Introduction to Quantum Computing
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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.
Introduction to Quantum Computing
- 1. Introduction to Quantum Computing Alejandro Jaramillo CSUC 13/12/2022
- 2. 2 2 What is Quantum Computing? Quantum Computing is a technology that takes advantage of the rules of Quantum Mechanics to solve problems faster and more efficiently 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 …
- 3. 3 3 Classical bit Binary state Deterministic Current, magnet… Qubit Mathematically: an element of a complex vector space Probabilistic Photon, current on a superconductor… The Quantum Bit Measurement postulate of QM: “When we measure a Quantum system, we will observe each state with a probability given by the modulus of its complex amplitude squared” State: Prob( ) Prob( ) 0 state 1 state
- 4. 4 4 Quantum Phenomena Quantum Mechanics’ math is, quite simply, linear algebra! 1. Superposition: be at several states at the same time 2. Entanglement: the state of one qubit depends on the actions performed on a different qubit 3. Interference: increase or decrease the probability of observing a state
- 5. 5 5 Quantum Circuit Model Quantum Gate: basic operation performed on one or a group of qubits. It is represented by a square matrix acting on the state vectors. Most important gates: X gate: generates a bit flip Z gate: adds a relative phase H gate: creates superposition CNOT gate: creates entanglement
- 6. 6 6 State of The Art We are here! (100’s of qubits) (10000’s of qubits)
- 7. 7 7 Quantum Algorithms: Grover Lov Grover (1996) Algorithm for unstructured search Quadratic improvement from classical algorithms: vs
- 8. 8 8 Quantum Algorithms: Shor Peter Shor (1994) Factorization of large composite numbers Exponential improvement from classical algorithms
- 9. 9 9 Hybrid Algorithms: VQE Variational Quantum Eigensolver: uses classical and Quantum resources to find an approximation to the energy of the ground state of a system (molecules, materials…). 1. Design a parametrized Quantum Circuit (ansatz) that approximates the ground state 2. Measure the energy of the state with a designed Quantum Circuit 3. Use a Classical Optimizer to vary the parameters 4. New iteration
- 10. 10 10 Applications of Quantum Computing Molecule and material simulation Machine learning Logistics and optimization Cryptography
- 11. 11 11 The Quantum Spain Project 1. Acquire and install a quantum computer, using superconducting technology 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 new Quantum Algorithms. 3. Develop useful Quantum Algorithms, applicable to real problems. These algorithms emphasize the development of Quantum Machine Learning. Impulsed by:
- 12. 12 12 Wrap-up 1. Quantum Technologies present a new paradigm for computing 2. New algorithms to solve problems more efficiently 3. Applications in many areas
- 13. https://quantumspain-project.es @QuantumSpain_ES quantum-spain-project "This work has been financially supported by the Ministry of Economic Affairs and Digital Transformation of the Spanish Government through the QUANTUM ENIA project call - QUANTUM SPAIN project, and by the European Union through the Recovery, Transformation and Resilience Plan - NextGenerationEU within the framework of the Digital Spain 2026 Agenda“.