Theses and Dissertations from UMD
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Item QUANTUM APPLICATIONS, PARALLEL OPERATIONS, AND NOISE CHARACTERIZATION ON A TRAPPED ION QUANTUM COMPUTER(2024) Zhu, Yingyue; Linke, Norbert M.; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum computing holds vast potential for solving classically hard problems ranging from optimization to simulations critical in material science research and drug discovery. While large-scale fault-tolerant quantum computers capable of these tasks are yet to come, small and noisy prototypes have been demonstrated on several candidate platforms. Among these, trapped-ion qubits have been at the forefront of quantum computing hardware because of their long coherence times, high-fidelity quantum gates, and all-to-all connectivity. This dissertation investigates new methods for efficient quantum computing at the interface of quantum information theory and trapped-ion experiments, and advances both the control of physical trapped-ion hardware and the characterization of their decoherence processes. We present a number of proof-of-principle experiments for early quantum applications on a trapped-ion quantum computer (TIQC). First, we experimentally show that the results of the Quantum Approximate Optimization Algorithm (QAOA)---a method to solve graph combinatorial optimization problems by applying multiple rounds of variational circuits---improve with deeper circuits for multiple graph-theoretic problems on several arbitrary graphs. We also demonstrate a modified version of QAOA that allows sampling of all optimal solutions with predetermined weights. Additionally, we implement the real-time evolution of a one-dimensional scattering process and demonstrate a more efficient and accurate method to extract the phase shift, forming a tentative first step toward the goal of lattice quantum chromodynamics (QCD) simulation. Furthermore, we demonstrate two Bell-type nonlocal games that can be used to prove quantum computational advantage as well as offer a set of practical and scalable benchmarks for quantum computers in the pre-fault-tolerant regime. Our experimental results indicate that the performance of quantum strategies for the non-local games exceeds basic classical bounds, and is on the cusp of demonstrating quantum advantage against more complicated classical strategies. We propose and demonstrate a high-fidelity and resource-efficient scheme for driving simultaneous entangling gates on different sets of orthogonal motional modes of a trapped-ion chain. We show the advantage of parallel operation with a simple digital quantum simulation where parallel implementation improves the overall fidelity significantly. We test and improve the performance of an ancilla-assisted protocol for learning Pauli noise in Clifford gates on a TIQC. With N ancilla, Pauli noise in an N-qubit Clifford gate can be learned with a sample size linear to N. We also design and demonstrate a way to improve the protocol's performance by reducing ancilla noise in post-processing.Item EXPLORING QUANTUM MANY-BODY SYSTEMS IN PROGRAMMABLE TRAPPED ION QUANTUM SIMULATORS(2024) De, Arinjoy; Monroe, Christopher R; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum simulation is perhaps the most natural application of a quantum computer, where a precisely controllable quantum system is designed to emulate a more complex or less accessible quantum system. Significant research efforts over the last decade have advanced quantum technology to the point where it is foreseeable to achieve `quantum advantage' over classical computers, to enable the exploration of complex phenomena in condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. While the realization of a universal fault-tolerant quantum computer remains a future goal, analog quantum simulators -- featuring continuous unitary evolution of many-body Hamiltonians -- have been developed across several experimental platforms. A key challenge in this field is balancing the control of these systems with the need to scale them up to address more complex problems. Trapped-ion platforms, with exceptionally high levels of control enabled by laser-cooled and electromagnetically confined ions, and all-to-all entangling capabilities through precise control over their collective motional modes, have emerged as a strong candidate for quantum simulation and provide a promising avenue for scaling up the systems. In this dissertation, I present my research work, emphasizing both the scalability and controllability aspects of \ion based trapped-ion platforms, with an underlying theme of analog quantum simulation. The initial part of my research involves utilizing a trapped ion apparatus operating within a cryogenic vacuum environment, suitable for scaling up to hundreds of ions. We address various challenges associated with this approach, particularly the impact of mechanical vibrations originating from the cryostat, which can induce phase errors during coherent operations. Subsequently, we detail the implementation of a scheme to generate phase-stable spin-spin interactions that are robust to vibration noise. In the second part, we use a trapped-ion quantum simulator operating at room temperature, to investigate the non-equilibrium dynamics of critical fluctuations following a quantum quench to the critical point. Employing systems with up to 50 spins, we show that the amplitude and timescale of post-quench fluctuations scale with system size, exhibiting distinct universal critical exponents. While a generic quench can lead to thermal critical behavior, a second quench from one critical state to another (i.e., double quench) results