Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, in both nanotechnology and biology. Progress in computing optimal protocols to extremize thermodynamic variables has, thus far, been limited to either simple systems or near-equilibrium evolution. Here, we present an approach for computing optimal protocols based on automatic differentiation. Our methodology is applicable to complex systems and multidimensional protocols and is valid arbitrarily far from equilibrium. We validate our method by reproducing theoretical optimal protocols for a Brownian particle in a time-varying harmonic trap. We also compute departures from near-equilibrium behavior for magnetization reversal on an Ising lattice and for barrier crossing driven by a harmonic trap, which is used to represent a range of biological processes including biomolecular unfolding reactions. Algorithms based on automatic differentiation outperform the near-equilibrium theory for far-from-equilibrium magnetization reversal and for driven barrier crossing beyond the linear regime. The optimal protocol for far-from-equilibrium driven barrier crossing is found to hasten the approach to, and slow the departure from, the barrier region compared to the near-equilibrium theoretical protocol. We demonstrate the utility of our method in a real-world use case by reducing the work required to unfold a DNA hairpin in the coarse-grained oxDNA model and improving its nonequilibrium free-energy landscape reconstruction compared to a naive linear protocol.

A solid loaded beyond the yield stress loses its elastic properties and becomes plastic. From a microscopic point of view, this limit corresponds to the condition where plastic regions become so densely packed that they give rise to system-spanning structures. This limit for glasses is abrupt, which makes experimental investigations challenging. Here, the yield point is reached by the alternative approach of increasing the density of plastic regions by generation of point defects during x-ray irradiation. For the case of a ${\mathrm{LiBO}}_2$ glass, we show that at low doses, i.e., for a low density of defects, the defects behave as isolated stress sources that induce atomic displacements typical of an elastic solid. As the density of defects increases, the mechanical response of the glass at the local scale changes from elastic to more and more plastic, until reaching the limit where it becomes characteristic of a flowing system, which signals that the yield point is reached.

Randomized benchmarking (RB) protocols are the most widely used methods for assessing the performance of quantum gates. However, the existing RB methods either do not scale to many qubits or cannot benchmark a universal gate set. Here, we introduce and demonstrate a technique for scalable RB of many universal and continuously parametrized gate sets, using a class of circuits called randomized mirror circuits. Our technique can be applied to a gate set containing an entangling Clifford gate and the set of arbitrary single-qubit gates, as well as gate sets containing controlled rotations about the Pauli axes. We use our technique to benchmark universal gate sets on four qubits of the Advanced Quantum Testbed, including a gate set containing a controlled-S gate and its inverse, and we investigate how the observed error rate is impacted by the inclusion of non-Clifford gates. Finally, we demonstrate that our technique scales to many qubits with experiments on a 27-qubit IBM Q processor. We use our technique to quantify the impact of crosstalk on this 27-qubit device, and we find that it contributes approximately $2/3$ of the total error per gate in random many-qubit circuit layers.

Chromosomes are exceedingly long topologically constrained polymers compacted in a cell nucleus. We recently suggested that chromosomes are organized into loops by an active process of loop extrusion. Yet loops remain elusive to direct observations in living cells; detection and characterization of myriads of such loops is a major challenge. The lack of a tractable physical model of a polymer folded into loops limits our ability to interpret experimental data and detect loops. Here, we introduce a new physical model—a polymer folded into a sequence of loops—and solve it analytically. Our model and a simple geometrical argument show how loops affect the statistics of contacts in a polymer across different scales, explaining universally observed shapes of the contact probability. Moreover, we reveal that folding into loops reduces the density of topological entanglements, a novel phenomenon we refer to as “the dilution of entanglements.” Supported by simulations, this finding suggests that up to approximately 1–2-Mb chromosomes with loops are not topologically constrained, yet become crumpled at larger scales. Our theoretical framework allows inference of loop characteristics, draws a new picture of chromosome organization, and shows how folding into loops affects topological properties of crumpled polymers.

