Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-10-01T16:46:31Z No. of bitstreams: 1 ELLOÁ BARRETO GUEDES DA COSTA - DISSERTAÇÃO PPGCC 2011..pdf: 1433883 bytes, checksum: fb9fa0561b94ab2b495915f5f377c364 (MD5) / Made available in DSpace on 2018-10-01T16:46:31Z (GMT). No. of bitstreams: 1 ELLOÁ BARRETO GUEDES DA COSTA - DISSERTAÇÃO PPGCC 2011..pdf: 1433883 bytes, checksum: fb9fa0561b94ab2b495915f5f377c364 (MD5) Previous issue date: 2011-03-25 / Este trabalho apresenta um ataque quântico de comprometimento permanente ao gerador pseudo-aleatório de Blum-Micali. A segurança deste gerador, classificado como criptograficamente seguro, baseia-se na hipótese de intratabilidade do problema do logaritmo discreto perante a Computação Clássica. O ataque proposto faz uso do algoritmo quântico de busca em conjunto com o algoritmo quântico para o logaritmo discreto para comprometer a imprevisibilidade do gerador, recuperando todas as saídas passadas e futuras do mesmo. O presente trabalho também descreve generalizações deste ataque que o adequam a uma gama mais vasta de geradores, incluindo geradores da Construção de Blum-Micali e geradores com múltiplos predicados difíceis. Tais generalizações também abrangem a realização de ataques em situações adversas, por exemplo, quando o adversário captura bits não consecutivos ou quando há menos bits que o requerido. Comparado à sua contrapartida clássica, o algoritmo quântico proposto nesse trabalho possui um ganho quadrático em relação à recuperação do representante do estado interno do gerador, seguido de um ganho superpolinomial na obtenção dos demais elementos do estado interno. Estes resultados caracterizam ameaças,elaboradas com Computação Quântica, contra a segurança de geradores utilizados em diversas aplicações criptográficas. / This dissertation presents a quantum permanent compromise attack to the Blum-Micali pseudorandom generator. The security of this generator, classified as cryptographically secure, is based on the hypothesis of intractability of the discrete logarithm problem in Classical Computing. The proposed attack is based on the quantum search algorithm jointly with the quantum discrete logarithm procedure and aims to compromise the unpredictability of the referred generator, recovering all of its past and future outputs. This work also describes generalizations that enables attacks to generators from the Blum-Micali construction and also to generators with multiple hard-core predicates. Such generalizations also allow attacks when the adversary intercepts non-consecutive bits or when there are less bits than required. Compared to its classical counterpart, the proposed algorithm has a quadractic speedup regarding the retrieval of the representant of the generator’s internal state followed by a super polynomial speedup regarding the obtention of the entire generator’sinternalstate. These results represent menaces of the Quantum Computing paradigm against the security of pseudorandom generators adopted in many real-world cryptosystems.

Utvecklandet av kvantdatorn är ett ytterst lovande projekt som kombinerar teoretisk och experimental kvantfysik, matematik, teori om kvantinformation och datalogi. Under första steget i utvecklandet av kvantdatorn låg huvudintresset på att skapa några algoritmer med framtida tillämpningar, klargöra grundläggande frågor och utveckla en experimentell teknologi för en leksakskvantdator som verkar på några kvantbitar. Då dominerade förväntningarna om snabba framsteg bland kvantforskare. Men det verkar som om dessa stora förväntningar inte har besannats helt. Många grundläggande och tekniska problem som dekoherens hos kvantbitarna och instabilitet i kvantstrukturen skapar redan vid ett litet antal register tvivel om en snabb utveckling av kvantdatorer som verkligen fungerar. Trots detta kan man inte förneka att stora framsteg gjorts inom kvantteknologin. Det råder givetvis ett stort gap mellan skapandet av en leksakskvantdator med 10-15 kvantregister och att t.ex. tillgodose de tekniska förutsättningarna för det projekt på 100 kvantregister som aviserades för några år sen i USA. Det är också uppenbart att svårigheterna ökar ickelinjärt med ökningen av antalet register. Därför är simulering av kvantdatorer i klassiska datorer en viktig del av kvantdatorprojektet. Självklart kan man inte förvänta sig att en kvantalgoritm skall lösa ett NP-problem i polynomisk tid i en klassisk dator. Detta är heller inte syftet med klassisk simulering. Den klassiska simuleringen av kvantdatorer kommer att täcka en del av gapet mellan den teoretiskt matematiska formuleringen av kvantmekaniken