in unique critical behavior not seen in equilibrium. Our results highlight the potential of quantum simulators to explore universal scaling beyond the equilibrium paradigm. In the final part of the thesis, we investigate an analog of the paradigmatic string-breaking phenomena using a quantum spin simulator. We employ an integrated trapped-ion apparatus with $13$ spins that utilizes the individual controllability of laser beams to program a uniform spin-spin interaction profile across the chain, alongside 3-dimensional control of the local magnetic fields. We introduce two static probe charges, realized through local longitudinal magnetic fields, that create string tension. By implementing quantum quenches across the string-breaking point, we monitor non-equilibrium charge evolution with spatio-temporal resolution that elucidates the dynamical string breaking. Furthermore, by initializing the charges away from the string boundary, we generate isolated charges and observe localization effects that arise from the interplay between confinement and lattice effects.Item SYMMETRIC-KEY CRYPTOGRAPHY AND QUERY COMPLEXITY IN THE QUANTUM WORLD(2024) Bai, Chen; Katz, Jonathan; Alagic, Gorjan; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum computers are likely to have a significant impact on cryptography. Many commonly used cryptosystems will be completely broken once large quantum computers are available. Since quantum computers can solve the factoring problem in polynomial time, the security of RSA would not hold against quantum computers. For symmetric-key cryptosystems, the primary quantum attack is key recovery via Grover search, which provides a quadratic speedup. One way to address this is to double the key length. However, recent results have shown that doubling the key length may not be sufficient in all cases. Therefore, it is crucial to understand the security of various symmetric-key constructions against quantum attackers. In this thesis, we give the first proof of post-quantum security for certain symmetric primitives. We begin with a fundamental block cipher, the Even-Mansour cipher, and the tweakable Even-Mansour construction. Our research shows that both are secure in a realistic quantum attack model. For example, we prove that 2^{n/3} quantum queries are necessary to break the Even-Mansour cipher. We also consider the practical applications that our work implies. Using our framework, we derive post-quantum security proofs for three concrete symmetric-key schemes: Elephant (an Authenticated Encryption (AE) finalist of NIST’s lightweight cryptography standardization effort), Chaskey (an ISO-standardized Message Authentication Code), and Minalpher (an AE second-round candidate of the CAESAR competition). In addition, we consider the two-sided permutation inversion problem in the quantum query model. In this problem, given an image y and quantum oracle access to a permutation P (and its inverse oracle), the goal is to find its pre-image x such that P(x)=y. We prove an optimal lower bound \Omega(\sqrt{2^n}) for this problem against an adaptive quantum adversary. Moreover, we apply our lower bound above to show that a natural encryption scheme constructed from random permutations is secure against quantum attacks.Item QUANTUM COMBINATORIAL OPTIMIZATION ALGORITHMS FOR PACKING PROBLEMS IN CLASSICAL COMPUTING AND NETWORKING(2023) Unsal, Cem Mehmet; Oruc, Yavuz A; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In Computer Engineering, packing problems play a central role in many aspects of hardware control. The field aims to maximize computer processing speed, network throughput, and dependability in industry applications. Many of these constrained maximization problems can be expressed as packing problems in integer programming when working with restrictions such as latency, memory size, race conditions, power, and component availability. Some of the most crucial of these integer programming problems are NP-hard for the global optimum. Therefore, real-world applications heavily rely on heuristics and meta-heuristics to find good solutions. With recent developments in quantum meta-heuristic methods and promising results in experimental quantum computing systems, quantum computing is rapidly becoming more and more relevant for complex real-world combinatorial optimization tasks. This thesis is about applications of quantum combinatorial optimization algorithms in classical computer engineering problems. These include novel quantum computing techniques that respect the constraints of state-of-the-art experimental quantum systems. This thesis includes five projects. FASTER QUANTUM CONCENTRATION VIA GROVER'S SEARCH:One of the most important challenges in information networks is to gather data from a larger set of nodes to a smaller set of nodes. This can be done via the use of a concentrator architecture in the connection topology. This chapter is a proof-of-concept that demonstrates a quantum-based controller in large interconnection networks can asymptotically perform this task faster. We specifically present quantum algorithms for routing concentration assignments on full-capacity fat-and-slim concentrators, bounded fat-and-slim concentrators, and regular fat-and-slim concentrators. Classically, the concentration assignment takes O(n) time on all these concentrators, where n is the number of inputs. Powered by Grover's quantum search algorithm, our algorithms take O(√(nc) ln(c)) time, where c is the capacity of the concentrator. Thus, our quantum algorithms are asymptotically faster than their classical counterparts when (c ln^2(c))=o(n). In general, c = n^μ satisfies (c ln^2(c))=o(n), implying a time