We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state $t$-designs from [Blume-Kohout et al., Commun. Math. Phys. 326, 755 (2014)], no state designs exist for $t\ge 2$. Similarly, we prove that no CV unitary $t$-designs exist for $t\ge 2$. We propose an alternative definition for CV state designs, which we call rigged $t$-designs, and provide explicit constructions for $t=2$. As an application of rigged designs, we develop a design-based shadow-tomography protocol for CV states. Using energy-constrained versions of rigged designs, we define an average fidelity for CV quantum channels and relate this fidelity to the CV entanglement fidelity. As an additional result of independent interest, we establish a connection between torus 2-designs and complete sets of mutually unbiased bases.

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps $n$. Here, we introduce a numerically exact algorithm to calculate process tensors—compact representations of environmental influences—which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent the environment. It is applicable to environments with Gaussian statistics, such as for spin-boson-type open quantum systems. Based on a divide-and-conquer strategy, our approach requires only $\mathcal{O}(n\log n)$ singular value decompositions for environments with infinite memory. Where the memory can be truncated after $n_c$ time steps, a nominal scaling $\mathcal{O}(n_c\log n_c)$ is found, which is independent of $n$. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach, we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dot-phonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The observed computation time is not necessarily proportional to the number of singular value decompositions because the matrix dimensions also depend on the number of time steps. Nevertheless, quasilinear and sublinear scaling of computation time is found in practice for a wide range of parameters. While there are instances where existing methods can achieve comparable nominal scaling by precalculating effective propagators for time-independent or periodic system Hamiltonians, process tensors contain all the information needed to extract arbitrary multitime correlation functions of the system when driven by arbitrary time-dependent system Hamiltonians. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but it also has fundamental implications for the simulation complexity of tensor network approaches.

Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyperoptimization over the compression and contraction strategy itself to minimize error and cost. We demonstrate that our protocol outperforms both handcrafted contraction strategies in the literature as well as recently proposed general contraction algorithms on a variety of synthetic and physical problems on regular lattices and random regular graphs. We further showcase the power of the approach by demonstrating approximate contraction of tensor networks for frustrated three-dimensional lattice partition functions, dimer counting on random regular graphs, and to access the hardness transition of random tensor network models, in graphs with many thousands of tensors.

Owing to their strong dipole moment and long coherence times, superconducting qubits have demonstrated remarkable success in hybrid quantum circuits. However, most qubit architectures are limited to the GHz frequency range, severely constraining the class of systems they can interact with. The fluxonium qubit, on the other hand, can be biased to very low frequency while being manipulated and read out with standard microwave techniques. Here, we design and operate a heavy fluxonium with an unprecedentedly low transition frequency of 1.8 MHz. We demonstrate resolved sideband cooling of the “hot” qubit transition with a final ground state population of 97.7%, corresponding to an effective temperature of $23\mathrm{\mu }\mathrm{K}$. We further demonstrate coherent manipulation with coherence times $T_1=34\mathrm{\mu }\mathrm{s}$, $T_2^{*}=39\mathrm{\mu }\mathrm{s}$, and single-shot readout of the qubit state. Importantly, by directly addressing the qubit transition with a capacitively coupled waveguide, we showcase its high sensitivity to a radio-frequency field. Through cyclic qubit preparation and interrogation, we transform this low-frequency fluxonium qubit into a frequency-resolved charge sensor. This method results in a charge sensitivity of $33\mathrm{\mu }\mathrm{e}/\sqrt{\mathrm{Hz}}$, or an energy sensitivity (in joules per hertz) of $2.8\hslash$. This method rivals state-of-the-art transport-based devices, while maintaining inherent insensitivity to dc-charge noise. The high charge sensitivity combined with large capacitive shunt unlocks new avenues for exploring quantum phenomena in the 1–10 MHz range, such as the strong-coupling regime with a resonant macroscopic mechanical resonator.

