilibrium effects, like the $\pi$-quasienergy splitting in discrete time crystals or $\pi$-edge modes in anomalous Floquet topological insulators. The spectrum of the average-energy operator is a susceptible indicator for both heating and spatiotemporal symmetry-breaking transitions. Last, we demonstrate that the periodic lab-frame Hamiltonian generates transitionless counterdiabatic driving for Floquet eigenstates. This work directly bridges seemingly unrelated areas of nonequilibrium physics.

Programmable optical tweezer arrays of molecules are an emerging platform for quantum simulation and quantum information science. For these applications, the reduction and mitigation of errors remain major challenges. In this work, we leverage the rich internal structure of molecules to mitigate two types of errors—internal state preparation and qubit leakage errors. First, we demonstrate robust measurement-enhanced tweezer preparation at a record fidelity using site-resolved error detection followed by tweezer movement. Second, using a new hyperfine qubit encoding well suited for use as a quantum memory, we demonstrate site-resolved detection of qubit leakage errors (erasures) induced by blackbody radiation. This approach constitutes the first demonstration of erasure conversion in molecules, a capability that has found recent interest in quantum error correction. Our work opens the door to new possibilities with molecular tweezer arrays: Measurement-enhanced preparation opens access to mesoscopic defect-free molecular arrays that are important for quantum simulation of interacting many-body systems; erasure conversion in molecular arrays lays the technical groundwork for midcircuit detection, an important capability for explorations in quantum information processing.

Single nitrogen vacancy (NV) centers in diamond have been used extensively for high-sensitivity nanoscale sensing, but conventional approaches use confocal microscopy to measure individual centers sequentially, limiting throughput and access to nonlocal physical properties, where simultaneous, high-fidelity measurement of multiple centers is required. Here, we design and implement a multiplexed NV sensing platform that allows us to read out many single NV centers simultaneously using a low-noise camera. Using this platform, we coherently manipulate and read out the spin states of hundreds of individual NV centers in parallel, achieving comparable magnetic field sensitivity to confocal measurements. We also implement a parallelized version of spin-to-charge-conversion readout for low NV center spin state readout noise and use it to demonstrate multiplexed covariance magnetometry, in which we measure ten two-point magnetic field correlators from five NV centers simultaneously. From these measurements, we demonstrate the quantitative reconstruction of spatially varying magnetic correlations arising from a current-carrying wire. The number of correlators we can measure is limited only by the available laser power, opening the door to massively multiplexed covariance magnetometry. In contrast to scanning probes for imaging spatially varying magnetic fields, our approach measures the temporal dynamics of the magnetic field at many precisely defined positions simultaneously, from which the local noise spectrum and nonlocal properties such as correlation functions can be computed. This high-fidelity readout platform will find immediate applications in studying condensed matter phenomena that are characterized by the noise spectrum or correlation functions, including quantum phase transitions, dynamics far from equilibrium, magnetic order, and correlated electron phenomena.

Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of interest. Recently, a strong notion of quantum ergodicity has been proposed, namely, that isolated, global quantum states uniformly explore their available state space, dubbed Hilbert-space ergodicity. Here, we observe signatures of this process with an experimental Rydberg quantum simulator and various numerical models, before generalizing to the case of a local quantum system interacting with its environment. For a closed system, where the environment is a complementary subsystem, we predict and observe a smooth quantum-to-classical transition in that observables progress from large, quantum fluctuations to small, Gaussian fluctuations as the bath size grows. This transition exhibits universal properties on a quantitative level among a wide range of systems, including those at finite temperature, those with itinerant particles, and random circuits. For an open system, where the environment is uncontrolled, we predict the statistics of observables under largely arbitrary noise channels including those with correlated errors, allowing us to discriminate between candidate error models both for continuous Hamiltonian time evolution and for digital random circuits. This allows for computationally efficient experimental noise learning and, more broadly, is a new avenue for quantitatively classifying the behavior of noisy quantum systems. Ultimately, our results clarify the role of ergodicity in quantum dynamics, with fundamental and practical consequences.

Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems [1]. However, existing control and measurement schemes for qudit systems scale unfavorably with qudit dimension since they decompose $SU(d)$ operations into series of qubitlike rotations and perform measurements on a small number of states [2–6]. Here, we address these challenges by employing simultaneous multifrequency drives to generate rotations and projections in an effective spin-$7/2$ system mapped onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the eight states using a multitone dispersive readout ($F_{\text{assignment}}=88.3\%$) and exploit the strong nonlinearity in a high-$E_J/E_C$ transmon to simultaneously address each transition and realize a spin displacement operator. Combining this displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in $\mathcal{O}(d)$ physical pulses and extract spin displacement gate fidelities ranging from 0.997 to 0.989 for virtual spins of size $j=1$ to $j=7/2$. We demonstrate the potential of our control scheme in three ways: the direct measurement of the spin qudit Wigner function, randomized benchmarking of a logical qubit encoded into the qudit state, and randomized benchmarking of the full qudit Clifford group. In the latter experiment, we implement the $d$-dimensional quantum Fourier transform with an average gate fidelity of 0.91(6) in $d=8$. Our multifrequency approach to qudit control and measurement can be readily extended to other physical platforms that realize a multilevel system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.

