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The article examines the issues of justification of the norms of clearance of obstructions of high passenger platforms of the railways 1520 mm wide. The authors conducted analysis of the valid regulatory documents establishing the clearance requirements to passenger platforms and developed the double-criteria method of assessment of the relevance of these requirements. Examinations were conducted by the scientists of JSC “VNIIZhT” together with the experts of Moscow directorate of infrastructure in order to make correct selection of the clearance of obstructions when constructing new high passenger platforms. Experts of JSC “VNIIZhT” developed explanation of the relevance of the clearance norms stated in GOST 9238–2013 and in the Standard code in the Russian Federation approved by the order of the Ministry of Transportation dated 21.12.2010 no. 286, as well as performed inspection of compliance of high passenger platforms recently constructed or being constructed now with the requirements of these regulatory documents.Analysis of actual clearance to obstructions of the used platforms by means of the double-criteria method of justification of the clearance of high passenger platforms allowed assessing compliance of the actual clearance to obstructions of the platforms with the passenger comfort requirements, as well as with GOST 9238–2013. Examinations confirmed that actual clearance to obstructions with regard to the tolerances in general comply with the standard. Requirements of GOST 9238–2013, which shall be followed for selection of the clearance to obstructions of high passenger platforms, are the primary requirements of the valid regulatory documents specifying the norms of the platform clearance to obstructions.

The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase of matter. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modifications of the dynamics, rendering their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two-qubit density matrices allows us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here detect affirmative quantum correlations and exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter.

In 2013, JSC “Russian Railways” railway network was put into operation high-speed electric multiple unit (EMU) ES1 “Lastochka” of dual supply with asynchronous traction drive produced by Siemens on Desiro platform. In accordance with the requirements of safety standards, and later the Technical Regulations of the Customs Union TR CU 001/2011 “On safety of railway rolling stock” experimental EMUs ES1 and ES2G completed a full range of tests, including their final stage - the complex tests of dynamics and impact on railway tracks and turnouts. The article summarizes the results of comprehensive testing of new high-speed EMUs intended for commuter and regional passenger service. Methodology of the study is based on the works of professor M. F. Verigo and includes experimental determination of combination of indicators of dynamic qualities and impact of trains on railway tracks in the complex tests in a single point in time. Study results of the set of dynamic performance qualities and impact of EMUs ES1 and ES2G “Lastochka” on the railway track with help of experimental and experimental-design methods have allowed to give recommendations on the level of permissible speeds, including run through tangent track sections - 160 km/h; in curved sections with radius of more than 400 m permissible speed can be set in terms of non-exceedance of unbalanced lateral acceleration of 0.9 m/s2, in curves of radius less than 400 m - in terms of non-exceedance of unbalanced lateral acceleration of 0.7 m/s2. On the basis of this combination of indicators with Norms of calculation of the strength of railway tracks a table of permissible speeds for trains is defined, which, as a normative document of JSC “Russian Railways”, introduced in the areas of circulation of these trains.

In 2009 there were constructed and brought into pilot operation two sections of RHEDA 2000 ballastless track designed by RailOne (Germany) with the participation of JSC ‘‘Roszheldorproekt”, one of them on the Moskovskaya Railway (in the VNIIZhT’s Testing Center at the station of Scherbinka) and another - on Oktyabr’skaya Railway (on the open line between Sablino and Kolpino). Prior to and in the course of pilot operation the VNIIZhT experts conducted actual loading tests at both sections and routine observations of various ballastless track components’ behaviour under increasing passed tonnage conditions. There are presented the most significant test and observation results as well as test results based conclusions.

The simulation complexity of predicting the time evolution of delocalized many-body quantum systems has attracted much recent interest, and simulations of such systems in real quantum hardware are promising routes to demonstrating a quantum advantage over classical machines. In these proposals, random noise is an obstacle that must be overcome for a faithful simulation, and a single error event can be enough to drive the system to a classically trivial state. We argue that this need not always be the case, and consider a modification to a leading quantum sampling problem—time evolution in an interacting Bose-Hubbard chain of transmon qubits [Neill et al., Science 360, 195 (2018)10.1126/science.aao4309]—where each site in the chain has a driven coupling to a lossy cavity and particle number is no longer conserved. With cavity noise (but not qubit error) now included in the problem definition, the resulting quantum dynamics are still complex and highly nontrivial. We argue that this problem is harder to simulate than the isolated chain, and that it can achieve volume-law entanglement even in the strong noise limit, likely persisting up to system sizes beyond the scope of classical simulation. Further, we show that the metrics which suggest classical intractability for the isolated chain point to similar conclusions in the noisy case. These results suggest that quantum sampling problems including nontrivial noise could be good candidates for demonstrating a quantum advantage in near-term hardware.

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 processors 1 . 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 available 2-8 . 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., (© 2024. The Author(s).)

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.

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.

A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks are manufacturing high-performance quantum hardware and engineering a control system that can reach its performance limits. The control challenge of scaling quantum gates from small to large processors without degrading performance often maps to non-convex, high-constraint, and time-dynamic control optimization over an exponentially expanding configuration space. Here we report on a control optimization strategy that can scalably overcome the complexity of such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunable superconducting qubits to execute single- and two-qubit gates while mitigating computational errors. When combined with a comprehensive model of physical errors across our processor, the strategy suppresses physical error rates by ~3.7× compared with the case of no optimization. Furthermore, it is projected to achieve a similar performance advantage on a distance-23 surface code logical qubit with 1057 physical qubits. Our control optimization strategy solves a generic scaling challenge in a way that can be adapted to a variety of quantum operations, algorithms, and computing architectures., (© 2024. The Author(s).)

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., (© 2022. The Author(s).)

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.

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters. We develop algorithms for performing this computation on both noisy near-term and future fault-tolerant quantum computers. We argue that the former is promising as an early beyond-classical quantum application since it only requires evolution of a local spin Hamiltonian. We investigate the example of a protein (ubiquitin) confined on a membrane as a benchmark of our method. We isolate small spin clusters, demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to non-ergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across many-body eigenstates of these clusters, and a transition in the structure of the Hessian of the learning cost function (from degenerate to learnable). Our hope is that such quantum computations might enable the interpretation and development of new NMR techniques for analyzing molecular structure.

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states 1 . However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases 2-8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC) 7,9-15 . Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order 7,16,17 . In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states 7,9,10 . Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors., (© 2021. The Author(s).)

Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error–correcting 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.

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.

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.

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor 1 . A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits 2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2 53 (about 10 16 ). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy 8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

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., (Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)