Presentació d'Alejandro Jaramillo, del CSUC, a la 6a Jornada de formació sobre l'ús del servei de càlcul.

1. Introduction to Quantum
Computing
Alejandro Jaramillo
CSUC
13/12/2022

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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
 …

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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

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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

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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

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State of The Art
We are here! (100’s of qubits)
(10000’s of qubits)

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Quantum Algorithms: Grover
 Lov Grover (1996)
 Algorithm for unstructured search
 Quadratic improvement from classical algorithms: vs

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Quantum Algorithms: Shor
 Peter Shor (1994)
 Factorization of large composite numbers
 Exponential improvement from classical algorithms

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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

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Applications of Quantum Computing
Molecule and material simulation Machine learning
Logistics and optimization Cryptography

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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:

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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“.