Single-well injection-withdrawal tests as a contaminant transport characterisation tool for landfilled waste.

A new single well injection withdrawal (SWIW) test was trialled at four landfills using the tracers lithium and deuterium, and by injecting clean water and measuring electrical conductivity. The aim of the research was to develop a practical test for measuring lateral contaminant transport to aid in the design of landfill flushing. Borehole dilution tests using dyes were undertaken prior to each SWIW test to determine background flow velocities. SWIW tests were performed at different scales by varying the volume of tracer injected (1 to 5,800 m3) and the test duration (2 to 266 days). Tracers were used individually, simultaneously or sequentially to examine repeatability and scaling. Mobile porosities, estimated from first arrival times in observation wells and from model fitting ranged from 0.02 to 0.14. The low mobile porosities measured rule out a purely advective-dispersive system and support a conceptual model of a highly preferential dual-porosity flow system with localised heterogeneity. A dual-porosity model was used to interpret the results. The model gave a good fit to the test data in 7 out of 11 tests (where R2 ≥ 0.98), and the parameters derived are compatible with previous experiments in MSW. Block diffusion times were estimated to range from 12 to 6,630 h, with a scaling relationship apparent between the size of the test (volume of tracer used and/or the duration) and the observed block diffusion time. This scaling relationship means affordable small-scale tests can inform larger-scale flushing operations.

Removing leakage-induced correlated errors in superconducting quantum error correction.

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.

AERMOD as a Gaussian dispersion model for planning tracer gas dispersion tests for landfill methane emission quantification.

The measurement of methane emissions from landfills is important to the understanding of landfills' contribution to greenhouse gas emissions. The Tracer Dispersion Method (TDM) is becoming widely accepted as a technique, which allows landfill emissions to be quantified accurately provided that measurements are taken where the plumes of a released tracer-gas and landfill-gas are well-mixed. However, the distance at which full mixing of the gases occurs is generally unknown prior to any experimental campaign. To overcome this problem the present paper demonstrates that, for any specific TDM application, a simple Gaussian dispersion model (AERMOD) can be run beforehand to help determine the distance from the source at which full mixing conditions occur, and the likely associated measurement errors. An AERMOD model was created to simulate a series of TDM trials carried out at a UK landfill, and was benchmarked against the experimental data obtained. The model was used to investigate the impact of different factors (e.g. tracer cylinder placements, wind directions, atmospheric stability parameters) on TDM results to identify appropriate experimental set ups for different conditions. The contribution of incomplete vertical mixing of tracer and landfill gas on TDM measurement error was explored using the model. It was observed that full mixing conditions at ground level do not imply full mixing over the entire plume height. However, when full mixing conditions were satisfied at ground level, then the error introduced by variations in mixing higher up were always less than 10%.

Measuring methane emissions from a UK landfill using the tracer dispersion method and the influence of operational and environmental factors.

The methane emissions from a landfill in south-east, UK were successfully quantified during a six-day measurement campaign using the tracer dispersion method. The fair weather conditions made it necessary to perform measurements in the late afternoon and in the evening when the lower solar flux resulted in a more stable troposphere with a lower inversion layer. This caused a slower mixing of the gasses, but allowed plume measurements up to 6700 m downwind from the landfill. The average methane emission varied between 217 ±â€¯14 and 410 ±â€¯18 kg h-1 within the individual measurement days, but the measured emission rates were higher on the first three days (333 ±â€¯27, 371 ±â€¯42 and 410 ±â€¯18 kg h-1) compared to the last three days (217 ±â€¯14, 249 ±â€¯20 and 263 ±â€¯22 kg h-1). It was not possible to completely isolate the extent to which these variations were a consequence of measuring artefacts, such as wind/measurement direction and measurement distance, or from an actual change in the fugitive emission. Such emission change is known to occur with changes in the atmospheric pressure. The higher emissions measured during the first three days of the campaign were measured during a period with an overall decrease in atmospheric pressure (from approximately 1014 mbar on day 1 to 987 mbar on day 6). The lower emissions measured during the last three days of the campaign were carried out during a period with an initial pressure increase followed by a period of slowly reducing pressure. The average daily methane recovery flow varied between 633 and 679 kg h-1 at STP (1 atm, 0 °C). The methane emitted to the atmosphere accounted for approximately 31% of the total methane generated, assuming that the methane generated is the sum of the methane recovered and the methane emitted to the atmosphere, thus not including a potential methane oxidation in the landfill cover soil.

Validation and error assessment of the mobile tracer gas dispersion method for measurement of fugitive emissions from area sources.