complexity of O(n^(0.5(1+ μ )) ln (n)), for any μ, 0 < μ < 1. QUANTUM ADVERSARIAL LEARNING IN EMULATION OF MONTE-CARLO METHODS FOR MAX-CUT APPROXIMATION: QAOA IS NOT OPTIMAL:One of the leading candidates for near-term quantum advantage is the class of Variational Quantum Algorithms. However, these algorithms suffer from classical difficulty in optimizing the variational parameters as the number of parameters increases. Therefore, it is important to understand the expressibility and power of various ansätze to produce target states and distributions. To this end, we apply notions of emulation to Variational Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA) to show that variational annealing schedules with equivalent numbers of parameters outperform QAOA. Our Variational Quantum Annealing schedule is based on a novel polynomial parameterization that can be optimized in a similar gradient-free way as QAOA, using the same physical ingredients. In order to compare the performance of ansätze types, we have developed statistical notions of Monte-Carlo methods. Monte-Carlo methods are computer programs that generate random variables that approximate a target number that is computationally hard to calculate exactly. While the most well-known Monte-Carlo method is Monte-Carlo integration (e.g., Diffusion Monte-Carlo or path-integral quantum Monte-Carlo), QAOA is itself a Monte-Carlo method that finds good solutions to NP-complete problems such as Max-cut. We apply these statistical Monte-Carlo notions to further elucidate the theoretical framework around these quantum algorithms. SCHEDULING JOBS IN A SHARED HIGH-PERFORMANCE COMPUTER WITH A NISQ COMPUTER:Several quantum approximation algorithms for NP-hard optimization problems have been described in the literature. The properties of quantum approximation algorithms have been well-explored for optimization problems of Ising type with 2-local Hamiltonians. A wide range of optimization problems can be mapped to Ising problems. However, the mapping overhead of many problem instances puts them out of the reach of Noisy Intermediate-scale Quantum (NISQ) devices. In this chapter, we develop a way of mapping constrained optimization problems to higher-order spin interactions to put a larger set of problem instances within reach of spin interaction devices with potential NISQ applications. We demonstrate the growth in the practicable set of problem instances by comparing the resource requirements as a function of coupling. As an example, we have demonstrated our techniques on the problem of scheduling jobs in a high-performance computer queue with limited memory and CPUs. PROTEIN STRUCTURES WITH OSCILLATING QPACKER:A significant challenge in designing proteins for therapeutic purposes is determining the structure of a protein to find the sidechain identities given a protein backbone. This problem can be easily and efficiently encoded as a quadratic binary optimization problem. There has been a significant effort to find ways to solve these problems in the field of quantum information, both exactly and approximately. An important initiative has applied experimental quantum annealing platforms to solve this problem and got promising results. This project is about optimizing the annealing schedule for the sidechain identity problem, inspired by cutting-edge developments in the algorithmic theory of quantum annealing. ON THE COMPLEXITY OF GENERALIZED DISCRETE LOGARITHM PROBLEM:The Generalized Discrete Logarithm Problem (GDLP) is an extension of the Discrete Logarithm Problem where the goal is to find x∈ℤ_s such that g^x mod s=y for a given g,y∈ℤ_s. The generalized discrete logarithm is similar, but instead of a single base element, it uses a number of base elements that do not necessarily commute. In this chapter, we prove that GDLP is NP-hard for symmetric groups. The lower-bound complexity of GDLP has been an open question since GDLP was defined in 2008 until our proof. Furthermore, we prove that GDLP remains NP-hard even when the base elements are permutations of at most three elements. Lastly, we discuss the implications and possible implications of our proofs in classical and quantum complexity theory.Item Optimization Problems in Quantum Machine Learning(2023) You, Xuchen; Wu, Xiaodi; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The variational algorithm is a paradigm for designing quantum procedures implementable on noisy intermediate-scale quantum (NISQ) machines. It is viewed as a promising candidate for demonstrating practical quantum advantage. In this dissertation, we look into the optimization aspect of the variational quantum algorithms as an attempt to answer when and why a variational quantum algorithm works. We mainly focus on two instantiations of the family of variational algorithms, the Variational Quantum Eigensolvers (VQEs) and the Quantum Neural Networks (QNNs). We first established that, for almost all QNN architecture designs, there exist hard problem instances leading to an optimization landscape swarmed by spurious local minima provided that the QNN is under-parameterized. This observation rules out the possibility of a universal good QNN design achieving exponential advantage against the classical neural networks on any dataset and calls for instance-dependent designs for variational circuits. We then show that VQE training converges linearly when the number of parameters exceeds an over-parameterization threshold. By tying the threshold to instance-dependent quantities, we developed variants of VQE algorithms that allow the training and testing of shallower variational circuits, as depths are usually the implementation bottlenecks on NISQ machines. For QNNs, by looking into its convergence, we show that the dynamics of QNN training are different from the dynamics of any kernel regression, therefore ruling out the popular conjecture that over-parameterized QNNs are equivalent to certain versions of neural tangent kernels like their classical counterparts. As a practical implication, our analysis showcases the measurement design as a way to accelerate the convergence of QNNs. At the end of this dissertation, we consider the classical problem of optimization with partial information, the Multi-arm Bandits (MABs). We show that, when enhanced with quantum access to the arms, there is a quadratic speed-up against the classical algorithms, which can serve as the building block for quantum reinforcement learning algorithms.Item A Verified Software Toolchain for Quantum Programming(2022) Hietala, Kesha; Hicks, Michael; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum computing is steadily moving from theory into practice, with small-scale quantum computers available for public use. Now quantum programmers are faced with a classical problem: How can they be sure that their code does what they intend it to do? I aim to show that techniques for classical program verification can be adapted to the quantum setting, allowing for the development of high-assurance quantum software, without sacrificing performance or programmability. In support of this thesis, I present several results in the application of formal methods to the domain of quantum programming, aiming to provide a high-assurance software toolchain for quantum programming. I begin by presenting SQIR, a small quantum intermediate representation deeply embedded in the Coq proof assistant, which has been used to implement and prove correct quantum algorithms such as Grover’s search and Shor’s factorization algorithm. Next, I present VOQC, a verified optimizer for quantum circuits that contains state-of-the-art SQIR program optimizations with performance on par with unverified tools. I additionally discuss VQO, a framework for specifying and verifying oracle programs, which can then be optimized with VOQC. Finally, I present exploratory work on providing high assurance for a high-level industry quantum programming language, Q#, in the F* proof assistant.Item Quantum Computing with Fluxonium: Digital and Analog Directions(2022) Somoroff, Aaron; Manucharyan, Vladimir E; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation explores quantum computing applications of fluxonium superconductingcircuits. Fluxonium’s high coherence time T2 and anharmonicity make it an excellent platform for both digital quantum processors and analog quantum simulators. Focusing on the digital quantum computing applications, we report recent work on improving the T2 and gate error rates of fluxonium qubits. Through enhancements in fabrication methods and engineering of fluxonium’s spectrum, a coherence time in excess of 1 millisecond is achieved, setting a new standard for the most coherent superconducting qubit. This highly coherent device is used to demonstrate a single-qubit gate fidelity greater than 99.99%, a level of control that had not been observed until now in a solid state quantum system. Utilizing the high energy relaxation time T1 of the qubit transition, a novel measurement of the circuit’s parity-protected 0-2 transition relaxation time is performed to extract additional sources of energy loss. To demonstrate fluxonium’s utility as a building block for analog quantum simulators,we investigate how to simulate quantum dynamics in the Transverse-Field Ising Model (TFIM) by inductively coupling 10 fluxonium circuits together. When the fluxonium loops are biased at half integer values of the magnetic flux quantum, the spectrum is highly anharmonic, and the qubit transition is well-approximated by a spin-1/2. This results in an effective Hamiltonian that is equivalent to the TFIM. By tuning the inter-qubit coupling across multiple devices, we can explore different regimes of the TFIM, establishing fluxonium as a prominent candidate for use in near-term quantum many-body simulations.Item Quantum Computing for Optimization and Machine Learning(2022) Chakrabarti, Shouvanik; Wu, Xiaodi; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Quantum Computing leverages the quantum properties of subatomic matter to enable computations faster than those possible on a regular computer. Quantum Computers have become increasingly practical in recent years, with some small-scale machines becoming available for public use. The rising importance of machine learning has highlighted a large class of computing and optimization problems that process massive amounts of data and incur correspondingly large computational costs. This raises the natural question of how quantum computers may be leveraged to solve these problems more efficiently. This dissertation presents some encouraging results on the design of quantum algorithms for machine learning and optimization. We first focus on tasks with provably more efficient quantum algorithms. We show a quantum speedup for convex optimization by extending quantum gradient estimation algorithms to efficiently compute subgradients of non-differentiable functions. We also develop a quantum framework for simulated annealing algorithms which is used to show a quantum speedup in estimating the volumes of convex bodies. Finally, we demonstrate a quantum algorithm for solving matrix games, which can be applied to a variety of learning problems such as linear classification, minimum enclosing ball, and $\ell-2$ margin SVMs. We then shift our focus to variational quantum algorithms, which describe a