Projective measurements in random quantum circuits lead to a rich breadth of entanglement phases and extend the realm of nonunitary quantum dynamics. Here, we explore the connection between measurement-only quantum circuits in one spatial dimension and the statistical mechanics of loop models in two dimensions. While Gaussian Majorana circuits admit a microscopic mapping to loop models, for non-Gaussian, i.e., generic Clifford, circuits, a corresponding mapping may emerge only on a coarse-grained scale. We then focus on a fundamental symmetry of loop models: the orientability of worldlines. We discuss how orientability enters in the measurement framework, acting as a separatrix for the universal long-wavelength behavior in a circuit. When orientability is broken, the circuit falls into the universality class of closely packed loops with crossings (CPLC) and features a Goldstone phase with a peculiar, universal ${\log }^2(L)$ scaling of the entanglement entropy. In turn, when orientability is preserved, the long-wavelength behavior of the circuit mimics that of (coupled) two-dimensional Potts models. We demonstrate the strength of the loop model approach by numerically simulating a variety of measurement-only Clifford circuits. Upon varying the set of measured operators, a rich circuit dynamics is observed, ranging from CPLC to the one-state Potts model (percolation), the two-state Potts model (Ising), and coupled Potts models (Berezhinskii-Kosterlitz-Thouless) universality class. Loop models, thus, provide a handle to access a large class of measurement-only circuits and yield a blueprint on how to realize desired entanglement phases by measurement.

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.

Twisted bilayer ${\mathrm{MoTe}}_2$ is a promising platform to investigate the interplay between band topology and many-body interactions. We present a theoretical study of its interaction-driven quantum phase diagrams based on a three-orbital model, which can be viewed as a generalization of the Kane-Mele-Hubbard model with one additional orbital and long-range Coulomb repulsion. We predict a cascade of phase transitions tuned by the twist angle $\theta$. At the hole-filling factor $\nu =1$ (one hole per moiré unit cell), the ground state can be in the multiferroic phase, with coexisting spontaneous layer polarization and magnetism; the quantum anomalous Hall phase; and finally, the topologically trivial magnetic phases, as $\theta$ increases from 1.5° to 5°. At $\nu =2$, the ground state can have a second-order phase transition between an antiferromagnetic phase and the quantum spin Hall phase as $\theta$ passes through a critical value. The dependence of the phase boundaries on model parameters, such as the gate-to-sample distance, the dielectric constant, and the moiré potential amplitude, is examined. The predicted phase diagrams can guide the search for topological phases in twisted transition metal dichalcogenide homobilayers.

Chiral molecules provide an ideal test platform to search for symmetry breaking in nature, due to the perfect parity symmetry of their left- and right-handed enantiomers under the electromagnetic interaction. This high degree of symmetry drives efforts to probe the two enantiomers individually after they have been chemically separated, but this allows external effects to influence the measurement, ultimately harming the precision. In particular, the complexity of such polyatomic molecules makes them difficult to control and detect precisely. Employing a more symmetrical measurement procedure can improve the experiment fidelity and alleviate issues associated with molecular complexity. To this end, we theoretically introduce a scheme to perform Ramsey spectroscopy on a racemic mixture of chiral molecules, simultaneously extracting the transition frequencies of the two enantiomers. By taking the difference between the enantiospecific frequencies, we isolate parity violating effects such as the weak force, which is predicted to break the symmetry between enantiomers. To perform the scheme, we design a pulse sequence that creates enantiospecific superpositions in a three-level system using the enantiomer-dependent sign of the electric-dipole moment components’ triple product. A delayed second pulse sequence completes the Ramsey interrogation sequence, enabling readout of the phase evolution for each enantiomer’s transition through a separate quantum state. Our technique overcomes the need to alternate between enantiopure samples to measure parity violation, and is applicable to both charged and neutral molecular species. We describe the advantages of the proposed method for precision metrology.

Metamaterials, from optics to radio frequencies and acoustics, have attracted significant attention over the last few decades, with promising applications in a wide range of technological areas. However, it has been recognized that their performance is often hindered by ubiquitous material loss and nonlocal phenomena. A canonical problem consists in imaging through metamaterial superlenses, which hold the promise of superresolution but which are, in practice, limited by material loss as we attempt to image deeply subwavelength details. Active metamaterials have been explored to compensate for loss; however, material gain introduces other obstacles, e.g., instabilities, nonlinearity, and noise. Here, we demonstrate that the temporal excitation of passive metamaterials using signals oscillating at complex frequencies can effectively compensate material loss, leading to resolution enhancement when applied to metamaterial superlenses. More broadly, our results demonstrate that virtual gain stemming from tailored forms of excitation can tackle the impact of loss in metamaterials, opening promising avenues for a broad range of applications from acoustic to photonic technologies.

