782 research outputs found
Simulación clásica de un algoritmo cuántico
Classical computing there are multiple algorithms to efficiently locate a certain element within a disorganized database; however, quantum computing can be applied more assertively in the face of problems in which it is complicated to verify a solution and at the same time to test multiple and possible solutions. Therefore, this article presents an introduction to Quantum Computing, developing some concepts of quantum formalism, and then approach Grover's algorithm which exploits the principle of superposition to the maximum. Finally, a classic simulation of this algorithm is performed, and the results obtained are compared with classical algorithms such as sequential search and binary search method. A 95% is obtained as a result of greater effectiveness in times -when solving the same search-, revealing the potential advantages of quantum computing.En la computación clásica existen múltiples algoritmos para localizar de manera eficiente un determinado elemento dentro de una base de datos desorganizada; sin embargo, la computación cuántica puede aplicarse de manera más asertiva frente a tales problemas cuando es complejo verificar una solución y a la vez probar múltiples y posibles soluciones. Por lo anterior, en este artículo se presenta una introducción a la Computación Cuántica -desarrollando algunos conceptos del formalismo cuántico-, y luego se aborda el algoritmo de Grover el cual explota al máximo el principio de superposición. Finalmente se realiza una simulación clásica de dicho algoritmo, y los resultados obtenidos se comparan con otros algoritmos clásicos como el método de búsqueda lineal y búsqueda binaria. Se obtiene como resultado un %95 de mayor efectividad en tiempos -a la hora de resolver la misma búsqueda- logrando poner de manifiesto las ventajas potenciales de la computación cuántica
Quantum computation of stopping power for inertial fusion target design
Stopping power is the rate at which a material absorbs the kinetic energy of
a charged particle passing through it -- one of many properties needed over a
wide range of thermodynamic conditions in modeling inertial fusion implosions.
First-principles stopping calculations are classically challenging because they
involve the dynamics of large electronic systems far from equilibrium, with
accuracies that are particularly difficult to constrain and assess in the
warm-dense conditions preceding ignition. Here, we describe a protocol for
using a fault-tolerant quantum computer to calculate stopping power from a
first-quantized representation of the electrons and projectile. Our approach
builds upon the electronic structure block encodings of Su et al. [PRX Quantum
2, 040332 2021], adapting and optimizing those algorithms to estimate
observables of interest from the non-Born-Oppenheimer dynamics of multiple
particle species at finite temperature. Ultimately, we report logical qubit
requirements and leading-order Toffoli costs for computing the stopping power
of various projectile/target combinations relevant to interpreting and
designing inertial fusion experiments. We estimate that scientifically
interesting and classically intractable stopping power calculations can be
quantum simulated with roughly the same number of logical qubits and about one
hundred times more Toffoli gates than is required for state-of-the-art quantum
simulations of industrially relevant molecules such as FeMoCo or P450
Angles and devices for quantum approximate optimization
A potential application of emerging Noisy Intermediate-Scale Quantum (NISQ) devices is that of approximately solving combinatorial optimization problems. This thesis investigates a gate-based algorithm for this purpose, the Quantum Approximate Optimization Algorithm (QAOA), in two major themes. First, we examine how the QAOA resolves the problems it is designed to solve. We take a statistical view of the algorithm applied to ensembles of problems, first, considering a highly symmetric version of the algorithm, using Grover drivers. In this highly symmetric context, we find a simple dependence of the QAOA state’s expected value on how values of the cost function are distributed. Furthering this theme, we demonstrate that, generally, QAOA performance depends on problem statistics with respect to a metric induced by a chosen driver Hamiltonian. We obtain a method for evaluating QAOA performance on worst-case problems, those of random costs, for differing driver choices. Second, we investigate a QAOA context with device control occurring only via single-qubit gates, rather than using individually programmable