Characterization of addressability by simultaneous randomized benchmarking

The control and handling of errors arising from cross talk and unwanted interactions in multiqubit systems is an important issue in quantum information processing architectures. We introduce a benchmarking protocol that provides information about the amount of addressability present in the system and implement it on coupled superconducting qubits. The protocol consists of randomized benchmarking experiments run both individually and simultaneously on pairs of qubits. A relevant figure of merit for the addressability is then related to the differences in the measured average gate fidelities in the two experiments. We present results from two similar samples with differing cross talk and unwanted qubit-qubit interactions. The results agree with predictions based on simple models of the classical cross talk and Stark shifts.

Efficient measurement of quantum gate error by interleaved randomized benchmarking

We describe a scalable experimental protocol for estimating the average error of individual quantum computational gates. This protocol consists of interleaving random Clifford gates between the gate of interest and provides an estimate as well as theoretical bounds for the average error of the gate under test, so long as the average noise variation over all Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find a bounded average error of 0.003 [0,0.016] for the single-qubit gates X(π/2) and Y(π/2). These bounded values provide better estimates of the average error than those extracted via quantum process tomography.

Frequency multiplexed superconducting quantum interference device readout of large bolometer arrays for cosmic microwave background measurements

A technological milestone for experiments employing transition edge sensor bolometers operating at sub-Kelvin temperature is the deployment of detector arrays with 100s-1000s of bolometers. One key technology for such arrays is readout multiplexing: the ability to read out many sensors simultaneously on the same set of wires. This paper describes a frequency-domain multiplexed readout system which has been developed for and deployed on the APEX-SZ and South Pole Telescope millimeter wavelength receivers. In this system, the detector array is divided into modules of seven detectors, and each bolometer within the module is biased with a unique ∼MHz sinusoidal carrier such that the individual bolometer signals are well separated in frequency space. The currents from all bolometers in a module are summed together and pre-amplified with superconducting quantum interference devices operating at 4 K. Room temperature electronics demodulate the carriers to recover the bolometer signals, which are digitized separately and stored to disk. This readout system contributes little noise relative to the detectors themselves, is remarkably insensitive to unwanted microphonic excitations, and provides a technology pathway to multiplexing larger numbers of sensors.

Measurements of quasiparticle tunneling dynamics in a band-gap-engineered transmon qubit

We have engineered the band gap profile of transmon qubits by combining oxygen-doped Al for tunnel junction electrodes and clean Al as quasiparticle traps to investigate energy relaxation due to quasiparticle tunneling. The relaxation time T1 of the qubits is shown to be insensitive to this band gap engineering. Operating at relatively low-E(J)/E(C) makes the transmon transition frequency distinctly dependent on the charge parity, allowing us to detect the quasiparticles tunneling across the qubit junction. Quasiparticle kinetics have been studied by monitoring the frequency switching due to even-odd parity change in real time. It shows the switching time is faster than 10  μs, indicating quasiparticle-induced relaxation has to be reduced to achieve T1 much longer than 100  μs.

Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture

Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three-dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubits are highly coherent, with T2 ∼ 10 to 20  μs without the use of spin echo, and highly stable, showing no evidence for 1/f critical current noise. These results suggest that the overall quality of Josephson junctions in these qubits will allow error rates of a few 10(-4), approaching the error correction threshold.

Invited article: millimeter-wave bolometer array receiver for the Atacama pathfinder experiment Sunyaev-Zel'dovich (APEX-SZ) instrument

The Atacama pathfinder experiment Sunyaev-Zel'dovich (APEX-SZ) instrument is a millimeter-wave cryogenic receiver designed to observe galaxy clusters via the Sunyaev-Zel'dovich effect from the 12 m APEX telescope on the Atacama plateau in Chile. The receiver contains a focal plane of 280 superconducting transition-edge sensor (TES) bolometers instrumented with a frequency-domain multiplexed readout system. The bolometers are cooled to 280 mK via a three-stage helium sorption refrigerator and a mechanical pulse-tube cooler. Three warm mirrors, two 4 K lenses, and a horn array couple the TES bolometers to the telescope. APEX-SZ observes in a single frequency band at 150 GHz with 1' angular resolution and a 22' field-of-view, all well suited for cluster mapping. The APEX-SZ receiver has played a key role in the introduction of several new technologies including TES bolometers, the frequency-domain multiplexed readout, and the use of a pulse-tube cooler with bolometers. As a result of these new technologies, the instrument has a higher instantaneous sensitivity and covers a larger field-of-view than earlier generations of Sunyaev-Zel'dovich instruments. The TES bolometers have a median sensitivity of 890 μK(CMB)√s (NEy of 3.5 × 10(-4) √s). We have also demonstrated upgraded detectors with improved sensitivity of 530 μK(CMB)√s (NEy of 2.2 × 10(-4) √s). Since its commissioning in April 2007, APEX-SZ has been used to map 48 clusters. We describe the design of the receiver and its performance when installed on the APEX telescope.