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.

Topological superconductivity is a long-sought state of matter in bulk materials, and the odd-parity superconductor ${\mathrm{UTe}}_2$ is a prime candidate. The recent observation of a field-trainable spontaneous Kerr signal in ${\mathrm{UTe}}_2$ at the onset of superconductivity provides strong evidence that the superconducting order parameter is multicomponent and breaks time-reversal symmetry. Here, we perform Kerr effect measurements on a number of ${\mathrm{UTe}}_2$ samples—grown via both chemical vapor transport and the molten-salt-flux methods—that show a single superconducting transition between 1.6 K and 2.1 K. Our results show no evidence for a spontaneous Kerr signal in zero-field measurements. This implies that the superconducting state of ${\mathrm{UTe}}_2$ does not intrinsically break time-reversal symmetry. Instead, we observe a field-trainable signal that varies in magnitude between samples and between different locations on a single sample, which is a sign of inhomogeneous magnetic regions. Our results provide an examination of representative ${\mathrm{UTe}}_2$ samples and place strong constraints on the superconducting order parameter of ${\mathrm{UTe}}_2$.

Quantum materials display rich and myriad types of magnetic, electronic, and structural ordering, often with these ordering modes either competing with one another or “intertwining,” that is, reinforcing one another. Low-dimensional quantum materials influenced strongly by competing interactions and/or geometric frustration are particularly susceptible to such ordering phenomena and thus offer fertile ground for understanding the consequent emergent collective quantum phenomena. Such is the case of the quasi-2D materials ${\mathrm{R}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ ($R=\mathrm{La}$, Pr), in which intertwined charge- and spin-density waves (CDW and SDW) on the Ni sublattice have been identified and characterized. Not unexpectedly, these density waves are largely quasi-2D as a result of weak coupling between planes, compounded with magnetic frustration. In the case of $R=\mathrm{Pr}$, however, we show here that exchange coupling between the transition-metal and rare-earth sublattices upon cooling overcomes both obstacles, leading to a dimensional crossover into a fully 3D-ordered and coupled SDW state on both sublattices, as an induced moment on notionally nonmagnetic ${\mathrm{Pr}}^{3+}$ opens exchange pathways in the third dimension. In the process, the structure of the SDW on the Ni sublattice is irreversibly altered, an effect that survives reheating of the material until the underlying CDW melts. This “bootstrapping” mechanism linking incommensurate SDWs on the two sublattices illustrates a new member of the multitude of quantum states that low-dimensional magnets can express, driven by coupled orders and modulated by frustrated exchange pathways.

Most natural and engineered information-processing systems transmit information via signals that vary in time. Computing the information transmission rate or the information encoded in the temporal characteristics of these signals requires the mutual information between the input and output signals as a function of time, i.e., between the input and output trajectories. Yet, this is notoriously difficult because of the high-dimensional nature of the trajectory space, and all existing techniques require approximations. We present an exact Monte Carlo technique called path weight sampling (PWS) that, for the first time, makes it possible to compute the mutual information between input and output trajectories for any stochastic system that is described by a master equation. The principal idea is to use the master equation to evaluate the exact conditional probability of an individual output trajectory for a given input trajectory and average this via Monte Carlo sampling in trajectory space to obtain the mutual information. We present three variants of PWS, which all generate the trajectories using the standard stochastic simulation algorithm. While direct PWS is a brute-force method, Rosenbluth-Rosenbluth PWS exploits the analogy between signal trajectory sampling and polymer sampling, and thermodynamic integration PWS is based on a reversible work calculation in trajectory space. PWS also makes it possible to compute the mutual information between input and output trajectories for systems with hidden internal states as well as systems with feedback from output to input. Applying PWS to the bacterial chemotaxis system, consisting of 182 coupled chemical reactions, demonstrates not only that the scheme is highly efficient but also that the number of receptor clusters is much smaller than hitherto believed, while their size is much larger.