family of heuristic algorithms that use parameterized quantum circuits as function models that can be fit for various learning and optimization tasks. We seek to analyze the properties of these algorithms including their efficient formulation and training, expressivity, and the convergence of the associated optimization problems. We formulate a model of quantum Wasserstein GANs in order to facilitate the robust and scalable generative learning of quantum states. We also investigate the expressivity of so called \emph{Quantum Neural Networks} compared to classical ReLU networks and investigate both theoretical and empirical separations. Finally, we leverage the theory of overparameterization in variational systems to give sufficient conditions on the convergence of \emph{Variational Quantum Eigensolvers}. We use these conditions to design principles to study and evaluate the design of these systems.Item Algorithms for quantum simulation: design, analysis, implementation, and application(2020) Su, Yuan; Childs, Andrew M; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Simulating the Hamiltonian dynamics of quantum systems is one of the most promising applications of digital quantum computers. In this dissertation, we develop an understanding of quantum simulation algorithms concerning their design, analysis, implementation, and application. We implement three leading simulation algorithms, employing diverse techniques to tighten their error analyses and optimize circuit implementations. We produce concrete resource estimates for simulating a Heisenberg spin system, a problem arising in condensed matter physics that is otherwise difficult to solve on a classical computer. The resulting circuits are orders of magnitude smaller than those for the simplest classically-infeasible instances of factoring and quantum chemistry, suggesting the simulation of spin systems as a promising candidate for an early demonstration of practical quantum computation. We design new simulation algorithms by using classical randomness. We show that by simply randomizing how the terms in the Hamiltonian are ordered, one can prove stronger bounds for product formulas and thereby give more efficient quantum simulations. We also develop a classical sampler for time-dependent Hamiltonians, using which we give a simulation algorithm that substantially improves over previous approaches when the Hamiltonian varies significantly with time. We propose a general theory to analyzing product formulas, an approach to quantum simulation widely used in experimental demonstrations but whose error scaling was poorly understood. Our approach directly exploits the commutativity of Hamiltonian, overcoming the limitations of prior error analyses. We prove new speedups of product formulas for simulating many quantum systems, including simulations of nearest-neighbor lattice systems, second-quantized plane-wave electronic structure, $k$-local Hamiltonians, rapidly decaying power-law interactions, and clustered Hamiltonians, nearly matching or even outperforming the best previous results in quantum simulation. We accompany our analysis with numerical calculation, which suggests that the bounds also have nearly tight constant prefactors. We identify applications of quantum simulation to designing other quantum algorithms and improving quantum Monte Carlo methods. We develop an algorithmic framework ``quantum singular value transformation'' using techniques from quantum simulation and apply it to implement principal component regression. We also apply our new analysis of product formulas and obtain improved quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets.Item Coherent Control of Low Anharmonicity Systems for Superconducting Quantum Computing(2018) Premaratne, Shavindra Priyanath; Wellstood, Frederick C; Palmer, Benjamin S; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation describes research to coherently control quantum states of superconducting devices. In the first project, the state of an 8 GHz 3D superconducting Al cavity at 20mK was manipulated to add a quantum of excitation. Preparing a harmonic resonator in a state with a well-defined number of excitations (Fock states) is not possible using one external classical drive. I generated Fock states by transferring a single excitation from a 5.5 GHz transmon qubit to a cavity using Stimulated Raman Adiabatic Passage (STIRAP). I also extended the STIRAP technique to put the cavity in higher Fock states, superpositions of Fock states, and Bell states between the qubit and the cavity. Master-equation simulations of the system’s density matrix were in good agreement with the data, and I obtained estimated fidelities of 89%, 68% and 43% for the first three Fock states, respectively. The second project involved implementing an entangling gate between two Al/AlOx/Al transmon qubits that were mounted in an Al cavity and cooled to 20mK. Pertinent system frequencies were as follows: one qubit was at 6.0 GHz, the other qubit at 6.8 GHz, the cavity at 7.7 GHz, and the qubit-qubit dispersive shift was -1MHz. By applying a specially-shaped pulse of duration tg = 907ns, I implemented a generalized CNOT gate using an all-microwave technique known as Speeding up Waveforms by Inducing Phases to Harmful Transitions (SWIPHT). Using quantum process tomography, I found that the gate fidelity was 80%–82%, close to the 87% fidelity expected from decoherence in the transmons during the gate time. Details of the device fabrication, device characterization, measurement techniques, and extensive modeling of device behavior are presented, along with chi-matrix characterization of single-qubit gates and SWIPHT gates.