one- and two-qubit gates. In this reduced control overhead scheme---the digital-analog scheme---the complexity of devices running QAOA circuits is decreased at the cost of errors which are shown to be non-harmful in certain regimes. We then explore hypothetical device designs one could use for this purpose.Eine mögliche Anwendung für “Noisy Intermediate-Scale Quantum devices” (NISQ devices) ist die näherungsweise Lösung von kombinatorischen Optimierungsproblemen. Die vorliegende Arbeit untersucht anhand zweier Hauptthemen einen gatterbasierten Algorithmus, den sogenannten “Quantum Approximate Optimization Algorithm” (QAOA). Zuerst prüfen wir, wie der QAOA jene Probleme löst, für die er entwickelt wurde. Wir betrachten den Algorithmus in einer Kombination mit hochsymmetrischen Grover-Treibern für statistische Ensembles von Probleminstanzen. In diesem Kontext finden wir eine einfache Abhängigkeit von der Verteilung der Kostenfunktionswerte. Weiterführend zeigen wir, dass die QAOA-Leistung generell von der Problemstatistik in Bezug auf eine durch den gewählten Treiber-Hamiltonian induzierte Metrik abhängt. Wir erhalten eine Methode zur Bewertung der QAOA-Leistung bei schwersten Problemen (solche zufälliger Kosten) für unterschiedliche Treiberauswahlen. Zweitens untersuchen wir eine QAOA-Variante, bei der sich die Hardware- Kontrolle nur auf Ein-Qubit-Gatter anstatt individuell programmierbare Ein- und Zwei-Qubit-Gatter erstreckt. In diesem reduzierten Kontrollaufwandsschema—dem digital-analogen Schema—sinkt die Komplexität der Hardware, welche die QAOASchaltungen ausführt, auf Kosten von Fehlern, die in bestimmten Bereichen als ungefährlich nachgewiesen werden. Danach erkunden wir hypothetische Hardware- Konzepte, die für diesen Zweck genutzt werden könnten
Quantum-enhanced symmetric cryptanalysis for S-AES
Advanced Encryption Standard is one of the most widely used and important
symmetric ciphers for today. It well known, that it can be subjected to the
quantum Grover's attack that twice reduces its key strength. But full AES
attack requires hundreds of qubits and circuit depth of thousands, that makes
impossible not only experimental research but also numerical simulations of
this algorithm. Here we present an algorithm for optimized Grover's attack on
downscaled Simplifed-AES cipher. Besides full attack we present several
approaches that allows to reduce number of required qubits if some nibbles of
the key are known as a result of side-channel attack. For 16-bit S-AES the
proposed attack requires 23 qubits in general case and 19, 15 or 11 if 4, 8 or
12 bits were leaked in specifc confguration. Comparing to previously known
32-qubits algorithm this approach potentially allows to run the attack on
today's NISQ-devices and perform numerical simulations with GPU, that may be
useful for further research of problem-specifc error mitigation and error
correction techniques.Comment: 15 pages, 7 figure
Advances in quantum machine learning
Here we discuss advances in the field of quantum machine learning. The
following document offers a hybrid discussion; both reviewing the field as it
is currently, and suggesting directions for further research. We include both
algorithms and experimental implementations in the discussion. The field's
outlook is generally positive, showing significant promise. However, we believe
there are appreciable hurdles to overcome before one can claim that it is a
primary application of quantum computation.Comment: 38 pages, 17 Figure
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
Automated Function Implementation via Conditional Parameterized Quantum Circuits with Applications to Finance
Classical Monte Carlo algorithms can theoretically be sped up on a quantum
computer by employing amplitude estimation (AE). To realize this, an efficient
implementation of state-dependent functions is crucial. We develop a
straightforward approach based on pre-training parameterized quantum circuits,
and show how they can be transformed into their conditional variant, making
them usable as a subroutine in an AE algorithm. To identify a suitable circuit,
we propose a genetic optimization approach that combines variable ansatzes and
data encoding. We apply our algorithm to the problem of pricing financial
derivatives. At the expense of a costly pre-training process, this results in a
quantum circuit implementing the derivatives' payoff function more efficiently
than previously existing quantum algorithms. In particular, we compare the
performance for European vanilla and basket options.Comment: 10 pages, 12 figures, 2 algorithm
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