Exotic quantum many-body states, such as Haldane and spin liquid phases, can exhibit remarkable features like fractional excitations and non-Abelian statistics and offer new understandings of quantum entanglement in many-body quantum systems. These phases are classified by nonlocal correlators that can be directly measured in atomic analog quantum simulating platforms, such as optical lattices and Rydberg atom arrays. However, characterizing these phases in large systems is experimentally challenging because they are sensitive to local errors like atom loss, which suppress its signals exponentially. Additionally, protocols for systematically identifying and mitigating uncorrelated errors in analog quantum simulators are lacking. Here, we address these challenges by developing an error-correction method for large-scale neutral atom quantum simulators using optical lattices. Our error-correction method can distinguish correlated particle-hole pairs from uncorrelated holes in the Mott insulator. After removing the uncorrelated errors, we observe a dramatic improvement in the nonlocal parity correlator and find the perimeter scaling law. Furthermore, the error model provides a statistical estimation of fluctuations in site occupation, from which we measure the generalized brane correlator and confirm that it can be an order parameter for Mott insulators in two dimensions. Our work provides a promising avenue for investigating and characterizing exotic phases of matters in large-scale quantum simulators.

The elementary excitations in weakly interacting quantum fluids have a nontrivial nature which is at the basis of defining quantum phenomena such as superfluidity. These excitations and the physics they lead to have been explored in closed quantum systems at thermal equilibrium both theoretically within the celebrated Bogoliubov framework and experimentally in quantum fluids of ultracold atoms. Over the past decade, the relevance of Bogoliubov excitations has become essential to understand quantum fluids of interacting photons. Their driven-dissipative character leads to distinct properties with respect to their equilibrium counterparts. For instance, the condensate coupling to the photonic vacuum environment leads to a nonzero generation rate of elementary excitations with many striking implications. In this work, considering that quantum fluids of light are often hosted in solid-state systems, we show within a joint theory-experiment analysis that the vibrations of the crystal constitute another environment that the condensate is fundamentally coupled to. This coupling leads to a unique heat transfer mechanism, resulting in a large generation rate of elementary excitations in typical experimental conditions, and to a fundamental nonzero contribution at vanishing temperatures. Our work provides a complete framework for solid-embedded quantum fluids of light, which is invaluable in view of achieving a regime dominated by photon-vacuum fluctuations.

A number of commercially available quantum computers, such as those based on trapped-ion or superconducting qubits, can now perform mid-circuit measurements and resets. In addition to being crucial for quantum error correction, this capability can help reduce the number of qubits needed to execute many types of quantum algorithms by measuring qubits as early as possible, resetting them, and reusing them elsewhere in the circuit. In this work, we introduce the idea of qubit-reuse compilation, which takes as input a quantum circuit and produces as output a compiled circuit that requires fewer qubits to execute due to qubit reuse. We present two algorithms for performing qubit-reuse compilation: an exact constraint programming optimization model and a greedy heuristic. We introduce the concept of dual circuits, obtained by exchanging state preparations with measurements and vice versa and reversing time, and show that optimal qubit-reuse compilation requires the same number of qubits to execute a circuit as its dual. We illustrate the performance of these algorithms on a variety of relevant near-term quantum circuits, such as one-dimensional and two-dimensional time-evolution circuits, and numerically benchmark their performance on the quantum adiabatic optimization algorithm (QAOA) applied to the MaxCut problem on random three-regular graphs. To demonstrate the practical benefit of these techniques, we experimentally realize an 80-qubit QAOA MaxCut circuit on the 20-qubit Quantinuum H1-1 trapped-ion quantum processor using qubit-reuse compilation algorithms.

We describe and benchmark a new quantum charge-coupled device (QCCD) trapped-ion quantum computer based on a linear trap with periodic boundary conditions, which resembles a race track. The new system successfully incorporates several technologies crucial to future scalability—including electrode broadcasting, multilayer rf routing, and magneto-optical trap (MOT) loading—while maintaining, and in some cases exceeding, the gate fidelities of previous QCCD systems. The system is initially operated with 32 qubits, but future upgrades will allow for more. We benchmark the performance of primitive operations, including an average state preparation and measurement error of $1.6(1)\times {10}^{-3}$, an average single-qubit gate infidelity of $2.5(3)\times {10}^{-5}$, and an average two-qubit gate infidelity of $1.84(5)\times {10}^{-3}$. The system-level performance of the quantum processor is assessed with mirror benchmarking, linear cross-entropy benchmarking, a quantum volume measurement of $\mathrm{QV}=2^{16}$, and the creation of 32-qubit entanglement in a GHZ state. We also tested application benchmarks, including Hamiltonian simulation, QAOA, error correction on a repetition code, and dynamics simulations using qubit reuse. We also discuss future upgrades to the new system aimed at adding more qubits and capabilities.