Simple all-microwave entangling gate for fixed-frequency superconducting qubits

We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88, and quantum process tomography reveals a gate fidelity of 81%.

Preparation and measurement of three-qubit entanglement in a superconducting circuit

Traditionally, quantum entanglement has been central to foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can have results at odds with classical behaviour. These discrepancies grow exponentially with the number of entangled particles. With the ample experimental confirmation of quantum mechanical predictions, entanglement has evolved from a philosophical conundrum into a key resource for technologies such as quantum communication and computation. Although entanglement in superconducting circuits has been limited so far to two qubits, the extension of entanglement to three, eight and ten qubits has been achieved among spins, ions and photons, respectively. A key question for solid-state quantum information processing is whether an engineered system could display the multi-qubit entanglement necessary for quantum error correction, which starts with tripartite entanglement. Here, using a circuit quantum electrodynamics architecture, we demonstrate deterministic production of three-qubit Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88 per cent, measured with quantum state tomography. Several entanglement witnesses detect genuine three-qubit entanglement by violating biseparable bounds by 830 ± 80 per cent. We demonstrate the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of this encoding with decoding and error-correcting steps in a feedback loop will be the next step for quantum computing with integrated circuits.

High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity

We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that, in the strongly driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.

Randomized benchmarking and process tomography for gate errors in a solid-state qubit

We present measurements of single-qubit gate errors for a superconducting qubit. Results from quantum process tomography and randomized benchmarking are compared with gate errors obtained from a double pi pulse experiment. Randomized benchmarking reveals a minimum average gate error of 1.1+/-0.3% and a simple exponential dependence of fidelity on the number of gates. It shows that the limits on gate fidelity are primarily imposed by qubit decoherence, in agreement with theory.

A balancing act: the consulting engineers' pragmatic view of process modelling

Modelling: what do we know, what do we want to know and why? The practical application of models to real projects is often circular because these questions weren't asked prior to making the decision to model the plant under study. Modelling wastewater treatment plants can provide insight into the inner workings of the process that might not be attainable any other way, but is that added process knowledge always needed or necessary and what criteria does one use to determine the level of effort required? These complex modelling decisions require education, communication, and improved understanding amongst both modellers and clients. This submission explores the use of models by consultants for consulting purposes and the balancing acts (time versus knowledge and cost versus benefit) that the consulting engineer must manage when embarking on any modelling project.

Controlling the spontaneous emission of a superconducting transmon qubit

We present a detailed characterization of coherence in seven transmon qubits in a circuit QED architecture. We find that spontaneous emission rates are strongly influenced by far off-resonant modes of the cavity and can be understood within a semiclassical circuit model. A careful analysis of the spontaneous qubit decay into a microwave transmission-line cavity can accurately predict the qubit lifetimes over 2 orders of magnitude in time and more than an octave in frequency. Coherence times T1 and T_{2};{*} of more than a microsecond are reproducibly demonstrated.

Coupling superconducting qubits via a cavity bus

Superconducting circuits are promising candidates for constructing quantum bits (qubits) in a quantum computer; single-qubit operations are now routine, and several examples of two-qubit interactions and gates have been demonstrated. These experiments show that two nearby qubits can be readily coupled with local interactions. Performing gate operations between an arbitrary pair of distant qubits is highly desirable for any quantum computer architecture, but has not yet been demonstrated. An efficient way to achieve this goal is to couple the qubits to a 'quantum bus', which distributes quantum information among the qubits. Here we show the implementation of such a quantum bus, using microwave photons confined in a transmission line cavity, to couple two superconducting qubits on opposite sides of a chip. The interaction is mediated by the exchange of virtual rather than real photons, avoiding cavity-induced loss. Using fast control of the qubits to switch the coupling effectively on and off, we demonstrate coherent transfer of quantum states between the qubits. The cavity is also used to perform multiplexed control and measurement of the qubit states. This approach can be expanded to more than two qubits, and is an attractive architecture for quantum information processing on a chip.