A controlled release test was carried out to assess the accuracy of the tracer gas dispersion method, which is used to measure whole-site landfill methane (CH4) emissions as well as fugitive emissions from other area sources. Two teams performed measurements using analytical instruments installed in two vehicles, to measure downwind concentrations of target (CH4) and tracer gases at distances of 1.2-3.5 km from the release locations. The controlled target gas release rates were either 5.3 or 10.9 kg CH4 h-1, and target and tracer gases were released at distances between 12 m and 140 m from each other. Five measurement campaigns were performed, where the plume was traversed between 2 and 31 times. The measured target gas emissions agreed well with the controlled releases, with rate differences no greater than 1.1 kg CH4 h-1 for Team A and 1.0 kg CH4 h-1 for Team B when quantifying a controlled release of 10.9 kg CH4 h-1. This corresponds to a maximum error of ±10%. A larger error of up to 18% was seen in the campaign with a lower target gas release rate (5.3 kg CH4 h-1). Using a cross plume integration method to calculate tracer gas to target gas ratios provided the most accurate results (lowest error), whereas larger errors (up to 49%) were observed when using other calculation methods. By establishment of an error budget and comparison with the measured error based on the release test, it could be concluded that following best practice when performing measurements, the overall error of a tracer gas dispersion measurement is very likely to be less than 20%.

Fluctuations of Energy-Relaxation Times in Superconducting Qubits.

Superconducting qubits are an attractive platform for quantum computing since they have demonstrated high-fidelity quantum gates and extensibility to modest system sizes. Nonetheless, an outstanding challenge is stabilizing their energy-relaxation times, which can fluctuate unpredictably in frequency and time. Here, we use qubits as spectral and temporal probes of individual two-level-system defects to provide direct evidence that they are responsible for the largest fluctuations. This research lays the foundation for stabilizing qubit performance through calibration, design, and fabrication.

A blueprint for demonstrating quantum supremacy with superconducting qubits.

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.

Doublet tracer tests to determine the contaminant flushing properties of a municipal solid waste landfill.

This paper describes a programme of research investigating horizontal fluid flow and solute transport through saturated municipal solid waste (MSW) landfill. The purpose is to inform engineering strategies for future contaminant flushing. Solute transport between injection/abstraction well pairs (doublets) is investigated using three tracers over five separate tests at well separations between 5m and 20m. Two inorganic tracers (lithium and bromide) were used, plus the fluorescent dye tracer, rhodamine-WT. There was no evidence for persistent preferential horizons or pathways at the inter-well scale. The time for tracer movement to the abstraction wells varied with well spacing as predicted for a homogeneous isotropic continuum. The time for tracer movement to remote observation wells was also as expected. Mobile porosity was estimated as ~0.02 (~4% of total porosity). Good fits to the tracer breakthrough data were achieved using a dual-porosity model, with immobile regions characterised by block diffusion timescales in the range of about one to ten years. This implies that diffusional exchanges are likely to be very significant for engineering of whole-site contaminant flushing and possibly rate-limiting.

Observation of Classical-Quantum Crossover of 1/f Flux Noise and Its Paramagnetic Temperature Dependence.

By analyzing the dissipative dynamics of a tunable gap flux qubit, we extract both sides of its two-sided environmental flux noise spectral density over a range of frequencies around 2k_{B}T/h≈1 GHz, allowing for the observation of a classical-quantum crossover. Below the crossover point, the symmetric noise component follows a 1/f power law that matches the magnitude of the 1/f noise near 1 Hz. The antisymmetric component displays a 1/T dependence below 100 mK, providing dynamical evidence for a paramagnetic environment. Extrapolating the two-sided spectrum predicts the linewidth and reorganization energy of incoherent resonant tunneling between flux qubit wells.

Digitized adiabatic quantum computing with a superconducting circuit.

Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, 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, which enables the construction of arbitrary interactions and is compatible with error correction, 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 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.

Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit.

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.

Digital quantum simulation of fermionic models with a superconducting circuit.

One of the key applications of quantum information is simulating nature. Fermions are ubiquitous in nature, appearing in condensed matter systems, chemistry and high energy physics. However, universally simulating their interactions is arguably one of the largest challenges, because of the difficulties arising from anticommutativity. Here we use digital methods to construct the required arbitrary interactions, and perform quantum simulation of up to four fermionic modes with a superconducting quantum circuit. We employ in excess of 300 quantum logic gates, and reach fidelities that are consistent with a simple model of uncorrelated errors. The presented approach is in principle scalable to a larger number of modes, and arbitrary spatial dimensions.

State preservation by repetitive error detection in a superconducting quantum circuit.

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) is capable of identifying and correcting them. Adding more qubits improves the preservation of states by guaranteeing that increasingly larger clusters of errors will not cause logical failure-a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here we report the protection of classical states from environmental bit-flip errors and demonstrate the suppression of these errors with increasing system size. We use a linear array of nine qubits, which is a natural step towards the two-dimensional surface code QEC scheme, and track errors as they occur by repeatedly performing projective quantum non-demolition parity measurements. Relative to a single physical qubit, we reduce the failure rate in retrieving an input state by a factor of 2.7 when using five of our nine qubits and by a factor of 8.5 when using all nine qubits after eight cycles. Additionally, we tomographically verify preservation of the non-classical Greenberger-Horne-Zeilinger state. The successful suppression of environment-induced errors will motivate further research into the many challenges associated with building a large-scale superconducting quantum computer.

