Lecture

Qubits: Understanding Quantum States and Operations

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In course

MICRO-444: La science quantique : une vision singulière

Les étudiants comprennent les caractéristiques de la science quantique. Ils en maitrisent le formalisme et l'appliquent dans les systèmes de base: puits, fils et boites quantiques, qubits. ...

Description

This lecture introduces the concept of qubits, the fundamental units of quantum information. It begins by defining qubits as systems with two states, often represented as spin-up and spin-down or horizontal and vertical polarizations. The instructor explains the significance of superposition, where a qubit can exist in a combination of both states, and discusses the mathematical representation of these states using complex numbers. The lecture covers the Bloch sphere, a geometrical representation of qubit states, and the role of phase in determining the state of a qubit. The instructor also explains the properties of Pauli matrices and their relevance in quantum mechanics. The discussion extends to Hamiltonians and propagators, illustrating how they govern the evolution of qubit states over time. The lecture concludes with examples of Rabi oscillations and the importance of resonance in controlling qubit transitions, emphasizing the practical applications of qubits in quantum computing and information processing.

Instructor

Pierre-André Besse

Teaching & PhD Past EPFL PhD Students Klaus Ehrmann Courses La science quantique : une vision singulière MICRO-444 Students understand the characteristics of quantum science. They master the formalism and use it in basic quantum systems: quantum wells, wires, dots or qubits. Physics of semiconductors devices MICRO-312 The students are able to explain the physics of semiconductor devices like diodes, transistors, and MOS devices. They use such devices in fundamental electroni

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Ontological neighbourhood

Theoretical computer science

Theory of computation: Quantum computing

Related concepts (32)

Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.

Quantum information

Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields.

Quantum mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.

Qubit

In quantum computing, a qubit (ˈkjuːbɪt) or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization.

Quantum information science

Quantum information science is a field that combines the principles of quantum mechanics with information science to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it does not include experimental research and can be confused with a subfield of quantum information science that deals with the processing of quantum information.

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