We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers, based on the Keldysh path-integral formalism and replica trick. In the limit of rare measurements, $\gamma /J\ll 1$ (where $\gamma$ is measurement rate per site and $J$ is hopping constant in the tight-binding model), we derive a nonlinear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is described by a $\mathrm{U}(2)/\mathrm{U}(1)\times \mathrm{U}(1)\simeq S^2$ sigma model with diffusive behavior, and the replica-asymmetric sector is a two-dimensional NLSM defined on $\mathrm{SU}(R)$ manifold with the replica limit $R\to 1$. On the Gaussian level, valid in the limit $\gamma /J\to 0$, this model predicts a logarithmic behavior for the second cumulant of number of particles in a subsystem and for the entanglement entropy. However, the one-loop renormalization group analysis allows us to demonstrate that this logarithmic growth saturates at a finite value $\sim (J/\gamma {)}^2$ even for rare measurements, which corresponds to the area-law phase. This implies the absence of a measurement-induced entanglement phase transition for free fermions. The crossover between logarithmic growth and saturation, however, happens at exponentially large scale, $\ln l_{\mathrm{corr}}\sim J/\gamma$. This makes this crossover very sharp as a function of the measurement frequency $\gamma /J$, which can be easily confused with a transition from the logarithmic to area law in finite-size numerical calculations. We have performed a careful numerical analysis, which supports our analytical predictions.

We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multiflavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators. Using the replica trick, we map the dynamics to the imaginary time evolution of an effective spin chain and use the number of flavors as a large parameter for a controlled derivation of the effective field theory. This is a nonlinear sigma model for an orthogonal $N\times N$ matrix, in the replica limit $N\to 1$. (On a boundary of the phase diagram, another sigma model with higher symmetry applies.) Together with known results for the renormalization-group beta function, this derivation establishes the existence of stable phases—nontrivially entangled and disentangled, respectively—in the physically relevant replica limit $N\to 1$. In the nontrivial phase, an asymptotically exact calculation shows that the bipartite entanglement entropy for a system of size $L$ scales as $(\ln L{)}^2$, in contrast to findings in previously studied models. Varying the relative strength of Hamiltonian evolution and monitoring, as well as a dimerization parameter, the model’s phase diagram contains transitions out of the nontrivial phase, which we map to vortex-unbinding transitions in the sigma model, and also contains separate critical points on the measurement-only axis. We highlight the close analogies as well as the differences with the replica approach to Anderson transitions in disordered systems.

Quantum critical systems constitute appealing platforms for exploring novel measurement-induced phenomena due to their innate sensitivity to perturbations. We study the impact of measurements on paradigmatic Ising quantum-critical chains using an explicit protocol, whereby correlated ancillae are entangled with the critical chain and then projectively measured. Using a perturbative analytic framework supported by extensive numerical simulations, we demonstrate that measurements can qualitatively alter critical correlations in a manner dependent on the choice of entangling gate, ancilla measurement basis, measurement outcome, and nature of ancilla correlations. We further show that measurement-altered Ising criticality can be pursued surprisingly efficiently in experiments featuring of order 100 qubits by postselecting for high-probability measurement outcomes or, in certain cases, by averaging observables separately over measurement outcomes residing in distinct symmetry sectors. Our framework naturally adapts to more exotic quantum-critical points and highlights opportunities for realization in noisy intermediate-scale quantum hardware and in Rydberg arrays.

