Physical Sciences and Mathematics Commons^™

Economic Entanglement: The Quantum Race Between The United States And China, Isabella Willhite

Regis University Student Publications (comprehensive collection)

The United States and China are both currently home to the strongest economies and militaries in the world. Despite their interdependence, trade wars have escalated between the two countries in the past few years. While past trade wars have been focused on purely economic protectionism or ideological stances, the trade wars of today signify a shift towards protecting critical emerging technologies. The important emerging technology of today is quantum computing, which will forever change the way that computers encrypt, process, and decode information. The United States and China are on the eve of the “quantum race,” in which they will …

Modeling Lithographic Quantum Dots And Donors For Quantum Computation And Simulation, Mitchell Ian Brickson

Physics & Astronomy ETDs

Our first focus is on few-hole quantum dots in germanium. We use discontinous Galerkin methods to discretize and solve the equations of a highly detailed k·p model that describes these systems, enabling a better understanding of experimental magnetospectroscopy results. We confirm the expected anisotropy of single-hole g-factors and describe mechanisms by which different orbital states have different g-factors. Building on this, we show that the g-factors in Ge holes are suciently sensitive to details of the device electrostatics that magnetospectroscopy data can be used to make a prediction of the underlying confinement potential. The second focus is on designing quantum …

The Quantum Computational Utility Of Symmetry-Protected Topological Order: From Near-Term Advantages To Universal Measurement-Based Quantum Computing, Austin Kevin Daniel

Physics & Astronomy ETDs

Quantum computers offer new avenues to approach difficult problems by taking advantage of the strange and often nonintuitive phenomena present in quantum physics. Though many quantum algorithms are believed or known to outperform the best known classical algorithms, the fundamental mechanism granting them their power remains elusive. In measurement-based quantum computation (MBQC), two key resources have been show to enable universal and provably nonclassical quantum computations, respectively. These are symmetry-protected topological order (SPTO), a notion describing a class of quantum magnets with hidden long-range correlations in their entanglement structure, and quantum contextuality, the fact that a quantum measurement outcome inherently …

A Menagerie Of Symmetry Testing Quantum Algorithms, Margarite Lynn Laborde

LSU Doctoral Dissertations

In Chapter 1, we establish the mathematical background used throughout this thesis. We review concepts from group and representation theory. We further establish fundamental concepts from quantum information. This will allow us to then define the different notions of symmetry necessary in the following chapters. In Chapter 2, we investigate Hamiltonian symmetries. We propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. Furthermore, we show that this algorithm is that this algorithm is DQC1-Complete. Finally, we execute one of our symmetry-testing algorithms on existing quantum computers for simple examples. In Chapter 3, we …

Compilation Optimizations To Enhance Resilience Of Big Data Programs And Quantum Processors, Travis D. Lecompte

LSU Doctoral Dissertations

Modern computers can experience a variety of transient errors due to the surrounding environment, known as soft faults. Although the frequency of these faults is low enough to not be noticeable on personal computers, they become a considerable concern during large-scale distributed computations or systems in more vulnerable environments like satellites. These faults occur as a bit flip of some value in a register, operation, or memory during execution. They surface as either program crashes, hangs, or silent data corruption (SDC), each of which can waste time, money, and resources. Hardware methods, such as shielding or error correcting memory (ECM), …

Quantum Error Detection Without Using Ancilla Qubits, Nicolas Guerrero

Theses and Dissertations

Quantum computers are beset by errors from a variety of sources. Although quantum error correction and detection codes have been developed since the 1990s, these codes require mid-circuit measurements in order to operate. In order to avoid these measurements we have developed a new error detection code that only requires state collapses at the end of the circuit, which we call no ancilla error detection (NAED). We investigate some of the mathematics behind NAED such as which codes can detect which errors. We then run NAED on three separate types of circuits: Greenberger–Horne–Zeilinger circuits, phase dependent circuits, and a quantum …

Optimization Of Quantum Circuits Using Spin Bus Multiqubit Gates For Quantum Dots, Miguel Gonzalo Rodriguez

Open Access Theses & Dissertations

The current conventional method for designing quantum circuits is to employ a number of single- and two-qubit gates, which often necessitate a lengthy sequence, imposing severe constraints on quantum coherence and quantum circuit complexity. Coupling multiple spin qubits to a common spin chain can result in a generically multiqubit gate. It is demonstrated that the multiqubit gate can substantially reduce the depth of quantum circuits and establish multiqubit entanglement considerably more quickly.

Quantum Computing Simulation Of The Hydrogen Molecule System With Rigorous Quantum Circuit Derivations, Yili Zhang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Quantum computing has been an emerging technology in the past few decades. It utilizes the power of programmable quantum devices to perform computation, which can solve complex problems in a feasible time that is impossible with classical computers. Simulating quantum chemical systems using quantum computers is one of the most active research fields in quantum computing. However, due to the novelty of the technology and concept, most materials in the literature are not accessible for newbies in the field and sometimes can cause ambiguity for practitioners due to missing details.

