Quantum error correction with biased noise

Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security.

At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level.

In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations.

In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction.

In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

Diffraction-limited imaging on the 200-inch telescope

We have used the technique of non-redundant masking at the Palomar 200-inch telescope and radio VLBI imaging software to make optical aperture synthesis maps of two binary stars, β Corona Borealis and σ Herculis. The dynamic range of the map of β CrB, a binary star with a separation of 230 milliarcseconds is 50:1. For σ Her, we find a separation of 70 milliarcseconds and the dynamic range of our image is 30:1. These demonstrate the potential of the non-redundant masking technique for diffraction-limited imaging of astronomical objects with high dynamic range.

We find that the optimal integration time for measuring the closure phase is longer than that for measuring the fringe amplitude. There is not a close relationship between amplitude errors and phase errors, as is found in radio interferometry. Amplitude self calibration is less effective at optical wavelengths than at radio wavelengths. Primary beam sensitivity correction made in radio aperture synthesis is not necessary in optical aperture synthesis.

The effects of atmospheric disturbances on optical aperture synthesis have been studied by Monte Carlo simulations based on the Kolmogorov theory of refractive-index fluctuations. For the non-redundant masking with τ_c-sized apertures, the simulated fringe amplitude gives an upper bound of the observed fringe amplitude. A smooth transition is seen from the non-redundant masking regime to the speckle regime with increasing aperture size. The fractional reduction of the fringe amplitude according to the bandwidth is nearly independent of the aperture size. The limiting magnitude of optical aperture synthesis with τ_c-sized apertures and that with apertures larger than τ_c are derived.

Monte Carlo simulations are also made to study the sensitivity and resolution of the bispectral analysis of speckle interferometry. We present the bispectral modulation transfer function and its signal-to-noise ratio at high light levels. The results confirm the validity of the heuristic interferometric view of image-forming process in the mid-spatial-frequency range. The signal-to- noise ratio of the bispectrum at arbitrary light levels is derived in the mid-spatial-frequency range.

The non-redundant masking technique is suitable for imaging bright objects with high resolution and high dynamic range, while the faintest limit will be better pursued by speckle imaging.

Lightweight deformable mirrors for future space telescopes

This thesis presents a concept for ultra-lightweight deformable mirrors based on a thin substrate of optical surface quality coated with continuous active piezopolymer layers that provide modes of actuation and shape correction. This concept eliminates any kind of stiff backing structure for the mirror surface and exploits micro-fabrication technologies to provide a tight integration of the active materials into the mirror structure, to avoid actuator print-through effects. Proof-of-concept, 10-cm-diameter mirrors with a low areal density of about 0.5 kg/m² have been designed, built and tested to measure their shape-correction performance and verify the models used for design. The low cost manufacturing scheme uses replication techniques, and strives for minimizing residual stresses that deviate the optical figure from the master mandrel. It does not require precision tolerancing, is lightweight, and is therefore potentially scalable to larger diameters for use in large, modular space telescopes. Other potential applications for such a laminate could include ground-based mirrors for solar energy collection, adaptive optics for atmospheric turbulence, laser communications, and other shape control applications.

The immediate application for these mirrors is for the Autonomous Assembly and Reconfiguration of a Space Telescope (AAReST) mission, which is a university mission under development by Caltech, the University of Surrey, and JPL. The design concept, fabrication methodology, material behaviors and measurements, mirror modeling, mounting and control electronics design, shape control experiments, predictive performance analysis, and remaining challenges are presented herein. The experiments have validated numerical models of the mirror, and the mirror models have been used within a model of the telescope in order to predict the optical performance. A demonstration of this mirror concept, along with other new telescope technologies, is planned to take place during the AAReST mission.

Accelerogram processing using reliability bounds and optimal correction methods

This study addresses the problem of obtaining reliable velocities and displacements from accelerograms, a concern which often arises in earthquake engineering. A closed-form acceleration expression with random parameters is developed to test any strong-motion accelerogram processing method. Integration of this analytical time history yields the exact velocities, displacements and Fourier spectra. Noise and truncation can also be added. A two-step testing procedure is proposed and the original Volume II routine is used as an illustration. The main sources of error are identified and discussed. Although these errors may be reduced, it is impossible to extract the true time histories from an analog or digital accelerogram because of the uncertain noise level and missing data. Based on these uncertainties, a probabilistic approach is proposed as a new accelerogram processing method. A most probable record is presented as well as a reliability interval which reflects the level of error-uncertainty introduced by the recording and digitization process. The data is processed in the frequency domain, under assumptions governing either the initial value or the temporal mean of the time histories. This new processing approach is tested on synthetic records. It induces little error and the digitization noise is adequately bounded. Filtering is intended to be kept to a minimum and two optimal error-reduction methods are proposed. The "noise filters" reduce the noise level at each harmonic of the spectrum as a function of the signal-to-noise ratio. However, the correction at low frequencies is not sufficient to significantly reduce the drifts in the integrated time histories. The "spectral substitution method" uses optimization techniques to fit spectral models of near-field, far-field or structural motions to the amplitude spectrum of the measured data. The extremes of the spectrum of the recorded data where noise and error prevail are then partly altered, but not removed, and statistical criteria provide the choice of the appropriate cutoff frequencies. This correction method has been applied to existing strong-motion far-field, near-field and structural data with promising results. Since this correction method maintains the whole frequency range of the record, it should prove to be very useful in studying the long-period dynamics of local geology and structures.