Robust spin-photon interfaces in solids are essential components in quantum networking and sensing technologies. Ideally, these interfaces combine a long-lived spin memory, coherent optical transitions, fast and high-fidelity spin manipulation, and straightforward device integration and scaling. The tin-vacancy center (SnV) in diamond is a promising spin-photon interface with desirable optical and spin properties at 1.7 K. However, the SnV spin lacks efficient microwave control, and its spin coherence degrades with higher temperature. In this work, we introduce a new platform that overcomes these challenges—SnV centers in uniformly strained thin diamond membranes. The controlled generation of crystal strain introduces orbital mixing that allows microwave control of the spin state with 99.36(9)% gate fidelity and spin coherence protection beyond a millisecond. Moreover, the presence of crystal strain suppresses temperature-dependent dephasing processes, leading to a considerable improvement of the coherence time up to $223(10)\mathrm{\mu }\mathrm{s}$ at 4 K, a widely accessible temperature in common cryogenic systems. Critically, the coherence of optical transitions is unaffected by the elevated temperature, exhibiting nearly lifetime-limited optical linewidths. Combined with the compatibility of diamond membranes with device integration, the demonstrated platform is an ideal spin-photon interface for future quantum technologies.

Midcircuit operations, such as qubit state measurement or reset, are central to many tasks in quantum information science, including quantum computing, entanglement generation, and metrology. For instance, in quantum error correction, the information gained from a measurement on a subset of qubits is used to influence the state of the remaining unmeasured qubits, rectifying inevitable errors that arise in a quantum circuit. Such partial projective operations pose a challenge for dense neutral atom arrays and trapped ions, where accidental exposure to resonant laser light during quantum state initialization and detection can spoil the state of untargeted qubits. In this work, we implement midcircuit operations in a 48-site array of neutral atoms, enabled by new methods for high-fidelity control of the omg (optical-metastable-ground-state qubit) architecture present in ${}^{171}\mathrm{Yb}$. Here, the quantum information is encoded in either of the three qubit manifolds and can be shuttled between them. With state-sensitive shelving between the ground and metastable states, we realize a nondestructive state detection for ${}^{171}\mathrm{Yb}$, incorporating global control and local feed-forward operations. Using new schemes for local addressing of the optical clock transition, we shelve a subset of qubits to the metastable state, hiding them from projective operations performed on the qubits remaining in the ground state, demonstrating midcircuit measurement, spin reset, and motional reset in the form of ground-state cooling.

Environment is assumed to play a negative role in quantum mechanics, destroying the coherence in a quantum system and, thus, randomly changing its state. However, for a quantum system that is initially in a degenerate ground state, the situation could be different. In this case, the infinite manifold of ground state eigenfunctions can contain a few states of zero entanglement, which can be demonstrated based on the minimization of the von Neumann entropy. Then, following quantum Darwinism, these “classical” combinations are selected and promoted by the quantum environment, which means that different independent observers find them in experiments. In this work, we find and explore such classical states in the eigenspectra of skyrmionic and antiferromagnetic quantum systems starting from a numerical realization of Anderson’s tower of states. The degeneracy of the quantum ground state is shown to be the key for explaining nontrivial properties of magnetic matter in the classical world including topological protection arising in the classical limit.

The quantum Jarzynski equality and the Crooks relation are fundamental laws connecting equilibrium processes with nonequilibrium fluctuations. They are promising tools to benchmark quantum devices and measure free energy differences. While they are well established theoretically and also experimental realizations for few-body systems already exist, their experimental validity in the quantum many-body regime has not been observed so far. Here, we present results for nonequilibrium protocols in systems with up to 16 interacting degrees of freedom obtained on trapped ion and superconducting qubit quantum computers, which test the quantum Jarzynski equality and the Crooks relation in the many-body regime. To achieve this, we overcome present-day limitations in the preparation of thermal ensembles and in the measurement of work distributions on noisy intermediate-scale quantum devices. We discuss the accuracy to which the Jarzynski equality holds on different quantum computing platforms subject to platform-specific errors. The analysis reveals the validity of Jarzynski’s equality in a regime with energy dissipation, compensated for by a fast unitary drive. This provides new insights for analyzing errors in many-body quantum simulators.

The amplitude-damping time $T_1$ has long stood as the major factor limiting quantum fidelity in superconducting circuits, prompting concerted efforts in the material science and design of qubits aimed at increasing $T_1$. In contrast, the dephasing time $T_{\varphi }$ can usually be extended above $T_1$ (via, e.g., dynamical decoupling) to the point where it does not limit fidelity. In this article, we propose a scheme for overcoming the conventional $T_1$ limit on fidelity by designing qubits in a way that amplitude-damping errors can be detected and converted into erasure errors. Compared to standard qubit implementations, our scheme improves the performance of fault-tolerant protocols, as numerically demonstrated by the circuit-noise simulations of the surface code. We describe two simple qubit implementations with superconducting circuits and discuss procedures for detecting amplitude-damping errors, performing entangling gates, and extending $T_{\varphi }$. Our results suggest that engineering efforts should focus on improving $T_{\varphi }$ and the quality of quantum coherent control, as they effectively become the limiting factor on the performance of fault-tolerant protocols.