och ett förverkligande av en kvantdator. Ett av de viktigaste problemen i vetenskapen om kvantdatorn är att utveckla ett nytt symboliskt språk för kvantdatorerna och att anpassa redan existerande symboliska språk för klassiska datorer till kvantalgoritmer. Denna avhandling ägnas åt en anpassning av det symboliska språket Mathematica till kända kvantalgoritmer och motsvarande simulering i klassiska datorer. Konkret kommer vi att representera Simons algoritm, Deutsch-Joszas algoritm, Grovers algoritm, Shors algoritm och kvantfelrättande koder i det symboliska språket Mathematica. Vi använder samma stomme i alla dessa algoritmer. Denna stomme representerar de karaktäristiska egenskaperna i det symboliska språkets framställning av kvantdatorn och det är enkelt att inkludera denna stomme i framtida algoritmer. / Quantum computing is an extremely promising project combining theoretical and experimental quantum physics, mathematics, quantum information theory and computer science. At the first stage of development of quantum computing the main attention was paid to creating a few algorithms which might have applications in the future, clarifying fundamental questions and developing experimental technologies for toy quantum computers operating with a few quantum bits. At that time expectations of quick progress in the quantum computing project dominated in the quantum community. However, it seems that such high expectations were not totally justified. Numerous fundamental and technological problems such as the decoherence of quantum bits and the instability of quantum structures even with a small number of registers led to doubts about a quick development of really working quantum computers. Although it can not be denied that great progress had been made in quantum technologies, it is clear that there is still a huge gap between the creation of toy quantum computers with 10-15 quantum registers and, e.g., satisfying the technical conditions of the project of 100 quantum registers announced a few years ago in the USA. It is also evident that difficulties increase nonlinearly with an increasing number of registers. Therefore the simulation of quantum computations on classical computers became an important part of the quantum computing project. Of course, it can not be expected that quantum algorithms would help to solve NP problems for polynomial time on classical computers. However, this is not at all the aim of classical simulation. Classical simulation of quantum computations will cover part of the gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. One of the most important problems in "quantum computer science" is the development of new symbolic languages for quantum computing and the adaptation of existing symbolic languages for classical computing to quantum algorithms. The present thesis is devoted to the adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulation on the classical computer. Concretely we shall represent in the Mathematica symbolic language Simon's algorithm, the Deutsch-Josza algorithm, Grover's algorithm, Shor's algorithm and quantum error-correcting codes. We shall see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include this framework in future algorithms.

Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital quantum simulation of the mirror inversion propagator corresponding to the time evolution of an XY spin chain. This simulation has been used to experimentally demonstrate the mirror inversion of quantum states, proposed by Albanese et al.[Phys.Rev.Lett.93,230502(2004)], by which entangled states can be transferred from one end of the chain to the other end. The experiments have been performed in a 5-qubit dipolar coupled nuclear spin system. For simulation, we make use of the recently proposed unitary operator decomposition algorithm along with the numerical pulse optimization techniques, which assisted in achieving high experimental fidelities. Chapter 5 contains a digital quantum simulation of the unitary propagator of a transverse Ising spin chain, which has been used to experimentally demonstrate the perfect state transfer protocol of Di Franco et al. [Phys.Rev.Lett.101,230502(2008)]. The importance of this protocol arises due to the fact that it achieves perfect state transfer from one end of the chain to the other end without the necessity of initializing the intermediate spins of the chain, whereas most of the previously proposed protocols require initialization. The experiments have been performed in a 3-spin nuclear spin system. The simulation has also been used to demonstrate the generation of a GHZ state.

