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Quantum computers must achieve large-scale, fault-tolerant operation to deliver on their promise of transformational processing power [1-4]. This will require thousands or millions of high-fidelity quantum gates and similar numbers of qubits [5]. Demonstrations using neutral-atom qubits trapped and manipulated by lasers have shown that this modality can provide high two-qubit gate (CZ) fidelities and scalable operation [6-10]. However, the gates in these demonstrations are driven by lasers that do not resolve individual qubits, with universal computation enabled by physical mid-circuit shuttling of the qubits. This relatively slow operation will greatly extend runtimes for useful, large-scale computation. Here we demonstrate a universal neutral-atom quantum computer with gate rates limited by optical switching times, rather than shuttling, by individually addressing tightly focused laser beams at an array of single atoms. We achieve CZ fidelity of 99.35(4)% and local single qubit RZ gate fidelity of 99.902(8)%. Moreover, we demonstrate non-destructive readout of alkali-atom qubits with sub-percent loss, which boosts operational speed. This technique also enables us to measure 99.73(3)% CZ fidelity with atom-loss events excluded, which is a record among long lived neutral-atom qubits and highlights the path to higher fidelity and error correction. Our results represent a critical step towards large-scale, fault-tolerant neutral-atom quantum computers that can execute computations on practical timescales.

The existence of steady-state multiplicity or multistationarity in the Earth System raises the possibility that the Earth may reach a "tipping point" and rapidly transition to a warmer steady-state from which recovery may be practically impossible. In detailed Earth models that require extensive computation time, it is difficult to make an a priori prediction of the existence of steady-state multiplicity. In this study, we demonstrate Chemical Reaction Network Theory (CRNT) analysis of a simple heuristic box model of the Earth System carbon cycle with the human intervention of direct air capture. The analysis reveals necessary conditions for the combination of system parameters where steady-state multiplicity may exist. With this method, other negative emissions technologies (NET) may be screened in a relatively simple manner to aid in the priority setting by policymakers., Comment: arXiv admin note: text overlap with arXiv:2209.12143

Quantum span program algorithms for function evaluation sometimes have reduced query complexity when promised that the input has a certain structure. We design a modified span program algorithm to show these improvements persist even without a promise ahead of time, and we extend this approach to the more general problem of state conversion. As an application, we prove exponential and superpolynomial quantum advantages in average query complexity for several search problems, generalizing Montanaro's Search with Advice [Montanaro, TQC 2010]., Comment: v2) New explicit description and analysis of distributions leading to average quantum advantages, accepted to Quantum. v1) 35 pages, 2 figures. This article supersedes arXiv/2012.01276 (expanded author list, new application, improved algorithm)

The pre-industrial state of the global carbon cycle is a significant aspect of studies related to climate change. In this paper, we recall the power law kinetic representations of the pre-industrial models of Schmitz (2002) and Anderies et al. (2013) from our earlier work. The power law kinetic representations, as uniform formalism, allow for a more extensive analysis and comparison of the different models for the same system. Using the mathematical theories of chemical reaction networks (with power-law kinetics), this work extends the analysis of the kinetic representations of the two models and assesses the similarities and differences in their structural and dynamic properties in relation to model construction assumptions. The analysis includes but is not limited to the coincidence of kinetic and stoichiometric spaces of the networks, capacity for equilibria multiplicity and co-multiplicity, and absolute concentration robustness in some species. Moreover, we bring together previously published results about the power law kinetic representations of the two models and consolidate them with new observations here. We also illustrate how the pre-industrial model of Anderies et al. may serve as a building block in the analysis of a kinetic representation of a global carbon cycle with carbon dioxide removal intervention., Comment: arXiv admin note: text overlap with arXiv:1109.2923 by other authors

Gate model quantum computers promise to solve currently intractable computational problems if they can be operated at scale with long coherence times and high fidelity logic. Neutral atom hyperfine qubits provide inherent scalability due to their identical characteristics, long coherence times, and ability to be trapped in dense multi-dimensional arrays\cite{Saffman2010}. Combined with the strong entangling interactions provided by Rydberg states\cite{Jaksch2000,Gaetan2009,Urban2009}, all the necessary characteristics for quantum computation are available. Here we demonstrate several quantum algorithms on a programmable gate model neutral atom quantum computer in an architecture based on individual addressing of single atoms with tightly focused optical beams scanned across a two-dimensional array of qubits. Preparation of entangled Greenberger-Horne-Zeilinger (GHZ) states\cite{Greenberger1989} with up to 6 qubits, quantum phase estimation for a chemistry problem\cite{Aspuru-Guzik2005}, and the Quantum Approximate Optimization Algorithm (QAOA)\cite{Farhi2014} for the MaxCut graph problem are demonstrated. These results highlight the emergent capability of neutral atom qubit arrays for universal, programmable quantum computation, as well as preparation of non-classical states of use for quantum enhanced sensing., Comment: 4 figures and supplemental material. V2 details on phase estimation and RB data included