This report provides a rigorous derivation of simulating quantum chemistry …

Methodologies For Quantum Circuit And Algorithm Design At Low And High Levels, Edison Tsai

Dissertations and Theses

Although the concept of quantum computing has existed for decades, the technology needed to successfully implement a quantum computing system has not yet reached the level of sophistication, reliability, and scalability necessary for commercial viability until very recently. Significant progress on this front was made in the past few years, with IBM planning to create a 1000-qubit chip by the end of 2023, and Google already claiming to have achieved quantum supremacy. Other major industry players such as Intel and Microsoft have also invested significant amounts of resources into quantum computing research.

Any viable computing system requires both hardware and …

Developing A Data Acquisition System For Use In Cold Neutral Atom Traps, Jonathan E. Fuzaro Alencar

Physics

The rising interest in quantum computing has led to new quantum systems being developed and researched. Among these are trapped neutral atoms which have several desirable features and may be configured and operated on using lasers in an optical lattice. This work describes the development of a new data acquisition system for use in tuning lasers near the precise hyperfine transition frequencies of Rb 87 atoms, a crucial step in the functionality of a neutral atom trap. This improves on previous implementations that were deprecated and limited in laser frequency sweep range. Integration into the experiment was accomplished using an …

Control And Calibration Strategies For Quantum Simulation, Paul M. Kairys

Doctoral Dissertations

The modeling and prediction of quantum mechanical phenomena is key to the continued development of chemical, material, and information sciences. However, classical computers are fundamentally limited in their ability to model most quantum effects. An alternative route is through quantum simulation, where a programmable quantum device is used to emulate the phenomena of an otherwise distinct physical system. Unfortunately, there are a number of challenges preventing the widespread application of quantum simulation arising from the imperfect construction and operation of quantum simulators. Mitigating or eliminating deleterious effects is critical for using quantum simulation for scientific discovery. This dissertation develops strategies …

Towards Highly Sensitive Capacitance Measurements Of A Quantum Anomalous Hall Phase In Van Der Waal Heterostructures, Kayla Cerminara

UNLV Theses, Dissertations, Professional Papers, and Capstones

One of the pioneering achievements in condensed matter physics of the 20th century is the observation of the quantum Hall e↵ect (QHE) in which the Hall resistance in a two-dimensional (2D) sample takes on quantized values in the presence of a strong perpendicular magnetic field. The precise quantization of the hall resistance to one part in a billion has provided a practical, worldwide resistance standard. A long-standing goal has been to realize a similar state of matter but without the need of a strong quantizing magnetic field. The quantum anomalous Hall e↵ect (QAHE) is such a state that is predicted …

Characterization Of High Mobility Channels For Use In Quantum Computing Devices, Payam Amin

Dissertations and Theses

Quantum computing promises computation that is fundamentally beyond the reach of classical computers. For the realization of a full-scale quantum computer, millions of quantum bits need to be fabricated on an integrated circuit and operated at cryogenic temperatures. Silicon and silicon-germanium based electron spin quantum bits have the advantage of leveraging decades of semiconductor industry knowledge for high volume manufacturability.

During the process development of any semiconductor device, material characterization is essential to understand and improve the process. Transmission electron microscopy is the only technique that could offer localized high spatial resolution characterization. In this work we have introduced two …

Determination Of Vortex Locations In A 2x2 Array Of Josephson Junctions For Topological Quantum Computation, Casey L. Kowalski

Theses and Dissertations

A large barrier to practical quantum computation exists in the form of qubit decoherence, which leads to high noise and error when implementing quantum algorithms. A potential solution to this problem is the use of topologically-protected Majorana-based qubits, as their nonlocal nature and unique non-abelian exchange statistics render them virtually immune to decoherence while still allowing the state to be easily manipulated. For such a qubit to be constructed, it is essential to know the locations of the Majorana-hosting vortices in the system. This work presents a solution for the formation locations of vortices in a 2x2 superconducting island array, …

Characterization And Benchmarking Of Quantum Computers, Megan L. Dahlhauser

Doctoral Dissertations

Quantum computers are a promising technology expected to provide substantial speedups to important computational problems, but modern quantum devices are imperfect and prone to noise. In order to program and debug quantum computers as well as monitor progress towards more advanced devices, we must characterize their dynamics and benchmark their performance. Characterization methods vary in measured quantities and computational requirements, and their accuracy in describing arbitrary quantum devices in an arbitrary context is not guaranteed. The leading techniques for characterization are based on fine-grain physical models that are typically accurate but computationally expensive. This raises the question of how to …

