Quantum Gate and Quantum State Preparation through Neighboring Optimal Control

Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold Pa exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: Pe < Pa. Estimates of Pa vary widely, though Pa ∼ 10−4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10−4. After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |β01⟩ = 1/√2(|01⟩ + |10⟩). I show that for ideal (non-ideal) control, an approximate |β01⟩ state could be prepared with error probability ϵ ∼ 10−6 (10−5) with one-shot local operations. Step 2 then takes a block of p pairs of physical qubits, each prepared in |β01⟩ state using Step 1, and fault-tolerantly prepares the logical Bell state for the C4 quantum error detection code.

High Quality Acoustic Time History Measurements of Rotor Harmonic Noise in Confined Spaces

A methodology has been developed and presented to enable the use of small to medium scale acoustic hover facilities for the quantitative measurement of rotor impulsive noise. The methodology was applied to the University of Maryland Acoustic Chamber resulting in accurate measurements of High Speed Impulsive (HSI) noise for rotors running at tip Mach numbers between 0.65 and 0.85 – with accuracy increasing as the tip Mach number was increased. Several factors contributed to the success of this methodology including: • High Speed Impulsive (HSI) noise is characterized by very distinct pulses radiated from the rotor. The pulses radiate high frequency energy – but the energy is contained in short duration time pulses. • The first reflections from these pulses can be tracked (using ray theory) and, through adjustment of the microphone position and suitably applied acoustic treatment at the reflected surface, reduced to small levels. A computer code was developed that automates this process. The code also tracks first bounce reflection timing, making it possible to position the first bounce reflections outside of a measurement window. • Using a rotor with a small number of blades (preferably one) reduces the number of interfering first bounce reflections and generally improves the measured signal fidelity. The methodology will help the gathering of quantitative hovering rotor noise data in less than optimal acoustic facilities and thus enable basic rotorcraft research and rotor blade acoustic design.

HIV Reverse Transcriptase Fidelity And Inhibition Are Modulated By Divalent Cations In A Concentration-Dependent Manner In Vitro

Human immunodeficiency virus (HIV) rapidly evolves through generation and selection of mutants that can escape drug therapy. This process is fueled, in part, by the presumably highly error prone polymerase reverse transcriptase (RT). Fidelity of polymerases can be influenced by cation co-factors. Physiologically, magnesium (Mg2+) is used as a co-factor by RT to perform catalysis, however, alternative cations including manganese (Mn2+), cobalt (Co2+), and zinc (Zn2+) can also be used. I demonstrate here that fidelity and inhibition of HIV RT can be influenced differently, in vitro, by divalent cations depending on their concentration. The reported mutation frequency for purified HIV RT in vitro is typically in the 10-4 range (per nucleotide addition), making the enzyme several-fold less accurate than most polymerases. Paradoxically, results examining HIV replication in cells indicate an error frequency that is ~10 times lower than the error rate obtained in the test tube. Here, I reconcile, at least in part, these discrepancies by showing that HIV RT fidelity in vitro is in the same range as cellular results, in physiological concentrations of free Mg2+ (~0.25 mM). At low Mg2+, mutation rates were 5-10 times lower compared to high Mg2+ conditions (5-10 mM). Alternative divalent cations also have a concentration-dependent effect on RT fidelity. Presumed promutagenic cations Mn2+ and Co2+ decreases the fidelity of RT only at elevated concentrations, and Zn2+, when present in low concentration, increases the fidelity of HIV-1 RT by ~2.5 fold compared to Mg2+. HIV-1 and HIV-2 RT inhibition by nucleoside (NRTIs) and non-nucleoside RT inhibitors (NNRTIs) in vitro is also affected by the Mg2+ concentration. NRTIs lacking 3'-OH group inhibited both enzymes less efficiently in low Mg2+ than in high Mg2+; whereas inhibition by the “translocation defective RT inhibitor”, which retains the 3ʹ-OH, was unaffected by Mg2+ concentration, suggesting that NRTIs with a 3ʹ-OH group may be more potent than other NRTIs. In contrast, NNRTIs were more effective in low vs. high Mg2+ conditions. Overall, the studies presented reveal strategies for designing novel RT inhibitors and strongly emphasize the need for studying HIV RT and RT inhibitors in physiologically relevant low Mg2+ conditions.

High Precision Plasma Etch for Pattern Transfer: Towards Fluorocarbon Based Atomic Layer Etching

A basic requirement of a plasma etching process is fidelity of the patterned organic materials. In photolithography, a He plasma pretreatment (PPT) based on high ultraviolet and vacuum ultraviolet (UV/VUV) exposure was shown to be successful for roughness reduction of 193nm photoresist (PR). Typical multilayer masks consist of many other organic masking materials in addition to 193nm PR. These materials vary significantly in UV/VUV sensitivity and show, therefore, a different response to the He PPT. A delamination of the nanometer-thin, ion-induced dense amorphous carbon (DAC) layer was observed. Extensive He PPT exposure produces volatile species through UV/VUV induced scissioning. These species are trapped underneath the DAC layer in a subsequent plasma etch (PE), causing a loss of adhesion. Next to stabilizing organic materials, the major goals of this work included to establish and evaluate a cyclic fluorocarbon (FC) based approach for atomic layer etching (ALE) of SiO2 and Si; to characterize the mechanisms involved; and to evaluate the impact of processing parameters. Periodic, short precursor injections allow precise deposition of thin FC films. These films limit the amount of available chemical etchant during subsequent low energy, plasma-based Ar+ ion bombardment, resulting in strongly time-dependent etch rates. In situ ellipsometry showcased the self-limited etching. X-ray photoelectron spectroscopy (XPS) confirms FC film deposition and mixing with the substrate. The cyclic ALE approach is also able to precisely etch Si substrates. A reduced time-dependent etching is seen for Si, likely based on a lower physical sputtering energy threshold. A fluorinated, oxidized surface layer is present during ALE of Si and greatly influences the etch behavior. A reaction of the precursor with the fluorinated substrate upon precursor injection was observed and characterized. The cyclic ALE approach is transferred to a manufacturing scale reactor at IBM Research. Ensuring the transferability to industrial device patterning is crucial for the application of ALE. In addition to device patterning, the cyclic ALE process is employed for oxide removal from Si and SiGe surfaces with the goal of minimal substrate damage and surface residues. The ALE process developed for SiO2 and Si etching did not remove native oxide at the level required. Optimizing the process enabled strong O removal from the surface. Subsequent 90% H2/Ar plasma allow for removal of C and F residues.