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Folding is ubiquitous in nature with examples ranging from the formation of cellular components to winged insects. It finds technological applications including packaging of solar cells and space structures, deployable biomedical devices and self-assembling robots and airbags. Here we demonstrate sequential self-folding structures realized by thermal activation of spatially-variable patterns that are 3D printed with digital shape memory polymers, which are digital materials with different shape memory behaviors. The time-dependent behavior of each polymer allows the temporal sequencing of activation when the structure is subjected to a uniform temperature. This is demonstrated via a series of 3D printed structures that respond rapidly to a thermal stimulus and self-fold to specified shapes in controlled shape changing sequences. Measurements of the spatial and temporal nature of self-folding structures are in good agreement with the companion finite element simulations. A simplified reduced-order model is also developed to rapidly and accurately describe the self-folding physics. An important aspect of self-folding is the management of self-collisions, where different portions of the folding structure contact and then block further folding. A metric is developed to predict collisions and is used together with the reduced-order model to design self-folding structures that lock themselves into stable desired configurations.

Quantum information scientists are getting closer to building a quantum computer that can perform calculations that a classical computer cannot. It has been estimated that such a computer would need around 50 qubits, but scaling up existing architectures to this number is tricky. Neill et al. explore how increasing the number of qubits from five to nine affects the quality of the output of their superconducting qubit device. If, as the number of qubits grows further, the error continues to increase at the same rate, a quantum computer with about 60 qubits and reasonable fidelity might be achievable with current technologies. Science , this issue p. 195 Scaling of errors and output with the number of qubits is explored in a five- to nine-qubit device. A key step toward demonstrating a quantum system that can address difficult problems in physics and chemistry will be performing a computation beyond the capabilities of any classical computer, thus achieving so-called quantum supremacy. In this study, we used nine superconducting qubits to demonstrate a promising path toward quantum supremacy. By individually tuning the qubit parameters, we were able to generate thousands of distinct Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert space. As the number of qubits increases, the system continues to explore the exponentially growing number of states. Extending these results to a system of 50 qubits has the potential to address scientific questions that are beyond the capabilities of any classical computer.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform 1 – 4 . However, the accuracy needed to outperform classical methods has not been achieved so far. Here, using 18 superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to investigate fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors, and measure the energy eigenvalues of this wire with an error of approximately 0.01 rad, whereas typical energy scales are of the order of 1 rad. Insight into the fidelity of this algorithm is gained by highlighting the robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 10 −4 rad. We also synthesize magnetic flux and disordered local potentials, which are two key tenets of a condensed-matter system. When sweeping the magnetic flux we observe avoided level crossings in the spectrum, providing a detailed fingerprint of the spatial distribution of local disorder. By combining these methods we reconstruct electronic properties of the eigenstates, observing persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation 5 , 6 and paves the way to study new quantum materials with superconducting qubits. As a blueprint for high-precision quantum simulation, an 18-qubit algorithm that consists of more than 1,400 two-qubit gates is demonstrated, and reconstructs the energy eigenvalues of the simulated one-dimensional wire to a precision of 1 per cent.

Measurement has a special role in quantum theory 1 : by collapsing the wavefunction, it can enable phenomena such as teleportation 2 and thereby alter the ‘arrow of time’ that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space–time 3 – 10 that go beyond the established paradigms for characterizing phases, either in or out of equilibrium 11 – 13 . For present-day noisy intermediate-scale quantum (NISQ) processors 14 , the experimental realization of such physics can be problematic because of hardware limitations and the stochastic nature of quantum measurement. Here we address these experimental challenges and study measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping 9 , 15 – 17 to avoid mid-circuit measurement and access different manifestations of the underlying phases, from entanglement scaling 3 , 4 to measurement-induced teleportation 18 . We obtain finite-sized signatures of a phase transition with a decoding protocol that correlates the experimental measurement with classical simulation data. The phases display remarkably different sensitivity to noise, and we use this disparity to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realizing measurement-induced physics at scales that are at the limits of current NISQ processors. Measurement-induced phases of quantum information have been observed in a system of 70 superconducting qubits.

Indistinguishability of particles is a fundamental principle of quantum mechanics 1 . For all elementary and quasiparticles observed to date—including fermions, bosons and Abelian anyons—this principle guarantees that the braiding of identical particles leaves the system unchanged 2 , 3 . However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions 4 – 8 . Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well-developed mathematical description of non-Abelian anyons and numerous theoretical proposals 9 – 22 , the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the many-body wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons 9 , 10 , we implement a generalized stabilizer code and unitary protocol 23 to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards fault-tolerant quantum computing. A unitary protocol for braiding projective non-Abelian Ising anyons in a generalized stabilizer code is implemented on a superconducting processor, allowing for verification of their fusion rules and realization of their exchange statistics.

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles 1 . The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states 2 – 9 . Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit. An experimental investigation of the dynamics of the spin ½ Floquet XXZ model finds bound states as predicted, and also robustness to noise and non-integrability when theoretical descriptions start to fail.

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Before fault-tolerant quantum computing, robust error-mitigation strategies were necessary to continue this growth. Here, we validate recently introduced error-mitigation strategies that exploit the expectation that the ideal output of a quantum algorithm would be a pure state. We consider the task of simulating electron systems in the seniority-zero subspace where all electrons are paired with their opposite spin. This affords a computational stepping stone to a fully correlated model. We compare the performance of error mitigations on the basis of doubling quantum resources in time or in space on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques such as postselection. We study how the gain from error mitigation scales with the system size and observe a polynomial suppression of error with increased resources. Extrapolation of our results indicates that substantial hardware improvements will be required for classically intractable variational chemistry simulations.It is hoped that simulations of molecules and materials will provide a near-term application of quantum computers. A study of the performance of error mitigation highlights the obstacles to scaling up these calculations to practically useful sizes.

— Phase equilibria in the quaternary system СaMoO 4 –СaSO 4 –СaF 2 –СaCl 2 have been studied using physicochemical analysis (differential thermal analysis). We have determined the composition, melting point, and enthalpy of fusion of the quaternary peritectic point (melting point, 650°C; composition: 33.8% CaF 2 , 45% CaCl 2 , 16.2% CaSO 4 , and 5% CaMoO 4 ; enthalpy of fusion, 256 ± 5.1 kJ/kg) and quaternary eutectic point (melting point, 586°C; composition: 15.8% CaF 2 , 73.3% CaCl 2 , 9.9% CaSO 4 , and 1% CaMoO 4 ; enthalpy of fusion, 485 ± 9.7 kJ/kg) in the system studied.

The purpose of this work was to justify the application of a less energy-intensive circulation lubrication system from two options for the installation of rotameter blocks: compact (with one block of rotameters installed on the front and drive sides of the drying section) and distributed (with four blocks of rotameters installed on the front and drive sides of the drying section). To achieve this goal, the following tasks were addressed: measuring and analyzing the temperature of the operating compact circulation lubrication system of the drying cylinders and fabric-leading rolls in the drying section; calculating the length of small diameter tubes with an internal diameter of d in = 8 mm for oil supply from the rotameters to the bearings of the drying cylinders and fabric-leading rolls for both the operating (compact) and group-distributed installations of rotameters in the drying section; determining the heat loss carried away by the circulating oil from the zone of the thermal insulation hood of the drying section during the operation of both the compact and group-distributed installations of rotameters. Experimental studies have shown that the temperature of the oil in the tubes with the compact installation of the rotameters increases by 27 to 29°C from the entry into the thermal insulation hood zone of the drying section to the entry into the bearing supports of the drying cylinders and fabric-leading rolls, reaching an average of 67°C. The calculated length of the oil supply tubes to the bearing supports when the rotameters are positioned before the drying groups is shorter than the corresponding tube length in the compact arrangement of the rotameters by 1501.52 m. Reducing the length of the tubes in the thermal insulation hood zone of the drying section under the established operating conditions significantly reduces the heating of the oil and the transfer of thermal energy from the paper drying zone. A calculation was performed to determine the reduction in the amount of heat carried away from the drying section when the rotameters are arranged in groups compared to the compact arrangement. It was established that over 1 h of operation of the drying section, the amount of heat carried away by the heated oil decreases by 74 844 kJ.

The direct effect of 5 mM L-NAME and 0.1 mM sodium nitroprusside on activity of lysosomal cysteine proteinases and permeability of lysosomal membrane was studied in vitro after 1, 2, and 4 h of incubation. Isolated from the liver of intact female rats lysosome suspensions were used. Both substances reduced total activity of cathepsin H and did not affect cathepsin B at all time intervals. L-NAME increased cathepsin L activity at all incubation times, while sodium nitroprusside increased activity of this enzyme after 2-h incubation and reduced it incubation after 4-h incubation. L-NAME demonstrated a membrane-destabilizing effect in in vitro experiments, while sodium nitroprusside on the contrary stabilized lysosomal membranes.