Multiple-tracer tests for contaminant transport process identification in saturated municipal solid waste.

Two column tests were performed in conditions emulating vertical flow beneath the leachate table in a biologically active landfill to determine dominant transport mechanisms occurring in landfills. An improved understanding of contaminant transport process in wastes is required for developing better predictions about potential length of the long term aftercare of landfills, currently measured in timescales of centuries. Three tracers (lithium, bromide and deuterium) were used. Lithium did not behave conservatively. Given that lithium has been used extensively for tracing in landfill wastes, the tracer itself and the findings of previous tests which assume that it has behaved conservatively may need revisiting. The smaller column test could not be fitted with continuum models, probably because the volume of waste was below a representative elemental volume. Modelling compared advection-dispersion (AD), dual porosity (DP) and hybrid AD-DP models. Of these models, the DP model was found to be the most suitable. Although there is good evidence to suggest that diffusion is an important transport mechanism, the breakthrough curves of the different tracers did not differ from each other as would be predicted based on the free-water diffusion coefficients. This suggested that solute diffusion in wastes requires further study.

Qubit Architecture with High Coherence and Fast Tunable Coupling.

We introduce a superconducting qubit architecture that combines high-coherence qubits and tunable qubit-qubit coupling. With the ability to set the coupling to zero, we demonstrate that this architecture is protected from the frequency crowding problems that arise from fixed coupling. More importantly, the coupling can be tuned dynamically with nanosecond resolution, making this architecture a versatile platform with applications ranging from quantum logic gates to quantum simulation. We illustrate the advantages of dynamical coupling by implementing a novel adiabatic controlled-z gate, with a speed approaching that of single-qubit gates. Integrating coherence and scalable control, the introduced qubit architecture provides a promising path towards large-scale quantum computation and simulation.

Emulating weak localization using a solid-state quantum circuit.

Quantum interference is one of the most fundamental physical effects found in nature. Recent advances in quantum computing now employ interference as a fundamental resource for computation and control. Quantum interference also lies at the heart of sophisticated condensed matter phenomena such as Anderson localization, phenomena that are difficult to reproduce in numerical simulations. Here, employing a multiple-element superconducting quantum circuit, with which we manipulate a single microwave photon, we demonstrate that we can emulate the basic effects of weak localization. By engineering the control sequence, we are able to reproduce the well-known negative magnetoresistance of weak localization as well as its temperature dependence. Furthermore, we can use our circuit to continuously tune the level of disorder, a parameter that is not readily accessible in mesoscopic systems. Demonstrating a high level of control, our experiment shows the potential for employing superconducting quantum circuits as emulators for complex quantum phenomena.

Investigating the effect of compression on solute transport through degrading municipal solid waste.

The effect of applied compression on the nature of liquid flow and hence the movement of contaminants within municipal solid waste was examined by means of thirteen tracer tests conducted on five separate waste samples. The conservative nature of bromide, lithium and deuterium tracers was evaluated and linked to the presence of degradation in the sample. Lithium and deuterium tracers were non-conservative in the presence of degradation, whereas the bromide remained effectively conservative under all conditions. Solute diffusion times into and out of less mobile blocks of waste were compared for each test under the assumption of dominantly dual-porosity flow. Despite the fact that hydraulic conductivity changed strongly with applied stress, the block diffusion times were found to be much less sensitive to compression. A simple conceptual model, whereby flow is dominated by sub-parallel low permeability obstructions which define predominantly horizontally aligned less mobile zones, is able to explain this result. Compression tends to narrow the gap between the obstructions, but not significantly alter the horizontal length scale. Irrespective of knowledge of the true flow pattern, these results show that simple models of solute flushing from landfill which do not include depth dependent changes in solute transport parameters are justified.

Optimal quantum control using randomized benchmarking.

We present a method for optimizing quantum control in experimental systems, using a subset of randomized benchmarking measurements to rapidly infer error. This is demonstrated to improve single- and two-qubit gates, minimize gate bleedthrough, where a gate mechanism can cause errors on subsequent gates, and identify control crosstalk in superconducting qubits. This method is able to correct parameters so that control errors no longer dominate and is suitable for automated and closed-loop optimization of experimental systems.

Fast accurate state measurement with superconducting qubits.

Faster and more accurate state measurement is required for progress in superconducting qubit experiments with greater numbers of qubits and advanced techniques such as feedback. We have designed a multiplexed measurement system with a bandpass filter that allows fast measurement without increasing environmental damping of the qubits. We use this to demonstrate simultaneous measurement of four qubits on a single superconducting integrated circuit, the fastest of which can be measured to 99.8% accuracy in 140 ns. This accuracy and speed is suitable for advanced multiqubit experiments including surface-code error correction.

Superconducting quantum circuits at the surface code threshold for fault tolerance.

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.