Error Detection In Quantum Algorithms, Simeon R. Hanks

Theses and Dissertations

Quantum computers need to be able to control highly entangled quantum states in the presence of environmental perturbations that lead to errors in calculations. Progress in superconducting qubits has enabled the development of computers capable of running small quantum circuits. The current era of Noise Intermediate Scale Quantum computing has a high error rate. To alleviate this error rate we apply an encoding scheme that allows us to remove results with known errors improving the quality of our results. The encoding uses multiple qubits as a single logical qubit and balances the natural tendency of state-of-the-art quantum computers to decohere …

Topological Realizations Of Entangling Quantum Gates, Adrian D. Scheppe

Theses and Dissertations

Topological systems are immune to decoherence and provide a hunting ground for qubits that are fault tolerant. The process of calculating linear operator representations of Majorana fermion exchanges or braids is well known and well documented; however, there is no documented intuition or algorithm which provides the opposite; braids from quantum gates. In this document, all possible linear representations of single, double, triple, and quadruple qubit gates are calculated to find several key patterns which provide crucial insight into the manifestation of qubit gates. A n x n gate will require n + 2 Majoranas with ½n + 1 trivial …

Tensor Network Approach For Simulation Of Quantum Many-Body Systems, Danylo Lykov

Graduate Research Theses & Dissertations

The simulation of quantum many-body systems and many-body statistical systems presents a challenge for classical computers. Quantum computation, which recently gained significant scientific interest, can provide a potential advantage over classical approaches in this area. While there are multiple methods for the simulation of the physics of many-body quantum systems, most of them scale exponentially with the number of elements. A Tensor Network approach allows to reduce this exponential scaling for some cases and reduces the pre-factor for others. This approach can be used for the simulation of classical statistical physics models, quantum many-body systems, and quantum computers in particular. …

Measurement, Dissipation, And Quantum Control With Superconducting Circuits, Patrick Harrington

Arts & Sciences Electronic Theses and Dissertations

The interaction between a superconducting circuit and its environment can cause decoherence. However, interactions with an environment are necessary for quantum state preparation and measurement. Through the dynamics of open quantum systems, the environment is a resource to control and readout superconducting circuit states. I present an experimental result demonstrating qubit state stabilization from engineered dissipation with a microwave photonic crystal. In addition, I discuss the statistical arrow of time in the dynamics of continuous quantum measurement. These results demonstrate an interplay between open quantum system dynamics and statistics, which highlights the role of both dissipation and measurement for quantum …

A Study Of Optical Nonlinearities At The Single-Photon Level For Quantum Logic, Balakrishnan Viswanathan

Graduate Theses and Dissertations

In this dissertation, we shall focus on theoretically studying quantum nonlinear optical schemes to construct a conditional phase gate at the single-photon level. With an aim to develop analytical models, we shall carry out a rigorous quantized multimode field analysis of some of these schemes involving only the interacting field operators. More specifically, we shall first study the three-wave mixing process involving two single-photons in a second-order nonlinear medium (x(2)) under two different cases viz. when the photons are traveling with equal velocities and when they are traveling with different velocities, and explore the possibility of using them for building …

Solving Combinatorial Optimization Problems Using The Quantum Approximation Optimization Algorithm, Nicholas J. Guerrero

Theses and Dissertations

The Quantum Approximation Optimization Algorithm (QAOA) is one of the most promising applications for noisy intermediate-scale quantum machines due to the low number of qubits required as well as the relatively low gate count. Much work has been done on QAOA regarding algorithm implementation and development; less has been done checking how these algorithms actually perform on a real quantum computer. Using the IBM Q Network, several instances of combinatorial optimization problems (the max cut problem and dominating set problem) were implemented into QAOA and analyzed. It was found that only the smallest toy max cut algorithms performed adequately: those …

Sparsity And Weak Supervision In Quantum Machine Learning, Seyran Saeedi

Theses and Dissertations

Quantum computing is an interdisciplinary field at the intersection of computer science, mathematics, and physics that studies information processing tasks on a quantum computer. A quantum computer is a device whose operations are governed by the laws of quantum mechanics. As building quantum computers is nearing the era of commercialization and quantum supremacy, it is essential to think of potential applications that we might benefit from. Among many applications of quantum computation, one of the emerging fields is quantum machine learning. We focus on predictive models for binary classification and variants of Support Vector Machines that we expect to be …

Improving The Readout Of Semiconducting Qubits, Matthew Jon Curry

Physics & Astronomy ETDs

Semiconducting qubits are a promising platform for quantum computers. In particular, silicon spin qubits have made a number of advancements recently including long coherence times, high-fidelity single-qubit gates, two-qubit gates, and high-fidelity readout. However, all operations likely require improvement in fidelity and speed, if possible, to realize a quantum computer.

