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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.

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.

The leakage of quantum information out of the two computational states of a qubit into other energy states represents a major challenge for quantum error correction. During the operation of an error-corrected algorithm, leakage builds over time and spreads through multi-qubit interactions. This leads to correlated errors that degrade the exponential suppression of the logical error with scale, thus challenging the feasibility of quantum error correction as a path towards fault-tolerant quantum computation. Here, we demonstrate a distance-3 surface code and distance-21 bit-flip code on a quantum processor for which leakage is removed from all qubits in each cycle. This shortens the lifetime of leakage and curtails its ability to spread and induce correlated errors. We report a tenfold reduction in the steady-state leakage population of the data qubits encoding the logical state and an average leakage population of less than 1 × 10−3throughout the entire device. Our leakage removal process efficiently returns the system back to the computational basis. Adding it to a code circuit would prevent leakage from inducing correlated error across cycles. With this demonstration that leakage can be contained, we have resolved a key challenge for practical quantum error correction at scale.

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.

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2–8that 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 order7,16,17. 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 states7,9,10. 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.

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 10−4rad. 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 simulation5,6and paves the way to study new quantum materials with superconducting qubits.

Faster algorithms for combinatorial optimization could prove transformative for diverse areas such as logistics, finance and machine learning. Accordingly, the possibility of quantum enhanced optimization has driven much interest in quantum technologies. Here we demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the planar connectivity graph native to our hardware; however, we also apply the QAOA to the Sherrington–Kirkpatrick model and MaxCut, non-native problems that require extensive compilation to implement. For hardware-native problems, which are classically efficient to solve on average, we obtain an approximation ratio that is independent of problem size and observe that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size. Circuits involving several thousand gates still present an advantage over random guessing but not over some efficient classical algorithms. Our results suggest that it will be challenging to scale near-term implementations of the QAOA for problems on non-native graphs. As these graphs are closer to real-world instances, we suggest more emphasis should be placed on such problems when using the QAOA to benchmark quantum processors.

Scalable quantum computing can become a reality with error correction, provided that coherent qubits can be constructed in large arrays1,2. The key premise is that physical errors can remain both small and sufficiently uncorrelated as devices scale, so that logical error rates can be exponentially suppressed. However, impacts from cosmic rays and latent radioactivity violate these assumptions. An impinging particle can ionize the substrate and induce a burst of quasiparticles that destroys qubit coherence throughout the device. High-energy radiation has been identified as a source of error in pilot superconducting quantum devices3–5, but the effect on large-scale algorithms and error correction remains an open question. Elucidating the physics involved requires operating large numbers of qubits at the same rapid timescales necessary for error correction. Here, we use space- and time-resolved measurements of a large-scale quantum processor to identify bursts of quasiparticles produced by high-energy rays. We track the events from their initial localized impact as they spread, simultaneously and severely limiting the energy coherence of all qubits and causing chip-wide failure. Our results provide direct insights into the impact of these damaging error bursts and highlight the necessity of mitigation to enable quantum computing to scale.

Stand-level retention is an important component of sustainable forest management which aims to balance ecological, social and economic objectives. Long-term retention of mature forest structures at the time of harvesting (variable retention) is intended to produce future forest stands that more closely resemble conditions that develop after natural disturbances, thereby maintaining greater diversity of habitats for a variety of organisms. Structure includes features such as live and dead trees representing multiple canopy layers, undisturbed understory vegetation and coarse woody debris. Over the past two decades, variable retention has become common on forest lands in the temperate rainforests of coastal British Columbia (BC) and has been applied to a lesser extent in inland forest types. Our review of studies in BC and in similar forest types in our region indicates that both aggregated and dispersed retention can contribute to biodiversity conservation by providing short-term ‘life-boating’ habitat for some species and by enhancing the structural characteristics of future stands. For example, greater abundance of species present in the pre-harvest forest have been documented for vegetation, birds, carabid beetles, gastropods, ectomycorrhizal fungi and soil fauna in retention cutblocks compared to clearcuts. There are, however, some negative consequences for timber production such as wind damage to retained trees and reduced growth rates of tree regeneration compared to clearcuts. The authors suggest an adaptive management approach for balancing competing objectives when faced with uncertainty. This includes monitoring the implementation and effectiveness of various strategies for achieving goals. Over two decades of experience applying variable retention harvesting to industrial-scale management of forest lands in BC suggests that it is possible to balance production of wood with biodiversity conservation.

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 qubits2–7to 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 supremacy8–14for this specific computational task, heralding a much-anticipated computing paradigm.

The intriguing many-body phases of quantum matter arise from the interplay of particle interactions, spatial symmetries, and external fields. Generating these phases in an engineered system could provide deeper insight into their nature. Using superconducting qubits, we simultaneously realize synthetic magnetic fields and strong particle interactions, which are among the essential elements for studying quantum magnetism and fractional quantum Hall phenomena. The artificial magnetic fields are synthesized by sinusoidally modulating the qubit couplings. In a closed loop formed by the three qubits, we observe the directional circulation of photons, a signature of broken time-reversal symmetry. We demonstrate strong interactions through the creation of photon vacancies, or ‘holes’, which circulate in the opposite direction. The combination of these key elements results in chiral ground-state currents. Our work introduces an experimental platform for engineering quantum phases of strongly interacting photons.