It is known that particles with exotic properties can emerge in systems made of simple constituents such as qubits, due to long-range quantum entanglement. In this paper, we provide quantitative characterizations of entanglement necessary for emergent anyons and fermions by using the geometric entanglement measure (GEM), which quantifies the maximal overlap between a given state and any short-range-entangled states. For systems with emergent anyons, based on the braiding statistics, we show that the GEM scales linearly in the system size regardless of microscopic details. The phenomenon of emergent anyons can also be understood within the framework of quantum error correction (QEC). Specifically, we show that the GEM of any 2D stabilizer codes must be at least quadratic in the code distance. Our proof is based on a generic prescription for constructing string operators, establishing a rigorous and direct connection between emergent anyons and QEC. For systems with emergent fermions, despite that the ground state subspaces could be exponentially huge and their coding properties could be rather poor, we show that the GEM also scales linearly in the system size. Our analysis establishes an intriguing link between quantum anomaly and entanglement: A quantum state respecting anomalous 1-form symmetries must be long-range entangled and have large GEM. Our results also extend to mixed states, such as the $ZX$-dephased toric code, providing a provably nontrivial class of intrinsically mixed-state phases.

We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in Calderbank-Shor-Steane stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice surgery and some of its recent generalizations are shown to be special cases of homological measurement. Using this framework, we develop a specific protocol called edge expanded homological measurement for fault-tolerant measurement of arbitrary logical Pauli operators of general quantum low density parity-check codes, requiring a number of ancillary qubits growing only linearly with the weight of the logical operator measured, and guarantee that the distance of the code is preserved. We further benchmark our protocol numerically in a photonic architecture based on Gottesman-Kitaev-Preskill qubits, showing that the logical error rates of various codes are on par with other methods requiring more ancilla qubits.

Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight $w$. For sufficiently small values of $w$ and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of $w$ values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.

A novel two-qubit entangling gate for trapped-ion quantum processors is proposed theoretically and demonstrated experimentally. During the gate, double-dressed quantum states are created by applying a phase-modulated continuous driving field. The speed of this quantum gate is an order of magnitude higher than that of previously demonstrated rf controlled two-qubit entangling gates in static magnetic field gradients. At the same time, the field driving the gate dynamically decouples the qubits from amplitude and frequency noise, increasing the qubits’ coherence time by 3 orders of magnitude. The gate requires only a single continuous rf field per qubit, making it well suited for scaling a quantum processor to large numbers of qubits. Implementing this entangling gate, we generate the Bell states $|{\mathrm{\Phi }}^{+}⟩$ and $|{\mathrm{\Psi }}^{+}⟩$ in less than or equal to $313\mathrm{\mu }\mathrm{s}$ with fidelities up to ${98}_{-3}^{+2}\%$ in a static magnetic gradient of only $19.09\mathrm{T}/\mathrm{m}$. At higher magnetic field gradients, the entangling gate speed can be further improved to match that of laser-based counterparts.

The AdS/CFT correspondence stipulates a duality between conformal field theories and certain theories of quantum gravity in one higher spatial dimension. However, probing this conjecture on contemporary classical or quantum computers is challenging. We formulate an efficiently implementable multiscale entanglement renormalization ansatz model of AdS/CFT, providing a mapping between a ($1+1$)-dimensional critical spin system and a ($2+1$)-dimensional bulk theory. Using a combination of numerics and analytics, we show that the bulk theory arising from this optimized tensor network furnishes excitations with attractive interactions. Remarkably, these excitations have one- and two-particle energies matching the predictions for matter coupled to AdS gravity at long distances, thus displaying key features of AdS physics. We show that these potentials arise as a direct consequence of entanglement renormalization and discuss how this approach can be used to efficiently simulate bulk dynamics using realistic quantum devices.

We describe a quantum algorithm for the Planted Noisy $k\mathrm{XOR}$ Problem (also known as Sparse Learning Parity with Noise) that achieves a nearly quartic (fourth-power) speedup over the best known classical algorithm while using exponentially less space. Our work generalizes and simplifies prior work of Hastings [Quantum 4, 237 (2020)], by building on his quantum algorithm for the tensor principal component analysis (PCA) problem. We achieve our quantum speedup using a general framework based on the Kikuchi method (recovering the quartic speedup for Tensor PCA), and we anticipate it will yield similar speedups for further planted inference problems. These speedups rely on the fact that planted inference problems naturally instantiate the guided sparse Hamiltonian problem. Since the Planted Noisy $k\mathrm{XOR}$ Problem has been used as a component of certain cryptographic constructions, our work suggests that some of these are susceptible to superquadratic quantum attacks.

In the realm of long-distance quantum communication, asynchronous measurement-device-independent quantum key distribution (AMDI-QKD) stands out for its experimental simplicity and high key rate generation. Despite these advantages, there exists a challenge in finding a balance between simplifying the laser system further and achieving high key rates. To address this challenge, we have devised a postmeasurement compensation scheme to accurately estimate the mutual frequency offset between two compact lasers using just the announced quantum-signal detection results, thereby obviating the need for optical reference light. As a result, we demonstrate an AMDI-QKD system operating at 2.5 GHz and achieving secure key rates (SKRs) of 537 and $101\mathrm{kbit}/\mathrm{s}$ at distances of 100 and 201 km, respectively, showcasing a significant key rate improvement compared to similar setups. By leveraging ultrastable lasers, we achieve the highest SKRs with measurement-device-independent security within the 100–400-km range. Over 100 km, we reach a remarkable key rate of $1.03\mathrm{Mbit}/\mathrm{s}$, which could enable real-time one-time-pad video encryption. These findings render AMDI-QKD as a promising contender for the establishment of high performance and cost-effective large-scale intercity quantum networks.