Title: Quantum computing algorithms for quantum chemistry Author: Jakub Višňák Abstract: The topic of this study is the simulation of the quantum algorithm for the diagonalization of the matrix representation of the all-electron Dirac-Coulomb hamiltonian of the SbH molecule. Two different limited CI expansions were used to describe both the ground state (X 0+ ) and the first excited doublet (A 1) by simulating the Iterative Phase Estinamtion Algorith (IPEA). In the simulations numerically performed in this work, the "compact mapping" has been employed for the representation of the evolution operator exp(i Hˆ t); in the theoretical part of the work, the "direct mapping" is described as well. The influence of the metodics for choosing the initial eigenvector estimate is studied in both IPEA A and IPEA B variants. For those variants, the success probabilities pm are computed for different single-points on the SbH dissociation curves. The initial eigenvector estimates based on the "CISD(2)" method are found to be sufficient for both studied LCI-expansions up to internuclear distance R  6 a0. The pm dependence on the overlap between the eigenvector in question and its inital estimate - 2 0  is studied the for IPEA B method. The usability of the both variants of the IPEA in possible later calculations is...

This Thesis focuses on different aspects of quantum computation theory: adiabatic quantum algorithms, decoherence during the adiabatic evolution and quantum simulators. After an overview on the area of quantum computation and setting up the formal ground for the rest of the Thesis we derive a general error estimate for adiabatic quantum computing. We demonstrate that the first-order correction, which has frequently been used as a condition for adiabatic quantum computation, does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections and shows that the computational error can be made exponentially small – which facilitates significantly shorter evolution times than the first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time of order of the inverse minimum energy gap is sufficient and necessary. Furthermore, exploiting the similarity between adiabatic quantum algorithms and quantum phase transitions, we study the impact of decoherence on the sweep through a second-order quantum phase transition for the prototypical example of the Ising chain in a transverse field and compare it to the adiabatic version of Grover’s search algorithm. It turns out that (in contrast to first-order transitions) the impact of decoherence caused by a weak coupling to a rather general environment increases with system size (i.e., number of spins/qubits), which might limit the scalability of the system. Finally, we propose the use of electron systems to construct laboratory systems based on present-day technology which reproduce and thereby simulate the quantum dynamics of the Ising model and the O(3) nonlinear sigma model.

Tesis por compendio / [ES] En esta tesis doctoral se propone y evalúa un sistema para detectar señales débiles (weak signals) relacionadas con cambios futuros trascendentales. Si bien la mayoría de las soluciones conocidas se basan en el uso de datos estructurados, el sistema propuesto detecta cuantitativamente estas señales utilizando información heterogénea y no estructurada de fuentes científicas, periodísticas y de redes sociales. La predicción de nuevas tendencias en un medio tiene muchas aplicaciones. Por ejemplo, empresas y startups se enfrentan a cambios constantes en sus mercados que son muy difíciles de predecir. Por esta razón, el desarrollo de sistemas para detectar automáticamente cambios futuros significativos en una etapa temprana es relevante para que cualquier organización tome decisiones acertadas a tiempo. Este trabajo ha sido diseñado para obtener señales débiles del futuro en cualquier campo dependiendo únicamente del conjunto de datos de entrada de documentos. Se aplican técnicas de minería de textos y procesamiento del lenguaje natural para procesar todos estos documentos. Como resultado, se obtiene un mapa con un ranking de términos, una lista de palabras clave clasificadas automáticamente y una lista de expresiones formadas por múltiples palabras. El sistema completo se ha probado en cuatro sectores diferentes: paneles solares, inteligencia artificial, sensores remotos e imágenes médicas. Este trabajo ha obtenido resultados prometedores, evaluados con dos metodologías diferentes. Como resultado, el sistema ha sido capaz de detectar de forma satisfactoria nuevas tendencias en etapas muy tempranas que se han vuelto cada vez más importantes en la actualidad. La computación cuántica es un nuevo paradigma para una multitud de aplicaciones informáticas. En esta tesis doctoral también se presenta un estudio de las tecnologías disponibles en la actualidad para la implementación física de qubits y puertas cuánticas, estableciendo sus principales ventajas y