Quantum noise imposes a fundamental limitation on the sensitivity of interferometric gravitational-wave detectors like LIGO, manifesting as shot noise and quantum radiation pressure noise. Here, we present the first realization of frequency-dependent squeezing in full-scale gravitational-wave detectors, resulting in the reduction of both shot noise and quantum radiation pressure noise, with broadband detector enhancement from tens of hertz to several kilohertz. In the LIGO Hanford detector, squeezing reduced the detector noise amplitude by a factor of 1.6 (4.0 dB) near 1 kHz; in the Livingston detector, the noise reduction was a factor of 1.9 (5.8 dB). These improvements directly impact LIGO’s scientific output for high-frequency sources (e.g., binary neutron star postmerger physics). The improved low-frequency sensitivity, which boosted the detector range by 15%–18% with respect to no squeezing, corresponds to an increase in the astrophysical detection rate of up to 65%. Frequency-dependent squeezing was enabled by the addition of a 300-meter-long filter cavity to each detector as part of the LIGO $\mathrm{A}+$ upgrade.

The expressive capacity of physical systems employed for learning is limited by the unavoidable presence of noise in their extracted outputs. Though present in physical systems across both the classical and quantum regimes, the precise impact of noise on learning remains poorly understood. Focusing on supervised learning, we present a mathematical framework for evaluating the resolvable expressive capacity (REC) of general physical systems under finite sampling noise and provide a methodology for extracting its extrema, the eigentasks. Eigentasks are a native set of functions that a given physical system can approximate with minimal error. We show that the REC of a quantum system is limited by the fundamental theory of quantum measurement and obtain a tight upper bound for the REC of any finitely sampled physical system. We then provide empirical evidence that extracting low-noise eigentasks can lead to improved performance for machine learning tasks such as classification, displaying robustness to overfitting. We present analyses suggesting that correlations in the measured quantum system enhance learning capacity by reducing noise in eigentasks. The applicability of these results in practice is demonstrated with experiments on superconducting quantum processors. Our findings have broad implications for quantum machine learning and sensing applications.

Electronic Fabry-Pérot interferometry is a powerful method to probe quasiparticle charge and anyonic braiding statistics in the fractional quantum Hall regime. We extend this technique to the hierarchy $\nu =2/5$ fractional quantum Hall state, possessing two edge modes that in our device can be interfered independently. The outer edge mode exhibits interference similar to the behavior observed at the $\nu =1/3$ state, indicating that the outer edge mode at $\nu =2/5$ has properties similar to the single mode at $\nu =1/3$. The inner mode shows an oscillation pattern with a series of discrete phase jumps indicative of distinct anyonic braiding statistics. After taking into account the impact of bulk-edge coupling, we extract an interfering quasiparticle charge $e^{*}=0.17\pm 0.02$ and anyonic braiding phase ${\theta }_a=(-0.43\pm 0.05)\times 2\pi$, which serve as experimental verification of the theoretically predicted values of $e^{*}=\frac{1}{5}$ and ${\theta }_a=-(4\pi /5)$.

The concept of space evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix rather than the time evolution operator. The infinite-volume limit is then described by the fixed points of the latter transfer matrix, also known as influence matrices. To establish the potential of this method as a bona fide computational scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. Here we begin this quest by presenting a systematic characterization of their entanglement—dubbed temporal entanglement—in chaotic quantum systems. We consider the most general form of space evolution, i.e., evolution in a generic spacelike direction, and present two fundamental results. First, we show that temporal entanglement always follows a volume law in time. Second, we identify two marginal cases—(i) pure space evolution in generic chaotic systems and (ii) any spacelike evolution in dual-unitary circuits—where Rényi entropies with index larger than one are sublinear in time while the von Neumann entanglement entropy grows linearly. We attribute this behavior to the existence of a product state with large overlap with the influence matrices. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution.