Phase transitions in random circuit sampling.

Undesired coupling to the surrounding environment destroys long-range correlations in quantum processors and hinders coherent evolution in the nominally available computational space. This noise is an outstanding challenge when leveraging the computation power of near-term quantum processors1. It has been shown that benchmarking random circuit sampling with cross-entropy benchmarking can provide an estimate of the effective size of the Hilbert space coherently available2-8. Nevertheless, quantum algorithms' outputs can be trivialized by noise, making them susceptible to classical computation spoofing. Here, by implementing an algorithm for random circuit sampling, we demonstrate experimentally that two phase transitions are observable with cross-entropy benchmarking, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak-link model, which allows us to vary the strength of the noise versus coherent evolution. Furthermore, by presenting a random circuit sampling experiment in the weak-noise phase with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers. Our experimental and theoretical work establishes the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors.

Formation of robust bound states of interacting microwave photons.

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 particles1. 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 states2-9. 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.

Accurately computing the electronic properties of a quantum ring.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform1-4. 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 simulation5,6 and paves the way to study new quantum materials with superconducting qubits.

Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms.

Quantum algorithms offer a dramatic speedup for computational problems in material science and chemistry. However, any near-term realizations of these algorithms will need to be optimized to fit within the finite resources offered by existing noisy hardware. Here, taking advantage of the adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a threefold reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an imaginary swap-like (iSWAP-like) gate to attain an arbitrary swap angle, θ, and a controlled-phase gate that generates an arbitrary conditional phase, ϕ. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic simulation (fSim) gate set. We benchmark the fidelity of the iSWAP-like and controlled-phase gate families as well as 525 other fSim gates spread evenly across the entire fSim(θ,ϕ) parameter space, achieving a purity-limited average two-qubit Pauli error of 3.8×10^{-3} per fSim gate.

Diabatic Gates for Frequency-Tunable Superconducting Qubits.

We demonstrate diabatic two-qubit gates with Pauli error rates down to 4.3(2)×10^{-3} in as fast as 18 ns using frequency-tunable superconducting qubits. This is achieved by synchronizing the entangling parameters with minima in the leakage channel. The synchronization shows a landscape in gate parameter space that agrees with model predictions and facilitates robust tune-up. We test both iswap-like and cphase gates with cross-entropy benchmarking. The presented approach can be extended to multibody operations as well.

Fluctuations of Energy-Relaxation Times in Superconducting Qubits.

Superconducting qubits are an attractive platform for quantum computing since they have demonstrated high-fidelity quantum gates and extensibility to modest system sizes. Nonetheless, an outstanding challenge is stabilizing their energy-relaxation times, which can fluctuate unpredictably in frequency and time. Here, we use qubits as spectral and temporal probes of individual two-level-system defects to provide direct evidence that they are responsible for the largest fluctuations. This research lays the foundation for stabilizing qubit performance through calibration, design, and fabrication.

A novel method to guide classification of para swimmers with limb deficiency.

The International Paralympic Committee has directed International Federations that govern Para sports to develop evidence-based classification systems. This study defined the impact of limb deficiency impairment on 100 m freestyle performance to guide an evidence-based classification system in Para Swimming, which will be implemented following the 2020 Tokyo Paralympic games. Impairment data and competitive race performances of 90 international swimmers with limb deficiency were collected. Ensemble partial least squares regression established the relationship between relative limb length measures and competitive 100 m freestyle performance. The model explained 80% of the variance in 100 m freestyle performance and found hand length and forearm length to be the most important predictors of performance. Based on the results of this model, Para swimmers were clustered into four-, five-, six-, and seven-class structures using nonparametric kernel density estimations. The validity of these classification structures, and effectiveness against the current classification system, were examined by establishing within-class variations in 100 m freestyle performance and differences between adjacent classes. The derived classification structures were found to be more effective than current classification based on these criteria. This study provides a novel method that can be used to improve the objectivity and transparency of decision-making in Para sport classification. Expert consensus from experienced coaches, Para swimmers, classifiers, and sport science and medicine personnel will benefit the translation of these findings into a revised classification system that is accepted by the Para swimming community.

Dry-land bilateral hand-force production and swimming performance in paralympic swimmers.

The effectiveness of human movement is the culmination of several musculoskeletal factors; asymmetry in movement could reduce optimal performance. The aims of this study were to quantify relationships between bilateral hand-force production, swimming performance, and the influence of fatigue. Paralympic swimmers (n=21, aged 20.9 ± 4.7 yr) were categorised into no, high- and low-range physical disability groups and performed two 100 m time trials to measure swimming performance. Bilateral hand-force was measured over two 60 s maximal tests on a swim-bench ergometer to quantify the degree of asymmetry. Large relationships between mean force and swimming velocity were seen for both the high- (r=0.62, ±0.45; r-value, ±90% confidence limits) and low-range (r=0.62, ±0.50) groups. Asymmetry was related to level of disability, with the smallest difference of 6.7, ±2.6 N in the no-musculoskeletal disability group. This difference increased to 13.1, ±10.0 N and 13.5, ±16.2 N in the high- and low-range groups. Between the first and last 15 s of the swim-bench test, reductions in mean force were small for the physical disabilities groups. Similarly, changes in asymmetry were small for both the no-physical and low-range groups. Paralympic swimmers with a more severe physical impairment typically generate substantially lower force and velocity.

The influence of the breathing action on net drag force production in front crawl swimming.

20 elite swimmers completed a total of 6 randomized net drag force trials in 2 conditions (i) 3 breathing and (ii) 3 non-breathing. Net drag force was measured using an assisted motorized dynamometer device mounted upon a Kistler force-platform. The male participants demonstrated no statistical differences in stroke rates between breathing and non-breathing trials. Female participants, however, demonstrated a statistical difference stroke rate. The male participants demonstrated that the breathing action caused a greater (26%) net drag force compared to the females (16%). To further understand the influence of breathing on swimming technique, each stroke was analyzed and comparisons were made between the breathing and non-breathing conditions. The male participants demonstrated a similar minimum net drag force when comparing the breathing and non-breathing conditions. Analysis showed that minimum net drag force and maximum net drag force for the males changed when integrating the breathing action, while female participants demonstrated similar swimming technique, regardless of condition or stroke.

Stable quantum-correlated many-body states through engineered dissipation.

Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain.

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain's center, [Formula: see text]. The first two moments of [Formula: see text] show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.

Noise-resilient edge modes on a chain of superconducting qubits.

Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with [Formula: see text] parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.

Removing leakage-induced correlated errors in superconducting quantum error correction.

Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing.

Realizing topologically ordered states on a quantum processor.

The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error­correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of ­ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.

The exercise profile of an ultra-long handcycling race: the Styrkeprøven experience.

BACKGROUND: The high mechanical efficiency of the geared handcycle makes it suitable for elite athletes to train and even compete in races with able-bodied (recreational) cyclists. However, the actual exercise profile for endurance events has not been quantified. OBJECTIVE: To guide future training regimes in a safe and effective process, the aim of this research was to quantify the workload, speed, cadence and heart rate parameters during 6000 km of training and within a 540 km ultra-long races. METHODS: One spinal cord injured participant (lesion level Th4, ASIA B) handcycle (modified Shark S Sopur--Sunrisemedical, Malsch, Germany) was equipped with Schoberer Bike Measurement System (SRM) crank. For the laboratory test, a Cyclus II Ergometer was used. The energy intake and quality was determined during the time of race (540 km). RESULTS: Workload at a defined metabolic situation was augmented through training by 63.8% from 90.0 to 147.6 W. The athlete finished the 540 km race with an average speed of 21.6 km h⁻¹ and a total race time of 38:52 h. CONCLUSIONS: Ultra-long-term races in a handcycle can be suited by well-trained persons with a spinal cord injury. The quality of the training preparation time (for example, intensity and volume) is of immense importance to reach an adequate physiological capacity and to avoid serious injuries or medical problems.

Control of spiracles in silk moths by oxygen and carbon dioxide.

Spiracles of insects open in high carbon dioxide tensions and close in high oxygen tensions. However, the targets of these gases in insects have never been identified. In diapausing pupae of the cecropia silk moth carbon dioxide acts primarily and directly on the spiracular apparatus itself (muscle or neuromuscular junctions), whereas oxygen has as its primary target the central nervous system. The spiracle behaves as an independent effector in response to carbon dioxide; this is quite different from the situation in vertebrates, where carbon dioxide acts primarily on the central nervous system. The roles of various nerves in controlling spiracular activity are discussed.

A blueprint for demonstrating quantum supremacy with superconducting qubits.

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.

The influence of 'Slacklining' on quadriceps rehabilitation, activation and intensity.

OBJECTIVES: To determine and compare the level of quadriceps activation for knee injured participants during kinetic open-chain, closed-chain and composite-chain (Slackline) clinical exercises. Quadriceps activation is a critical component of lower limb movement and subsequently, rehabilitation. However, selective activation can be difficult due to pain, loss of function and impaired neuro-motor activation. DESIGN: Repeated measures (within-subjects) ANOVA. METHODS: Consecutive physiotherapy outpatients (n=49, 41.8±16.8 years, range 13-72 years, 57% female) with an acute (<2 weeks) knee injury were recruited. Participants were assessed for quadriceps activation using skin mounted electromyography during five separate clinical quadriceps activation exercises: two open-chain, inner range quads and straight leg raise; two closed-chain, step down and step up; and a composite-chain, slacklining step-up. Outcome measures were: median score on electromyography as measured in microvolts (µV); and perceived exertion on an 11-point numerical rating scale. RESULTS: Median scores of the open- and closed-chain exercises showed no statistical difference, while composite-chain Slackline exercise showed significantly (p<0.0001) higher quadriceps activation (F(2.52, 121.00)=21.53, p<0.0001) at significantly lower exertion (F(1.62, 77.70)=26.88, p<0.0001). CONCLUSIONS: The use of Slackline rehabilitation training can provide significant increases in activation and recruitment of the quadriceps for composite-chain exercises in the clinical setting. This activation occurs spontaneously at significantly lower levels of perceived exertion. This spontaneous quadriceps activation in a selective and simple manner is a valuable adjunct exercise for lower limb rehabilitation programmes. This is of particular relevance for the outpatient setting and circumstances where the quadriceps is inhibited and activation is required.

Conformational selection of inhibitors and substrates by proteolytic enzymes: implications for drug design and polypeptide processing.

Inhibitors of proteolytic enzymes (proteases) are emerging as prospective treatments for diseases such as AIDS and viral infections, cancers, inflammatory disorders, and Alzheimer's disease. Generic approaches to the design of protease inhibitors are limited by the unpredictability of interactions between, and structural changes to, inhibitor and protease during binding. A computer analysis of superimposed crystal structures for 266 small molecule inhibitors bound to 48 proteases (16 aspartic, 17 serine, 8 cysteine, and 7 metallo) provides the first conclusive proof that inhibitors, including substrate analogues, commonly bind in an extended beta-strand conformation at the active sites of all these proteases. Representative superimposed structures are shown for (a) multiple inhibitors bound to a protease of each class, (b) single inhibitors each bound to multiple proteases, and (c) conformationally constrained inhibitors bound to proteases. Thus inhibitor/substrate conformation, rather than sequence/composition alone, influences protease recognition, and this has profound implications for inhibitor design. This conclusion is supported by NMR, CD, and binding studies for HIV-1 protease inhibitors/substrates which, when preorganized in an extended conformation, have significantly higher protease affinity. Recognition is dependent upon conformational equilibria since helical and turn peptide conformations are not processed by proteases. Conformational selection explains the resistance of folded/structured regions of proteins to proteolytic degradation, the susceptibility of denatured proteins to processing, and the higher affinity of conformationally constrained 'extended' inhibitors/substrates for proteases. Other approaches to extended inhibitor conformations should similarly lead to high-affinity binding to a protease.