desventajas, y los marcos disponibles para la programación e implementación de circuitos cuánticos. Con el fin de mejorar la efectividad del sistema, se describe un diseño de un circuito cuántico basado en máquinas de vectores de soporte (SVM) para la resolución de problemas de clasificación. Este circuito está especialmente diseñado para los ruidosos procesadores cuánticos de escala intermedia (NISQ) que están disponibles actualmente. Como experimento, el circuito ha sido probado en un computador cuántico real basado en qubits superconductores por IBM como una mejora para el subsistema de minería de texto en la detección de señales débiles. Los resultados obtenidos con el experimento cuántico muestran también conclusiones interesantes y una mejora en el rendimiento de cerca del 20% sobre los sistemas convencionales, pero a su vez confirman que aún se requiere un desarrollo tecnológico continuo para aprovechar al máximo la computación cuántica. / [CA] En aquesta tesi doctoral es proposa i avalua un sistema per detectar senyals febles (weak signals) relacionats amb canvis futurs transcendentals. Si bé la majoria de solucions conegudes es basen en l'ús de dades estructurades, el sistema proposat detecta quantitativament aquests senyals utilitzant informació heterogènia i no estructurada de fonts científiques, periodístiques i de xarxes socials. La predicció de noves tendències en un medi té moltes aplicacions. Per exemple, empreses i startups s'enfronten a canvis constants als seus mercats que són molt difícils de predir. Per això, el desenvolupament de sistemes per detectar automàticament canvis futurs significatius en una etapa primerenca és rellevant perquè les organitzacions prenguen decisions encertades a temps. Aquest treball ha estat dissenyat per obtenir senyals febles del futur a qualsevol camp depenent únicament del conjunt de dades d'entrada de documents. S'hi apliquen tècniques de mineria de textos i processament del llenguatge natural per processar tots aquests documents. Com a resultat, s'obté un mapa amb un rànquing de termes, un llistat de paraules clau classificades automàticament i un llistat d'expressions formades per múltiples paraules. El sistema complet s'ha provat en quatre sectors diferents: panells solars, intel·ligència artificial, sensors remots i imatges mèdiques. Aquest treball ha obtingut resultats prometedors, avaluats amb dues metodologies diferents. Com a resultat, el sistema ha estat capaç de detectar de manera satisfactòria noves tendències en etapes molt primerenques que s'han tornat cada cop més importants actualment. La computació quàntica és un paradigma nou per a una multitud d'aplicacions informàtiques. En aquesta tesi doctoral també es presenta un estudi de les tecnologies disponibles actualment per a la implementació física de qubits i portes quàntiques, establint-ne els principals avantatges i desavantatges, i els marcs disponibles per a la programació i implementació de circuits quàntics. Per tal de millorar l'efectivitat del sistema, es descriu un disseny d'un circuit quàntic basat en màquines de vectors de suport (SVM) per resoldre problemes de classificació. Aquest circuit està dissenyat especialment per als sorollosos processadors quàntics d'escala intermèdia (NISQ) que estan disponibles actualment. Com a experiment, el circuit ha estat provat en un ordinador quàntic real basat en qubits superconductors per IBM com una millora per al subsistema de mineria de text. Els resultats obtinguts amb l'experiment quàntic també mostren conclusions interessants i una millora en el rendiment de prop del 20% sobre els sistemes convencionals, però a la vegada confirmen que encara es requereix un desenvolupament tecnològic continu per aprofitar al màxim la computació quàntica. / [EN] In this doctoral thesis, a system to detect weak signals related to future transcendental changes is proposed and tested. While most known solutions are based on the use of structured data, the proposed system quantitatively detects these signals using heterogeneous and unstructured information from scientific, journalistic, and social sources. Predicting new trends in an environment has many applications. For instance, companies and startups face constant changes in their markets that are very difficult to predict. For this reason, developing systems to automatically detect significant future changes at an early stage is relevant for any organization to make right decisions on time. This work has been designed to obtain weak signals of the future in any field depending only on the input dataset of documents. Text mining and natural language processing techniques are applied to process all these documents. As a result, a map of ranked terms, a list of automatically classified keywords and a list of multi-word expressions are obtained. The overall system has been tested in four different sectors: solar panels, artificial intelligence, remote sensing, and medical imaging. This work