Generating single microwave photons in a circuit

Microwaves have widespread use in classical communication technologies, from long-distance broadcasts to short-distance signals within a computer chip. Like all forms of light, microwaves, even those guided by the wires of an integrated circuit, consist of discrete photons. To enable quantum communication between distant parts of a quantum computer, the signals must also be quantum, consisting of single photons, for example. However, conventional sources can generate only classical light, not single photons. One way to realize a single-photon source is to collect the fluorescence of a single atom. Early experiments measured the quantum nature of continuous radiation, and further advances allowed triggered sources of photons on demand. To allow efficient photon collection, emitters are typically placed inside optical or microwave cavities, but these sources are difficult to employ for quantum communication on wires within an integrated circuit. Here we demonstrate an on-chip, on-demand single-photon source, where the microwave photons are injected into a wire with high efficiency and spectral purity. This is accomplished in a circuit quantum electrodynamics architecture, with a microwave transmission line cavity that enhances the spontaneous emission of a single superconducting qubit. When the qubit spontaneously emits, the generated photon acts as a flying qubit, transmitting the quantum information across a chip. We perform tomography of both the qubit and the emitted photons, clearly showing that both the quantum phase and amplitude are transferred during the emission. Both the average power and voltage of the photon source are characterized to verify performance of the system. This single-photon source is an important addition to a rapidly growing toolbox for quantum optics on a chip.

Applications and limitations of ADM 1 in municipal wastewater solids treatment

The ADM 1 model has been implemented in a steady-state whole wastewater plant simulator. The ADM 1 model has been in use with good success for approximately 2 years on a wide range of wastewater treatment facilities. However, a number of modifications were necessary to allow it to be used in the context of municipal wastewater treatment. It was found that the model's use was greatly simplified if used in conjunction with a larger plant simulator to assist in the feed fractionation. It was also found that a better fit to actual operating data was achieved if some of the slowly biodegradable particulate fraction was partitioned into ADM particulate fractions other than the composite fraction. Another significant limitation of the model is in the absence of phosphorus modeling. The ADM model needs to have phosphorus handling for all the relevant fractions, and needs to include the handling of inorganic reactions such as struvite precipitation and metal phosphate/metal hydroxide precipitation. Activity effects on chemical equilibria are significant when considering phosphorus. Also of importance in wastewater treatment is the fate of sulfur compounds. This includes the generation of H2S in the digester gas and the fate of the sulfur species in the digested sludge (as a predictor of odour-generating potential).

Application of the IWA anaerobic digestion model (ADM1) for simulating full-scale anaerobic sewage sludge digestion

A steady-state implementation of the IWA Anaerobic Digestion Model No. 1 (ADM1) has been applied to the anaerobic digesters in two wastewater treatment plants. The two plants have a wastewater treatment capacity of 76,000 and 820,000 m3/day, respectively, with approximately 12 and 205 dry metric tons sludge fed to digesters per day. The main purpose of this study is to compare the ADM1 model results with full-scale anaerobic digestion performance. For both plants, the prediction of the steady-state ADM1 implementation using the suggested physico-chemical and biochemical parameter values was able to reflect the results from the actual digester operations to a reasonable degree of accuracy on all parameters. The predicted total solids (TS) and volatile solids (VS) concentration in the digested biosolids, as well as the digester volatile solids destruction (VSD), biogas production and biogas yield are within 10% of the actual digester data. This study demonstrated that the ADM1 is a powerful tool for predicting the steady-state behaviour of anaerobic digesters treating sewage sludges. In addition, it showed that the use of a whole wastewater treatment plant simulator for fractionating the digester influent into the ADM1 input parameters was successful.