Investigation of Fundamental Processes Governing Secondary Organic Aerosol Formation in Laboratory Chambers

Our understanding of the processes and mechanisms by which secondary organic aerosol (SOA) is formed is derived from laboratory chamber studies. In the atmosphere, SOA formation is primarily driven by progressive photooxidation of SOA precursors, coupled with their gas-particle partitioning. In the chamber environment, SOA-forming vapors undergo multiple chemical and physical processes that involve production and removal via gas-phase reactions; partitioning onto suspended particles vs. particles deposited on the chamber wall; and direct deposition on the chamber wall. The main focus of this dissertation is to characterize the interactions of organic vapors with suspended particles and the chamber wall and explore how these intertwined processes in laboratory chambers govern SOA formation and evolution.

A Functional Group Oxidation Model (FGOM) that represents SOA formation and evolution in terms of the competition between functionalization and fragmentation, the extent of oxygen atom addition, and the change of volatility, is developed. The FGOM contains a set of parameters that are to be determined by fitting of the model to laboratory chamber data. The sensitivity of the model prediction to variation of the adjustable parameters allows one to assess the relative importance of various pathways involved in SOA formation.

A critical aspect of the environmental chamber is the presence of the wall, which can induce deposition of SOA-forming vapors and promote heterogeneous reactions. An experimental protocol and model framework are first developed to constrain the vapor-wall interactions. By optimal fitting the model predictions to the observed wall-induced decay profiles of 25 oxidized organic compounds, the dominant parameter governing the extent of wall deposition of a compound is identified, i.e., wall accommodation coefficient. By correlating this parameter with the molecular properties of a compound via its volatility, the wall-induced deposition rate of an organic compound can be predicted based on its carbon and oxygen numbers in the molecule.

Heterogeneous transformation of δ-hydroxycarbonyl, a major first-generation product from long-chain alkane photochemistry, is observed on the surface of particles and walls. The uniqueness of this reaction scheme is the production of substituted dihydrofuran, which is highly reactive towards ozone, OH, and NO3, thereby opening a reaction pathway that is not usually accessible to alkanes. A spectrum of highly-oxygenated products with carboxylic acid, ester, and ether functional groups is produced from the substituted dihydrofuran chemistry, thereby affecting the average oxidation state of the alkane-derived SOA.

The vapor wall loss correction is applied to several chamber-derived SOA systems generated from both anthropogenic and biogenic sources. Experimental and modeling approaches are employed to constrain the partitioning behavior of SOA-forming vapors onto suspended particles vs. chamber walls. It is demonstrated that deposition of SOA-forming vapors to the chamber wall during photooxidation experiments can lead to substantial and systematic underestimation of SOA. Therefore, it is likely that a lack of proper accounting for vapor wall losses that suppress chamber-derived SOA yields contribute substantially to the underprediction of ambient SOA concentrations in atmospheric models.

The Atmospheric Dynamics of Pulsar Companions

Pulsars emit radiation over an extremely wide frequency range, from radio through gamma. Recently, systems in which this radiation significantly alters the atmospheres of low-mass pulsar companions have been discovered. These systems, ranging from ones with highly anisotropic heating to those with transient X-ray emissions, represent an exciting opportunity to investigate pulsars through the changes they induce in their companions. In this work, we present both analytic and numerical work investigating these phenomena, with a particular focus on atmospheric heat transport, transient phenomena, and the possibility of deep heating via gamma rays. We find that certain classes of binary systems may explain decadal-timescale X-ray transient phenomena, as well as the formation of so-called redback companion systems. We also posit an explanation for the formation of high-eccentricity millisecond pulsars with white dwarf companions. In addition, we examine the temperature anisotropy induced by the Pulsar in its companion, and demonstrate that this may be used to infer properties of both the companion and the Pulsar wind. Finally, we explore the possibility of spontaneously generated banded winds in rapidly rotating convecting objects.

Joule-Thomson coefficients of propane and n-butane

Experimental Joule-Thomson measurements were made on gaseous propane at temperatures from 100 to 280˚F and at pressures from 8 to 66 psia. Joule-Thomson measurements were also made on gaseous n-butane at temperatures from 100 to 280˚ and at pressures from 8 to 42 psia. For propane, the values of these measurements ranged from 0.07986˚F/psi at 280˚F and 8.01 psia to 0.19685˚F/psi at 100˚F and 66.15 psia. For n-butane, the values ranged from 0.11031˚F/psi at 280˚F and 9.36 psia to 0.30141˚F/psi at 100˚F and 41.02 psia. The experimental values have a maximum error of 1.5 percent.