has obtained promising results that have been evaluated with two different methodologies. As a result, the system was able to successfully detect new trends at a very early stage that have become more and more important today. Quantum computing is a new paradigm for a multitude of computing applications. This doctoral thesis also presents a study of the technologies that are currently available for the physical implementation of qubits and quantum gates, establishing their main advantages and disadvantages and the available frameworks for programming and implementing quantum circuits. In order to improve the effectiveness of the system, a design of a quantum circuit based on support vector machines (SVMs) is described for the resolution of classification problems. This circuit is specially designed for the noisy intermediate-scale quantum (NISQ) computers that are currently available. As an experiment, the circuit has been tested on a real quantum computer based on superconducting qubits by IBM as an improvement for the text mining subsystem in the detection of weak signals. The results obtained with the quantum experiment show interesting outcomes with an improvement of close to 20% better performance than conventional systems, but also confirm that ongoing technological development is still required to take full advantage of quantum computing. / Griol Barres, I. (2022). Modelling of a System for the Detection of Weak Signals Through Text Mining and NLP. Proposal of Improvement by a Quantum Variational Circuit [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/183029 / TESIS / Compendio

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The future is here. New digital, disruptive innovations are changing and affecting industries across society. And the emerging Quantum Computing (QC) industry is not an exception. Billions of dollars have been invested by actors such as governments, large enterprises like IBM and AWS, and by smaller to medium firms towards achieving a fully working QC-technology. Therefore, firms who are looking to adopt it must address the barriers that come with it. This thesis therefore explores what barriers, with the objective on key ones, that exist when firms are adopting QC-technology as a service into their business strategy. The geographical scope of this study is the European and North American industries. The applied method is qualitative and based on the methodology of grounded theory where six semi-structured interviews are carried out with key experts in the field . Furthermore, the analytical PESTLE-framework was used to systemically code and categorize the barriers found from the interviews to analyze the political, economic, social, technological, legal, and environmental factors connected to the research question. By using key experts from different parts of the industry and this framework, it resulted in a holistic view of the industry’s barriers. The findings of this study are that the QC-industry is still in its early era with 34 barriers of adoption identified and eight of them deemed to be the key ones because of their significance and frequency of mentions. The eight key barriers are QC-technology is costly, impatient investors, funding issues, lack of consistent revenue streams, lack of awareness from top management, insufficient ecosystem, lack of skilled labor and immature technology. The most important minor barriers of the other 26 include lack of standardization and benchmarks, lack of collaboration between certain geographical parties, misinformation from vendors and not using external advisors. Nonetheless, the QC-technology is on the up-rise and is projected to affect industries across the world. Firms in these industries must therefore learn to adopt to the dynamic changes that come with what the QC industry brings. Therefore again, it is the intention of this thesis to explore the key barriers and mitigation strategies to overcome them. / Framtiden är här. Nya digitala, disruptiva innovationer håller just nu på att förändra och påverka industrier över hela samhället. Den växande kvantdatorindustrin är inte ett undantagsfall. Flertalet miljarder dollar med målet att uppnå en fullt funktionell kvantdator har investerats av aktörer som stater, stora företag som IBM och AWS samt små till medelstora företag. Därför bör företag som kommer att påverkas av effekterna adressera barriärerna som finns. Den här uppsatsen undersöker därför vilka barriärer, med fokus på de essentiella, som existerar för företag när de ska adaptera kvantdatorteknologi som en service i deras affärsstrategi. Den geografiska omfattningen berör den nordamerikanska samt den europeiska marknaden. Metodiken som användes var ”Grounded theory”- metodologin där sex semi-strukturerade intervjuer utfördes med nyckelexperter i industrin. Fortsättningsvis så användes PESTLE-ramverket för att systematiskt koda samt kategorisera de identifierade barriärerna utifrån