Quantum span program algorithms for function evaluation commonly have reduced query complexity when promised that the input has a certain structure. We design a modified span program algorithm to show these speed-ups persist even without having a promise ahead of time, and we extend this approach to the more general problem of state conversion. For example, there is a span program algorithm that decides whether two vertices are connected in an $n$-vertex graph with $O(n^{3/2})$ queries in general, but with $O(\sqrt{k}n)$ queries if promised that, if there is a path, there is one with at most $k$ edges. Our algorithm uses $\tilde{O}(\sqrt{k}n)$ queries to solve this problem if there is a path with at most $k$ edges, without knowing $k$ ahead of time., Comment: 19 pages, v2: organization improved, typos fixed, function evaluation error bound improved

There have been recent theoretic results that provide sufficient conditions for the existence of a species displaying absolute concentration robustness (ACR) in a power law kinetic (PLK) system. One such result involves the detection of ACR among networks of high deficiency by considering a lower deficiency subnetwork with ACR as a local property. In turn, this "smaller" subnetwork serves as a "building block" for the larger ACR-possessing network. Here, with this theorem as foundation, we construct an algorithm that systematically checks ACR in a PLK system. By slightly modifying the algorithm, we also provide a procedure that identifies balanced concentration robustness (BCR), a weaker form of concentration robustness than ACR, in a PLK system.

Poly-PL kinetic systems are kinetic systems consisting of nonnegative linear combinations of power law functions. In this contribution, we analyze these kinetic systems using two main approaches: (1) we define a canonical power law representation of a poly-PL system, and (2) we transform a poly-PL system into a dynamically equivalent power law kinetic system that preserves the stoichiometric subspace of the system. These approaches led us to establish results that concern important dynamical properties of poly-PL systems such as existence and parametrization of complex balanced steady states, capacity for multiple complex balanced equilibria in a stoichiometric compatibility class, concentration robustness of some species, and linear stability of complex balanced equilibria., Comment: The uploader (Noel Fortun) dropped out of the project

Absolute concentration robustness (ACR) is a condition wherein a species in a chemical kinetic system possesses the same value for any positive steady state the network may admit regardless of initial conditions. Thus far, results on ACR center on chemical kinetic systems with deficiency one. In this contribution, we use the idea of dynamic equivalence of chemical reaction networks to derive novel results that guarantee ACR for some classes of power law kinetic systems with deficiency zero. Furthermore, using network decomposition, we identify ACR in higher deficiency networks (i.e. deficiency $\geq$ 2) by considering the presence of a low deficiency subnetwork with ACR. Network decomposition also enabled us to recognize and define a weaker form of concentration robustness than ACR, which we named as `balanced concentration robustness'. Finally, we also discuss and emphasize our view of ACR as a primarily kinetic character rather than a condition that arises from structural sources., Comment: submitted for publication; 26 pages. arXiv admin note: text overlap with arXiv:1908.04497

Robustness against the presence of environmental disruptions can be observed in many systems of chemical reaction network. However, identifying the underlying components of a system that give rise to robustness is often elusive. The influential work of Shinar and Feinberg established simple yet subtle network-based conditions for absolute concentration robustness (ACR), a phenomena in which a species in a mass-action system has the same concentration for any steady state the network may admit. In this contribution, we extend this result to embrace kinetic systems more general than mass-action systems, namely, power-law kinetic systems with reactant-determined interactions (denoted by "PL-RDK"). In PL-RDK, the kinetic order vectors (which we call "interactions") of reactions with the same reactant complex are identical. As illustration, we considered a scenario in the pre-industrial state of global carbon cycle. A power-law approximation of the dynamical system of this scenario is found to be dynamically equivalent to an ACR-possessing PL-RDK system., Comment: JCDCG^3 2018, Manila (21st Japan Conference on Discrete and Computational Geometry, Graphs, and Games; Ateneo de Manila University, Philippines)