Readout fidelity and speed, in general, are limited by circuit challenges centered on extracting low signal from a device in a dilution refrigerator connected to room temperature amplifiers by long coaxial cables with relatively high capacitance. Readout fidelity specifically is limited by the time it takes to reliably distinguish qubit …

Optimization Of An Injection Locked Laser System For Cold Neutral Atom Traps, Elliot M. Lehman

Physics

Many types of quantum systems are being explored for use in quantum computers. One type of quantum system that shows promise for quantum computing is trapped neutral atoms. They have long coherence times, since they have multiple stable ground states and have minimal coupling with other atoms and their environment, and they can be trapped in arrays, making them individu- ally addressable. Once trapped, they can be initialized and operated on using laser pulses. This experiment utilizes a pinhole diffraction pattern, which can trap atoms in both bright and dark areas. To maximize trap strength, an injection-locked laser amplification system …

Assembling And Characterizing The Efficiency Of An Injection Locked Laser System For Cold Neutral Atom Optical Traps, Alexandra Papa Crawford

Physics

Creating a quantum computer requires a system of particles that can be well-controlled to achieve quantum operations. We need a large array of these particles – called qubits – with long coherence times, which can be initialized, operated on by single and two qubit gates, and read out. For neutral atoms, the qubit states are stable ground states that interact minimally with the environment, leading to long coherence times. Experimentally, the qubits are manipulated using carefully timed laser beam pulses with controlled frequency and intensity, but the outstanding issue for optically trapping cold atoms is finding a light pattern that …

Efficient Quantum Approximation : Examining The Efficiency Of Select Universal Gate Sets In Approximating 1-Qubit Quantum Gates., Brent A. Mode

College of Arts & Sciences Senior Honors Theses

Quantum computation is of current ubiquitous interest in physics, computer science, and the public interest. In the not-so-distant future, quantum computers will be relatively common pieces of research equipment. Eventually, one can expect an actively quantum computer to be a common feature of life. In this work, I study the approximation efficiency of several common universal quantum gate sets at short sequence lengths using an implementation of the Solovay-Kitaev algorithm. I begin by developing from almost nothing the relevant formal mathematics to rigorously describe what one means by the terms universal gate set and covering efficiency. I then describe some …

Explorations Of Quantum Entanglement, John Stanton

Honor Scholar Theses

This thesis develops an undergraduate level understanding of quantum entanglement by expressing its properties in three unique mediums: mathematical formalism, application in technology and experiment. The mathematical formalism of entanglement is developed by working through theoretical experiments that utilize the entangled polarization states of photons. Notation used to describe entangled photon states is then used to illustrate how other types of entangled quantum states can be used in real technology, such as is the case with quantum computing. Finally, the theoretical predictions associated with entanglement are discussed in reference to two quantum optics experiments.

Developing An Imaging System To Monitor Atom Traps For Neutral Atom Quantum Computing, Jenna Valdez

Physics

Quantum computing exploits the laws of quantum mechanics to exponentially increase computing rate for certain processes. A realized quantum computer could break encryptions and simulate large quantum systems previously unbreakable and unattainable with classical computers. Neutral atom quantum computing is a viable candidate for building these devices that satisfies four of the five criteria for a successful quantum computer. We are exploring a novel method in creating neutral atom qubits that involves a magneto-optical trap and a dipole trap created in the diffraction pattern behind an array of pinholes. The magneto-optical trap works to cool the atoms and centralize them …

Quantum Information In Rydberg-Dressed Atoms, Tyler Emerson Keating

Physics & Astronomy ETDs

In any physical platform, two ingredients are essential for quantum information processing: single-qubit control, and entangling interactions between qubits. Neutral atoms can be individually controlled with high fidelity and are resilient to environmental noise, making them attractive candidates for implementing quantum information protocols. However, achieving strong interactions remains a major obstacle. One way to increase the interaction strength between neutral atoms is to excite them into high-lying Rydberg states, which exhibit large electric dipole moments (and by extension, strong electric dipole-dipole interactions). By slowly ramping up the Rydberg level coupling in a system, one can "dress'' the atomic ground states …

Monitoring Atom Traps For Neutral Atom Quantum Computing, Taylor Shannon

Physics

To increase computing power for numerous practical advantages, scientists are actively researching the field of quantum computing. Neutral atom quantum computing is a promising avenue towards building a quantum computer that satisfies four of the five DiVincenzo criteria. This involves a magneto-optical trap to cool the atoms and move them to a cloud in the center of a vacuum chamber. Then laser light will be shone through an array of pinholes to trap the atoms in an array of dipole traps. In order to ensure the atoms are trapped, I have set up an imaging system that consists of a …