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Abstract We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.

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 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.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform.sup.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.sup.-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.sup.5,6 and paves the way to study new quantum materials with superconducting qubits. As a blueprint for high-precision quantum simulation, an 18-qubit algorithm that consists of more than 1,400 two-qubit gates is demonstrated, and reconstructs the energy eigenvalues of the simulated one-dimensional wire to a precision of 1 per cent., Author(s): C. Neill [sup.1] , T. McCourt [sup.1] , X. Mi [sup.1] , Z. Jiang [sup.1] , M. Y. Niu [sup.1] , W. Mruczkiewicz [sup.1] , I. Aleiner [sup.1] , [...]

Per- and polyfluoroalkyl substances (PFAS) may interact with peroxisome proliferator activated receptors (PPARs) and alter lipid homeostasis. Using Xenopus laevis, we investigated the effect of PFAS on (a) lipid homeostasis and whether this correlated to changes in body and hepatic condition; (b) the expression of hepatic genes regulated by PPAR; and (c) the hepatic lipidome. We chronically exposed tadpoles to 0.5 µg/L of either PFOS, PFHxS, PFOA, PFHxA, a binary mixture of PFOS and PFHxS (0.5 µg/L of each), or a control, from NF stage 52 through metamorphic climax. Growth, development, and survival were not affected, but we detected a sex-specific decrease in body condition at NF 66 (6.8%) and in hepatic condition (16.6%) across metamorphic climax for male tadpoles exposed to PFOS. We observed weak evidence for the transient downregulation of apolipoprotein-V (apoa5) at NF 62 in tadpoles exposed to PFHxA. Acyl-CoA oxidase 1 (acox1) was downregulated only in males exposed to PFHxS (Ln(Fold Change) = −0.54). We detected PFAS-specific downregulation of structural glycerophospholipids, while semi-quantitative profiling detected the upregulation in numerous glycerophospholipids, sphingomyelins, and diglycerides. Overall, our findings indicate that PFAS can induce sex-specific effects that change across larval development and metamorphosis. We demonstrate that PFAS alter lipid metabolism at environmentally relevant concentrations through divergent mechanisms that may not be related to PPARs, with an absence of effects on body condition, demonstrating the need for more molecular studies to elucidate mechanisms of PFAS-induced lipid dysregulation in amphibians and in other taxa. [ABSTRACT FROM AUTHOR]

Many superconducting qubit systems use the dispersive interaction between the qubit and a coupled harmonic resonator to perform quantum state measurement. Previous works have found that such measurements can induce state transitions in the qubit if the number of photons in the resonator is too high. We investigate these transitions and find that they can push the qubit out of the two-level subspace, and that they show resonant behavior as a function of photon number. We develop a theory for these observations based on level crossings within the Jaynes-Cummings ladder, with transitions mediated by terms in the Hamiltonian that are typically ignored by the rotating wave approximation. We find that the most important of these terms comes from an unexpected broken symmetry in the qubit potential. We confirm the theory by measuring the photon occupation of the resonator when transitions occur while varying the detuning between the qubit and resonator.

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.

Weak measurement has provided new insight into the nature of quantummeasurement, by demonstrating the ability to extract average state informationwithout fully projecting the system. For single qubit measurements, thispartial projection has been demonstrated with violations of the Leggett-Garginequality. Here we investigate the effects of weak measurement on a maximallyentangled Bell state through application of the Hybrid Bell-Leggett-Garginequality (BLGI) on a linear chain of four transmon qubits. By correlating theresults of weak ancilla measurements with subsequent projective readout, weachieve a violation of the BLGI with 27 standard deviations of certainty.

Leakage errors occur when a quantum system leaves the two-level qubit subspace. Reducing these errors is critically important for quantum error correction to be viable. To quantify leakage errors, we use randomized benchmarking in conjunction with measurement of the leakage population. We characterize single qubit gates in a superconducting qubit, and by refining our use of derivative reduction by adiabatic gate pulse shaping along with detuning of the pulses, we obtain gate errors consistently below 10^{-3} and leakage rates at the 10^{-5} level. With the control optimized, we find that a significant portion of the remaining leakage is due to incoherent heating of the qubit.

A precise measurement of dephasing over a range of time scales is critical for improving quantum gates beyond the error correction threshold. We present a metrological tool based on randomized benchmarking capable of greatly increasing the precision of Ramsey and spin-echo sequences by the repeated but incoherent addition of phase noise. We find our superconducting-quantum-interference-device-based qubit is not limited by 1/f flux noise at short time scales but instead observe a telegraph noise mechanism that is not amenable to study with standard measurement techniques.

A precise measurement of dephasing over a range of time scales is critical for improving quantum gates beyond the error correction threshold. We present a metrological tool based on randomized benchmarking capable of greatly increasing the precision of Ramsey and spin-echo sequences by the repeated but incoherent addition of phase noise. We find our superconducting-quantum-interference-device-based qubit is not limited by 1/f flux noise at short time scales but instead observe a telegraph noise mechanism that is not amenable to study with standard measurement techniques.

One of the key challenges in quantum information is coherently manipulating the quantum state. However, it is an outstanding question whether control can be realized with low error. Only gates from the Clifford group - containing π, π/2, and Hadamard gates - have been characterized with high accuracy. Here, we show how the Platonic solids enable implementing and characterizing larger gate sets. We find that all gates can be implemented with low error. The results fundamentally imply arbitrary manipulation of the quantum state can be realized with high precision, providing practical possibilities for designing efficient quantum algorithms.

We demonstrate a high-efficiency deterministic quantum receiver to convert flying qubits to stationary qubits. We employ a superconducting resonator, which is driven with a shaped pulse through an adjustable coupler. For the ideal "time-reversed" shape, we measure absorption and receiver fidelities at the single microwave photon level of, respectively, 99.41% and 97.4%. These fidelities are comparable with gates and measurement and exceed the deterministic quantum communication and computation fault-tolerant thresholds, enabling new designs of deterministic qubit interconnects and hybrid quantum computers. © 2014 American Physical Society.

A quantum computer can solve hard problems, such as prime factoring, database searching and quantum simulation, at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection by distributing a logical state among many physical quantum bits (qubits) by means of quantum entanglement. Superconductivity is a useful phenomenon in this regard, because it allows the construction of large quantum circuits and is compatible with microfabrication. For superconducting qubits, the surface code approach to quantum computing is a natural choice for error correction, because it uses only nearest-neighbour coupling and rapidly cycled entangling gates. The gate fidelity requirements are modest: the per-step fidelity threshold is only about 99 per cent. Here we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92 per cent and a two-qubit gate fidelity of up to 99.4 per cent. This places Josephson quantum computing at the fault-tolerance threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger state using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

The quantum behavior of superconducting qubits coupled to resonators is verysimilar to that of atoms in optical cavities [1, 2], in which the resonantcavity confines photons and promotes strong light-matter interactions. Thecavity end-mirrors determine the performance of the coupled system, with highermirror reflectivity yielding better quantum coherence, but higher mirrortransparency giving improved measurement and control, forcing a compromise. Analternative is to control the mirror transparency, enabling switching betweenlong photon lifetime during quantum interactions and large signal strength whenperforming measurements. Here we demonstrate the superconducting analogue,using a quantum system comprising a resonator and a qubit, with variablecoupling to a measurement transmission line. The coupling can be adjustedthrough zero to a photon emission rate 1,000 times the intrinsic photon decayrate. We use this system to control photons in coherent states as well as innon-classical Fock states, and dynamically shape the waveform of releasedphotons. This has direct applications to circuit quantum electrodynamics [3],and may enable high-fidelity quantum state transfer between distant qubits, forwhich precisely-controlled waveform shaping is a critical and non-trivialrequirement [4, 5].

Quantum mechanics can help to solve complex problems in physics (1) and chemistry (2), provided they can be programmed in a physical device. In adiabatic quantum computing (3-5), a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing (6), which enables the construction of arbitrary interactions and is compatible with error correction (7,8), but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation (9-12) of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable., A key challenge in adiabatic quantum computing is to construct a device that is capable of encoding problem Hamiltonians that are classically intractable, that is, non-stoquastic (13). Such Hamiltonians would [...]

Quantum computing becomes viable when a quantum state can be protected from environment-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) (1-6) [...]

The intensification of agricultural systems in sub‐Saharan Africa (SSA) is necessary to reduce poverty and improve food security, but increased nutrient applications in smallholder systems could have negative consequences for water quality, greenhouse gas emissions, and air quality. We tracked nitrogen (N) inputs and measured maize (Zea mays) biomass, grain yields, N leaching, and nitric oxide (NO) and nitrous oxide fluxes from a clayey soil in Yala, Kenya and a sandy soil in Tumbi, Tanzania, with application rates of 0, 50, 75, 100, 150, and 200 kg N ha−1 yr−1 over two cropping seasons. Maize yields were 4.5 times higher in Yala than Tumbi, but yields plateaued at both sites with fertilizer applications at or above 100 kg N ha−1 yr−1. Partial N budgets in Yala were typically negative, meaning more N was exported in maize biomass plus grain or lost from the system than was added in fertilizer. In Tumbi, N budgets were negative at lower fertilizer levels but positive at higher fertilizer levels. At both sites most (96%) of the N was lost through maize biomass/grain removal and N leaching. Fertilizer additions at or less than 50 kg N ha−1 yr−1 on these two contrasting sites resulted in minor gaseous N losses, and fertilizer additions less than 200 kg N ha−1 yr−1 caused relatively little change to N leaching losses. This indicates that the modest increases in fertilizer use required to improve maize yields will not greatly increase cropland N losses. Plain Language Summary: Crop yields in smallholder agriculture across sub‐Saharan Africa are low but could be increased by greater applications of nitrogen fertilizer. However, greater use of nitrogen fertilizer creates potential for higher emissions of nitrogen trace gases and nitrogen leaching losses. This study added nitrogen fertilizer doses (0, 50, 75, 100, 150, and 200 kg of nitrogen per hectare) to maize cropland in two smallholder farming sites, one on clay‐rich soils in Kenya and one on sandy soils in Tanzania. It tracked removal of nitrogen fertilizer via harvested maize and losses as nitrous oxide (a greenhouse gas), NO (an air pollutant), and leaching of soil solution. Yields were 4.5 times higher on the clayey soil; yields plateaued at nitrogen application above 100 kg per hectare. Leaching losses far exceeded gaseous losses at both sites: 96% of nitrogen was removed in harvested crops and soil solution. Nitrogen additions at or below 50 kg of nitrogen per hectare led to minor increases in gaseous nitrogen losses and additions less than 200 kg of nitrogen per hectare did not increase soil solution losses. This indicates that the modest increases in fertilizer use required to improve maize yields will not greatly increase cropland nitrogen losses. Key Points: Agriculture is intensifying across sub‐Saharan Africa (SSA) with implications for nitrogen cyclingMaize yields in Kenya trials were 4.5 times higher than in Tanzania, but yields plateaued with fertilizer additions above 100 kg N ha−1 yr−1Fertilizer applications below 50 kg N ha−1 yr−1 did not lead to major losses of nitrogen from maize agroecosystems in SSA [ABSTRACT FROM AUTHOR]