A time crystal is a state of periodically driven matter that breaks discrete time-translation symmetry. Time crystals have been demonstrated experimentally in various programmable quantum simulators, and they exemplify how nonequilibrium, driven quantum systems can exhibit intriguing and robust properties absent in systems at equilibrium. These robust driven states need to be stabilized by some mechanism, with the preeminent candidates being many-body localization and prethermalization. This introduces additional constraints that make it challenging to experimentally observe time crystallinity in naturally occurring systems. Recent theoretical work has developed the notion of prethermalization without temperature, expanding the class of time-crystal systems to explain time-crystalline observations at (or near) infinite temperature. In this work, we conclusively observe the emergence of a prethermal $U(1)$ time-crystalline state at quasi-infinite temperature in a solid-state NMR quantum emulator by verifying the requisites of prethermalization without temperature. In addition to observing the signature period-doubling behavior, we show the existence of a long-lived prethermal regime whose lifetime is significantly enhanced by strengthening an emergent $U(1)$ conservation law. Not only do we measure this enhancement through the global magnetization, but we also exploit on-site disorder to measure local observables, ruling out the possibility of many-body localization and confirming the emergence of long-range correlations.

As spin-based quantum processors grow in size and complexity, maintaining high fidelities and minimizing crosstalk will be essential for the successful implementation of quantum algorithms and error-correction protocols. In particular, recent experiments have highlighted pernicious transient qubit frequency shifts associated with microwave qubit driving. Work-arounds for small devices, including prepulsing with an off-resonant microwave burst to bring a device to a steady state, wait times prior to measurement, and qubit-specific calibrations all bode ill for device scalability. Here, we make substantial progress in understanding and overcoming this effect. We report a surprising nonmonotonic relation between mixing chamber temperature and spin Larmor frequency which is consistent with observed frequency shifts induced by microwave and baseband control signals. We find that purposefully operating the device at 200 mK greatly suppresses the adverse heating effect while not compromising qubit coherence or single-qubit fidelity benchmarks. Furthermore, systematic non-Markovian crosstalk is greatly reduced. Our results provide a straightforward means of improving the quality of multispin control while simplifying calibration procedures for future spin-based quantum processors.

Continuum mechanics describes compressive failure as a standard bifurcation in the response of a material to an increasing load: Damage, which initially grows uniformly in the material, localizes within a thin band at failure. Yet, experiments recording the acoustic activity preceding localization evidence power-law-distributed failure precursors of increasing size, suggesting that compressive failure is a critical phenomenon. We examine here this apparent contradiction by probing the spatial organization of the damage activity and its evolution until localization during compression experiments of 2D cellular solids. The intermittent damage evolution measured in our experiments is adequately described by a nonstationary depinning equation derived from damage mechanics and reminiscent of critical phenomena. In this description, precursors are damage cascades emerging from the interplay between the material’s disorder and the long-range stress redistributions following individual damage events. Yet, the divergence of their characteristic size close to failure, which we observe in our experiments, is not the signature of a transition toward criticality. Instead, the system remains at a fixed distance to the critical point at all stages of the damage evolution. The divergence results from the progressive loss of stability of the material as it is driven toward localization. Thus, our study shows that compressive failure is a standard bifurcation for which the material disorder plays a marginal role. It also implies that the precursory acoustic activity behaves as a tracer of the evolution of materials toward failure and can therefore be used to assess their residual lifetime.

The requirements for fault-tolerant quantum error correction can be simplified by leveraging structure in the noise of the underlying hardware. In this work, we identify a new type of structured noise motivated by neutral-atom qubits, biased erasure errors, which arises when qubit errors are dominated by detectable leakage from only one of the computational states of the qubit. We study the performance of this model using gate-level simulations of the $XZZX$ surface code. Using the predicted erasure fraction and bias of metastable ${}^{171}\mathrm{Yb}$ qubits, we find a threshold of 8.2% for two-qubit gate errors, which is 1.9 times higher than the threshold for unbiased erasures and 7.5 times higher than the threshold for depolarizing errors. Surprisingly, the improved threshold is achieved without bias-preserving controlled-not gates and, instead, results from the lower noise entropy in this model. We also introduce an $XZZX$ cluster state construction for measurement-based error correction, hybrid fusion, that is optimized for this noise model. By combining fusion operations and deterministic entangling gates, this construction preserves the intrinsic symmetry of the $XZZX$ code, leading to a higher threshold of 10.3% and enabling the use of rectangular codes with fewer qubits. We discuss a potential physical implementation using a single plane of atoms and movable tweezers.