A comparison between the theory and reality of full-scale step-feed nutrient removal systems

Capacity enhancement and volume reduction benefits of step-feeding fully aerobic bioreactors has been well documented. Application of step-feed technology to biological nutrient removal (BNR) systems, particularly those removing nitrogen alone or both nitrogen and phosphorus, is relatively new to the industry. In recent years, a number of full-scale step-feed facilities have been brought into service. This paper reviews nine full-scale step-feed biological nutrient removal systems--both nitrogen removal alone, and nitrogen and phosphorus removal. The objective is to compare the theoretical benefits of such systems with their actual operation. The predicted benefits of reduced bioreactor volume or increased process capacity, reduced energy usage, more robust nitrification performance, and the flexibility to tune (or de-tune) nitrification efficiency were verified in full-scale systems. Equations are also presented that may be used in the prediction of step-feed benefits. There are two primary drivers for considering a step-feed biological reactor system: 1. Reduced bioreactor volume for a defined capacity or performance or increased process capacity given a fixed bioreactor volume. 2. More robust nitrification performance. Full-scale operation of these step-feed nutrient removal systems provides a real world basis for the claimed benefits of step-feed operation. These systems have uniformly shown additional capacity. A number of them have also exhibited more robust performance, especially during storms. Where possible, side-by-side comparisons of full-scale step-feed systems with non-step-feed systems have exhibited greater process reliability and flexibility.

Tools for physiology labs: an inexpensive high-performance amplifier and electrode for extracellular recording

The cost of electronic equipment can be a critical barrier to including neurophysiology exercises in biology teaching programs. We describe the construction of a simple and inexpensive AC preamplifier with performance comparable to that of commercial products. The amplifier consists of two integrated circuits in five stages: differential input, fixed gain, variable gain (100 or 1000), low-pass filter (5 or 20 kHz), and 50 or 60 Hz notch filter. We compared our amplifier with two commercial units, the A-M Systems Model 1700 and the Grass P15. The quality of extracellular recording from a typical student preparation (spontaneously active crayfish motor nerve) was the same for all three amplifiers, although our amplifier has slightly higher internal noise than the P15 and slightly lower common-mode rejection than the 1700 and P15. In addition, we describe a simple suction electrode for extracellular nerve recording. It is easily constructed from readily available materials and uses a disposable plastic pipette tip, instead of the traditional glass tip, to contact the nerve. This tip is easily replaced if broken or clogged, and can be adapted to different recording conditions by selecting a different tip size or stretching the plastic. Development of this equipment is part of an ongoing project to promote neuroscience education by expanding the neurophysiology options available to laboratory instructors.

Guanylyl cyclase-C receptor mRNA distribution along the rat nephron

Guanylin (GN) and uroguanylin (UGN) are two recently identified peptides that have been shown to affect water and electrolyte transport in both the intestine and the kidney. Mechanistically, the effects of both peptides are thought to be mediated by intracellular cGMP which results from ligand binding to a plasma membrane guanylyl cyclase-C (GC-C) receptor. To date, the specific intrarenal site(s) of GN and UGN action have not been established. To begin to address this issue, the present studies utilized semi-quantitative RT-PCR to assess the distribution of GC-C mRNA in specific microdissected segments of the rat nephron. GC-C mRNA expression was highest in the cortical collecting tubule, followed by the proximal convoluted tubule, medullary thick ascending limb and collecting tubule, and thin limbs of Henle's loop. Expression levels were significantly lower in all other segments tested, including the glomerulus. The renal tubular expression pattern for cGMP-dependent protein kinase II (cGK-II) mRNA, which is activated in response to GN/UGN-dependent cGMP accumulation, was similar to that for GC-C. Notably, both GN and UGN mRNAs were also expressed along the nephron. The highest levels of expression for both peptides were detected in the medullary collecting tubule. Lower, but comparable levels of GN and UGN expression also occurred in the cortical collecting tubule, cortical and medullary thick ascending limb, and thin limbs of Henles loop. In the proximal convoluted tubule, GN mRNA expression was also quite high, while UGN mRNA was almost undetectable. The presence of renal GC-C and cGK-II in the kidney are consistent with a proposed endocrine function for GN and UGN. In addition however, the present data suggest that intrarenally synthesized GN and UGN may also contribute to the regulation of renal tubular transport.

Sexual violence: the perpetrator

In addition to assessing and treating victims of sexual violence, mental health professionals are also called upon to provide similar services for sexually violent perpetrators. This chapter addresses these concerns along with the forensic issues surrounding those who commit sexual violence.

Assessing the risk for violence

In addition to taking steps to ensure their own safety, clinicians also have a role in predicting violence. In the past the clinician's ability to accurately assess the risk for violence has been seriously questioned. This chapter provides guidance for making acceptable predictions.