politiska-, ekonomiska-, sociala- , teknologiska-, legala- samt miljöaspekterna. Genom att ha erhållit data från nyckelexperter från olika delar av industrin samt använt ramverket så gav det en holistisk bild av industrins barriärer. Resultatet av studien är att kvantdatorindustrin är i ett tidigt skede med 34 barriärer identifierade och åtta av dem som anses vara de mest essentiella på grund av deras signifikans samt frekvens av omnämnanden. De åtta nyckelbarriärerna inkluderar att kvantdatorteknologin är dyr att investera i, otåliga finansiella investerare, finansieringsproblem, brist på konsistenta intäktsflöden, brist på medvetenhet av ledningen, bristfällande ekosystem, brist på kompetent personal och icke-mogen teknologi. De viktigaste mindre barriärerna utav de 26 inkluderar brist på standardisering samt riktmärken, brist på samarbete mellan vissa geografiska områden, felaktig information från industrin till köparna, samt att inte ta hjälp av externa rådgivare. Vidare, så är kvantdatorteknologin samt industrin i helhet i en uppgång och förväntat att förändra industrier över hela världen. Företagen i dessa industrier bör därför lära sig redan idag att adaptera sig till de dynamiska förändringarna som kvantdator industrin medför. Därför är syftet för det här examensarbetet att utforska nyckelbarriärerna och strategierna som i syfte för att överkomma dem.

<p> The Bias-Variance Trade-off, where restricting the size of a hypothesis class can limit the generalization error of a model, is a canonical problem in Machine Learning, and a particular issue for high-variance models like Neural Networks that do not have enough parameters to enter the interpolating regime. Regularization techniques add bias to a model to lower testing error at the cost of increasing training error. This paper applies quantum circuits as activation functions in order to regularize a Feed-Forward Neural Network. The network using Quantum Activation Functions is compared against a network of the same dimensions except using Rectified Linear Unit (ReLU) activation functions, which can fit any arbitrary function. The Quantum Activation Function network is then shown to have comparable training performance to ReLU networks, both with and without regularization, for the tasks of binary classification, polynomial regression, and regression on a multicollinear dataset, which is a dataset whose design matrix is rank-deficient. The Quantum Activation Function network is shown to achieve regularization comparable to networks with L2-Regularization, the most commonly used method for neural network regularization today, with regularization parameters in the range of λ ∈ [.1, .5], while still allowing the model to maintain enough variance to achieve low training error. While there are limitations to the current physical implementation of quantum computers, there is potential for future architecture, or hardware-based, regularization methods that leverage the aspects of quantum circuits that provide lower generalization error. </p>

<p>The recent groundbreaking demonstrations of quantum supremacy in noisy intermediate scale quantum (NISQ) computing era has triggered an intense activity in establishing finer boundaries between classical and quantum computing. In this dissertation, we use established techniques based on quantum Monte Carlo (QMC) to map quantum problems into probabilistic networks where the fundamental unit of computation, p-bit, is inherently probabilistic and can be tuned to fluctuate between ‘0’ and ‘1’ with desired probability. We can view this mapped network as a Boltzmann machine whose states each represent a Feynman path leading from an initial configuration of q-bits to a final configuration. Each such path, in general, has a complex amplitude, ψ which can be associated with a complex energy. The real part of this energy can be used to generate samples of Feynman paths in the usual way, while the imaginary part is accounted for by treating the samples as complex entities, unlike ordinary Boltzmann machines where samples are positive. This mapping of a quantum circuit onto a Boltzmann machine with complex energies should be particularly useful in view of the advent of special-purpose hardware accelerators known as Ising Machines which can obtain a very large number of samples per second through massively parallel operation. We also demonstrate this acceleration using a recently used quantum problem and speeding its QMC simulation by a factor of ∼ 1000× compared to a highly optimized CPU program. Although this speed-up has been demonstrated using a graph colored architecture in FPGA, we project another ∼ 100× improvement with an architecture that utilizes clockless analog circuits. We believe that this will contribute significantly to the growing efforts to push the boundaries of the simulability of quantum circuits with classical/probabilistic resources and comparing them with NISQ-era quantum computers. </p>