For n-butane, the measurements of this study did not agree with previous Joule-Thomson measurements made in the Laboratory in 1935. The application of a thermal-transfer correction to the previous experimental measurements would cause the two sets of data to agree. Calculated values of the Joule-Thomson coefficient from other types of p-v-t data did agree with the present measurements for n-butane.

The apparatus used to measure the experimental Joule-Thomson coefficients had a radial-flow porous thimble and was operated at pressure changes between 2.3 and 8.6 psi. The major difference between this and other Joule-Thomson apparatus was its larger weight rates of flow (up to 6 pounds per hour) at atmospheric pressure. The flow rate was shown to have an appreciable effect on non-isenthalpic Joule-Thomson measurements.

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Field and Laboratory Studies of Atmospheric Organic Aerosol

This thesis is the culmination of field and laboratory studies aimed at assessing processes that affect the composition and distribution of atmospheric organic aerosol. An emphasis is placed on measurements conducted using compact and high-resolution Aerodyne Aerosol Mass Spectrometers (AMS). The first three chapters summarize results from aircraft campaigns designed to evaluate anthropogenic and biogenic impacts on marine aerosol and clouds off the coast of California. Subsequent chapters describe laboratory studies intended to evaluate gas and particle-phase mechanisms of organic aerosol oxidation.

The 2013 Nucleation in California Experiment (NiCE) was a campaign designed to study environments impacted by nucleated and/or freshly formed aerosol particles. Terrestrial biogenic aerosol with > 85% organic mass was observed to reside in the free troposphere above marine stratocumulus. This biogenic organic aerosol (BOA) originated from the Northwestern United States and was transported to the marine atmosphere during periodic cloud-clearing events. Spectra recorded by a cloud condensation nuclei counter demonstrated that BOA is CCN active. BOA enhancements at latitudes north of San Francisco, CA coincided with enhanced cloud water concentrations of organic species such as acetate and formate.

Airborne measurements conducted during the 2011 Eastern Pacific Emitted Aerosol Cloud Experiment (E-PEACE) were aimed at evaluating the contribution of ship emissions to the properties of marine aerosol and clouds off the coast of central California. In one study, analysis of organic aerosol mass spectra during periods of enhanced shipping activity yielded unique tracers indicative of cloud-processed ship emissions (m/z 42 and 99). The variation of their organic fraction (f₄₂ and f₉₉) was found to coincide with periods of heavy (f₄₂ > 0.15; f₉₉ > 0.04), moderate (0.05 < f₄₂ < 0.15; 0.01 < f₉₉ < 0.04), and negligible (f₄₂ < 0.05; f₉₉ < 0.01) ship influence. Application of these conditions to all measurements conducted during E-PEACE demonstrated that a large fraction of cloud droplet (72%) and dry aerosol mass (12%) sampled in the California coastal study region was heavily or moderately influenced by ship emissions. Another study investigated the chemical and physical evolution of a controlled organic plume emitted from the R/V Point Sur. Under sunny conditions, nucleated particles composed of oxidized organic compounds contributed nearly an order of magnitude more cloud condensation nuclei (CCN) than less oxidized particles formed under cloudy conditions. The processing time necessary for particles to become CCN active was short ( < 1 hr) compared to the time needed for particles to become hygroscopic at sub-saturated humidity ( > 4 hr).

Laboratory chamber experiments were also conducted to evaluate particle-phase processes influencing aerosol phase and composition. In one study, ammonium sulfate seed was coated with a layer of secondary organic aerosol (SOA) from toluene oxidation followed by a layer of SOA from α-pinene oxidation. The system exhibited different evaporative properties than ammonium sulfate seed initially coated with α-pinene SOA followed by a layer of toluene SOA. This behavior is consistent with a shell-and-core model and suggests limited mixing among different SOA types. Another study investigated the reactive uptake of isoprene epoxy diols (IEPOX) onto non-acidified aerosol. It was demonstrated that particle acidity has limited influence on organic aerosol formation onto ammonium sulfate seed, and that the chemical system is limited by the availability of nucleophiles such as sulfate.

Flow tube experiments were conducted to examine the role of iron in the reactive uptake and chemical oxidation of glycolaldehyde. Aerosol particles doped with iron and hydrogen peroxide were mixed with gas-phase glycolaldehyde and photochemically aged in a custom-built flow reactor. Compared to particles free of iron, iron-doped aerosols significantly enhanced the oxygen to carbon (O/C) ratio of accumulated organic mass. The primary oxidation mechanism is suggested to be a combination of Fenton and photo-Fenton reactions which enhance particle-phase OH radical concentrations.