Quantum computing harnesses quantum mechanics to outperform classical computers in problem-solving efficiency. Key features include the use of qubits, quantum phenomena like superposition and entanglement, and innovative algorithms such as Grover's and Shor's for searching and factorization. The document also discusses the Quantum Spain project, which aims to install a quantum computer and develop practical algorithms for various applications.

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Introduction to Quantum Computing

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  Introduction to QuantumComputingAlejandroJaramilloCSUC13/12/2022
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  22What is QuantumComputing?Quantum Computing is a technology that takes advantage of therules of Quantum Mechanics to solve problems faster and moreefficiently than classical computers. Allows to perform new algorithms Better for simulating Quantum systems Implementable with many different technologies Compatible with classical computing More energy efficient …
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  33Classical bit Binarystate Deterministic Current, magnet…Qubit Mathematically: an element ofa complex vector space Probabilistic Photon, current on asuperconductor…The Quantum BitMeasurement postulate of QM:“When we measure a Quantumsystem, we will observe eachstate with a probability given bythe modulus of its complexamplitude squared”State:Prob( ) Prob( )0 state 1 state
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  44Quantum PhenomenaQuantum Mechanics’math is, quite simply,linear algebra!1. Superposition: be at several states atthe same time2. Entanglement: the state of one qubitdepends on the actions performed on adifferent qubit3. Interference: increase or decrease theprobability of observing a state
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  55Quantum Circuit ModelQuantumGate: basic operationperformed on one or a group ofqubits. It is represented by asquare matrix acting on the statevectors.Most important gates: X gate: generates a bit flip Z gate: adds a relative phase H gate: creates superposition CNOT gate: creates entanglement
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  66State of TheArtWe are here! (100’s of qubits)(10000’s of qubits)
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  77Quantum Algorithms: GroverLov Grover (1996) Algorithm for unstructured search Quadratic improvement from classical algorithms: vs
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  88Quantum Algorithms: ShorPeter Shor (1994) Factorization of large composite numbers Exponential improvement from classical algorithms
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  99Hybrid Algorithms: VQEVariationalQuantum Eigensolver: uses classical and Quantum resourcesto find an approximation to the energy of the ground state of a system(molecules, materials…).1. Design a parametrizedQuantum Circuit (ansatz) thatapproximates the groundstate2. Measure the energy of thestate with a designedQuantum Circuit3. Use a Classical Optimizer tovary the parameters4. New iteration
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  1010Applications of QuantumComputingMolecule and material simulation Machine learningLogistics and optimization Cryptography
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  1111The Quantum SpainProject1. Acquire and install a quantum computer, using superconductingtechnology as qubits.2. Create a remote access service in the cloud to the Quantum processor,to allow the industry and the public sector to experiment with the newQuantum Algorithms.3. Develop useful Quantum Algorithms, applicable to real problems. Thesealgorithms emphasize the development of Quantum Machine Learning.Impulsed by:
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  1212Wrap-up1. Quantum Technologiespresent a new paradigm forcomputing2. New algorithms to solve problems more efficiently3. Applications in many areas
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  https://quantumspain-project.es @QuantumSpain_ES quantum-spain-project"Thiswork has been financially supported by the Ministry of Economic Affairs and Digital Transformation of the Spanish Government through the QUANTUMENIA project call - QUANTUM SPAIN project, and by the European Union through the Recovery, Transformation and Resilience Plan - NextGenerationEU withinthe framework of the Digital Spain 2026 Agenda“.