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however, the occurrence of ergodic behaviour has remained an outstanding question. Here, we demonstrate ergodic dynamics in a small quantum system consisting of only three superconducting qubits. The qubits undergo a sequence of rotations and interactions and we measure the evolution of the density matrix. Maps of the entanglement entropy show that the full system can act like a reservoir for individual qubits, increasing their entropy through entanglement. Surprisingly, these maps bear a strong resemblance to the phase space dynamics in the classical limit; classically, chaotic motion coincides with higher entanglement entropy. We further show that in regions of high entropy the full multi-qubit system undergoes ergodic dynamics. Our work illustrates how controllable quantum systems can investigate fundamental questions in non-equilibrium thermodynamics.

A digitized approach to adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the digital method, is implemented using a superconducting circuit to find the ground states of arbitrary Hamiltonians.

Humans are distinguished from the other living apes in having larger brains and an unusual life history that combines high reproductive output with slow childhood growth and exceptional longevity. This suite of derived traits suggests major changes in energy expenditure and allocation in the human lineage, but direct measures of human and ape metabolism are needed to compare evolved energy strategies among hominoids. Here we used doubly labelled water measurements of total energy expenditure (TEE; kcal day−1) in humans, chimpanzees, bonobos, gorillas and orangutans to test the hypothesis that the human lineage has experienced an acceleration in metabolic rate, providing energy for larger brains and faster reproduction without sacrificing maintenance and longevity. In multivariate regressions including body size and physical activity, human TEE exceeded that of chimpanzees and bonobos, gorillas and orangutans by approximately 400, 635 and 820 kcal day−1, respectively, readily accommodating the cost of humans’ greater brain size and reproductive output. Much of the increase in TEE is attributable to humans’ greater basal metabolic rate (kcal day−1), indicating increased organ metabolic activity. Humans also had the greatest body fat percentage. An increased metabolic rate, along with changes in energy allocation, was crucial in the evolution of human brain size and life history.

A single-base deletion within the protein-coding region of the adenovirus type 5 early region 1A (E1A) genes, 399 bases downstream from the transcription start site, depresses transcription to 2% of the wild-type rate. Complementation studies demonstrated that this was due to two effects of the mutation: first, inactivation of an E1A protein, causing a reduction by a factor of 5; second, a defect which acts in cis to depress E1A mRNA and nuclear RNA concentrations by a factor of 10. A larger deletion within the protein-coding region of E1A which overlaps the single-base deletion produces the same phenotype. In contrast, a linker insertion which results in a similar truncated E1A protein does not produce the cis-acting defect in E1A transcription. These results demonstrate that a critical cis-acting transcription control region occurs within the protein coding sequence in adenovirus type 5 E1A. The single-base deletion occurs in a sequence which shows extensive homology with a sequence from the enhancer regions of simian virus 40 and polyomavirus. This region is not required for E1A transcription during the late phase of infection.

The de Haas-van Alphen effect has been measured in the layer compound PdTe2. Frequency branches from 0.1 kT to 4.5 kT were observed in the three principal planes. Effective masses were also measured. The number of branches suggests a complicated Fermi surface which is not well explained by existing band structures.

Human peripheral blood mononuclear cells obtained by ficoll-hypaque sedimentation were depleted of Fc-receptor-bearing (FcR+) cells. Cytotoxicity (direct killing of target cells by effector cells), tested in a 40 h assay, was significantly decreased against a variety of target cells. Tests in which no FcR+ cells could be detected were also positive for “natural killing” (NK) against a spectrum of target cells from normal donors. NK in this system was mediated by more than one subpopulation of lymphocytes. Monocytes probably did not play a significant role.

The de Haas-van Alphen effect has been observed in the quadrivalent ß-brass compound MgHg. Five frequency groups have been measured in the {110} and {100} planes along with some effective masses at high symmetry points. All five groups observed are well explained by Skriver's relativistic LMTO band calculation. A football-shaped piece predicted in the third band has the size and shape of an observed closed section which was inverted with tetragonal harmonics. The remaining orbits arise from the multipliconnected second band surface, a surface formed by connecting pockets at G andR with arms along <111>.

Two casesof melanoacanthoma occurring on oral mucous membranes are presented. Melanoacanthoma is considered to be a benign mixed tumor of keratinocytes admixed with pigment‐laden dendritic melanocytes. All intraoral melanoacanthomas reported thus far have been pigmented lesions of the buccal mucosa and have occurred in young to middle‐aged black females. These tumors may grow rapidly and therefore they often mimic the radial growth phase of an intraoral melanoma. Because melanoacanthomas have no distinguishing clinical features, biopsy is mandatory.

The de Haas-van Alphen effect has been measured in the ordered alloy ß'-AgZn by the modulation method, improving and extending the results of earlier observations. The results are in good agreement with recent theoretical calculations of the Fermi surface, although some of the predicted orbits have not been observed. The hole octahedron in the first band and the triangular hole in the second band have been identified unambiguously, and the shape of the octahedron has been determined by inversion.