Quantum supremacy using a programmable superconducting processor.

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. 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 qubits2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). 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 supremacy8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

Exponentially Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians.

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that while naive transverse-field quantum annealing on the D-Wave 2X device can find the ground-state energy of the problems, it is not well suited in identifying all degenerate ground-state configurations associated with a particular instance. Even worse, some states are exponentially suppressed, in agreement with previous studies on toy model problems [New J. Phys. 11, 073021 (2009)NJOPFM1367-263010.1088/1367-2630/11/7/073021]. These results suggest that more complex driving Hamiltonians are needed in future quantum annealing machines to ensure a fair sampling of the ground-state manifold.

Evidence for soft bounds in Ubuntu package sizes and mammalian body masses.

The development of a complex system depends on the self-coordinated action of a large number of agents, often determining unexpected global behavior. The case of software evolution has great practical importance: knowledge of what is to be considered atypical can guide developers in recognizing and reacting to abnormal behavior. Although the initial framework of a theory of software exists, the current theoretical achievements do not fully capture existing quantitative data or predict future trends. Here we show that two elementary laws describe the evolution of package sizes in a Linux-based operating system: first, relative changes in size follow a random walk with non-Gaussian jumps; second, each size change is bounded by a limit that is dependent on the starting size, an intriguing behavior that we call "soft bound." Our approach is based on data analysis and on a simple theoretical model, which is able to reproduce empirical details without relying on any adjustable parameter and generates definite predictions. The same analysis allows us to formulate and support the hypothesis that a similar mechanism is shaping the distribution of mammalian body sizes, via size-dependent constraints during cladogenesis. Whereas generally accepted approaches struggle to reproduce the large-mass shoulder displayed by the distribution of extant mammalian species, this is a natural consequence of the softly bounded nature of the process. Additionally, the hypothesis that this model is valid has the relevant implication that, contrary to a common assumption, mammalian masses are still evolving, albeit very slowly.

Helium isotope enrichment by resonant tunneling through nanoporous graphene bilayers.

Graphene is impermeable to gases, but introducing subnanometer pores can allow for selective gas separation. Because graphene is only one atom thick, tunneling can play an important role, especially for low-mass gases such as helium, and this has been proposed as a means of separating (3)He from (4)He. In this paper, we consider the possibility of utilizing resonant tunneling of helium isotopes through nanoporous graphene bilayers. Using a model potential fit to previously reported DFT potential energy surfaces, we calculate the thermal rate constant as a function of interlayer separation using a recently described time-independent method for arbitrary multibarrier potentials. Resonant transmission allows for the total flux rate of (3)He to remain the same as the best-known single-barrier pores but doubles the selectivity with respect to (4)He when the optimal interlayer spacing of 4.6 Å is used. The high flux rate and selectivity are robust against variations of the interlayer spacing and asymmetries in the potential that may occur in experiment.

Optimization and benchmarking of the thermal cycling algorithm.

Optimization plays a significant role in many areas of science and technology. Most of the industrial optimization problems have inordinately complex structures that render finding their global minima a daunting task. Therefore, designing heuristics that can efficiently solve such problems is of utmost importance. In this paper we benchmark and improve the thermal cycling algorithm [Phys. Rev. Lett. 79, 4297 (1997)PRLTAO0031-900710.1103/PhysRevLett.79.4297] that is designed to overcome energy barriers in nonconvex optimization problems by temperature cycling of a pool of candidate solutions. We perform a comprehensive parameter tuning of the algorithm and demonstrate that it competes closely with other state-of-the-art algorithms such as parallel tempering with isoenergetic cluster moves, while overwhelmingly outperforming more simplistic heuristics such as simulated annealing.

Information scrambling in quantum circuits.

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.

Feeding the multitude: A polynomial-time algorithm to improve sampling.

A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution space tends to be favored while, in the worst case, some solutions can never be accessed by the algorithm used. Here we present a simple postprocessing technique that improves sampling for any optimization approach, either quantum or classical. More precisely, starting from a pool of a few optimal configurations, the algorithm generates potentially new solutions via rejection-free cluster updates at zero temperature. Although the method is not ergodic and there is no guarantee that all the solutions can be found, fair sampling is typically improved. We illustrate the effectiveness of our method by improving the exponentially biased data produced by the D-Wave 2X quantum annealer [S. Mandrà et al., Phys. Rev. Lett. 118, 070502 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.070502], as well as data from three-dimensional Ising spin glasses. As part of the study, we also show that sampling is improved when suboptimal states are included and discuss sampling at a finite fixed temperature.

Patch-planting spin-glass solution for benchmarking.

We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then the individual patches are stitched together to create a large problem with a known planted solution. Because in these problems frustration is typically smaller than in random problems, we first assess the typical computational complexity of the individual patches using population annealing Monte Carlo, and introduce an approach that allows one to fine-tune the typical computational complexity of the patch-planted system. The scaling of the typical computational complexity of these planted instances with various numbers of patches and patch sizes is investigated and compared to random instances.

Gas Separation through Bilayer Silica, the Thinnest Possible Silica Membrane.

Membrane-based gas separation processes can address key challenges in energy and environment, but for many applications the permeance and selectivity of bulk membranes is insufficient for economical use. Theory and experiment indicate that permeance and selectivity can be increased by using two-dimensional materials with subnanometer pores as membranes. Motivated by experiments showing selective permeation of H2/CO mixtures through amorphous silica bilayers, here we perform a theoretical study of gas separation through silica bilayers. Using density functional theory calculations, we obtain geometries of crystalline free-standing silica bilayers (comprised of six-membered rings), as well as the seven-, eight-, and nine-membered rings that are observed in glassy silica bilayers, which arise due to Stone-Wales defects and vacancies. We then compute the potential energy barriers for gas passage through these various pore types for He, Ne, Ar, Kr, H2, N2, CO, and CO2 gases, and use the data to assess their capability for selective gas separation. Our calculations indicate that crystalline bilayer silica, which is less than a nanometer thick, can be a high-selectivity and high-permeance membrane material for 3He/4He, He/natural gas, and H2/CO separations.

Soft bounds on diffusion produce skewed distributions and Gompertz growth.

Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the increments of the diffusing variable are subject to configuration-dependent bounds. This work explores theoretically some of the revealing landmarks of such phenomenology, termed "soft bound." At long times, the system reaches a steady state irreversibly (i.e., violating detailed balance), characterized by a skewed "shoulder" in the density distribution, and by a net local probability flux, which has entropic origin. The largest point in the support of the distribution follows a saturating dynamics, expressed by the Gompertz law, in line with empirical observations. Finally, we propose a generic allometric scaling for the origin of soft bounds. These findings shed light on the impact on a system of such "scaling" constraint and on its possible generating mechanisms.

Coevolution of Glauber-like Ising dynamics and topology.

We study the coevolution of a generalized Glauber dynamics for Ising spins with tunable threshold and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model, the threshold and the rewiring probability. The diagram displays phase transitions of different types: spin ordering, percolation, and connectedness. At variance with traditional coevolution models, in which all spins of each connected component of the graph have equal value in the stationary state, we find that, for suitable choices of the parameters, the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like-signed spins. Mean field calculations enable one to estimate some features of the phase diagram.