#### In quantum computing, a **qubit** or **quantum bit** (sometimes **qbit**) is the basic unit of quantum information: Q

### Quantum

In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be “quantized” is referred to as “the hypothesis of quantization”. This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.

For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature.

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### Quantum chemistry

Quantum chemistry, also called molecular quantum mechanics, is a branch of chemistry focused on the application of quantum mechanics to chemical systems. Understanding electronic structure and molecular dynamics using the Schrödinger equations are central topics in quantum chemistry.

Chemists rely heavily on spectroscopy through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy, and scanning probe microscopy.Quantum chemistry studies the ground state of individual atoms and molecules, and the excited states, and transition states that occur during chemical reactions.

On the calculations, quantum chemical studies use also semi-empirical and other methods based on quantum mechanical principles, and deal with time dependent problems. Many quantum chemical studies assume the nuclei are at rest (Born–Oppenheimer approximation). Many calculations involve iterative methods that include self-consistent field methods. Major goals of quantum chemistry include increasing the accuracy of the results for small molecular systems, and increasing the size of large molecules that can be processed, which is limited by scaling considerations—the computation time increases as a power of the number of atoms.

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### Quantum computing

Quantum computing is the use of quantum phenomena such as superposition and entanglement to perform computation. Computers that perform quantum computations are known as quantum computers. Quantum computers are believed to be able to solve certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science.

Quantum computing began in the early 1980s, when physicist Paul Benioff proposed a quantum mechanical model of the Turing machine. Richard Feynman and Yuri Manin later suggested that a quantum computer had the potential to simulate things that a classical computer could not. In 1994, Peter Shor developed a quantum algorithm for factoring integers that had the potential to decrypt RSA-encrypted communications. Despite ongoing experimental progress since the late 1990s, most researchers believe that “fault-tolerant quantum computing [is] still a rather distant dream.” In recent years, investment into quantum computing research has increased in both the public and private sector. On 23 October 2019, Google AI, in partnership with the U.S. National Aeronautics and Space Administration (NASA), claimed to have performed a quantum computation that is infeasible on any classical computer.

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### Quantum cryptography

Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical (i.e. non-quantum) communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed (no-cloning theorem). This could be used to detect eavesdropping in quantum key distribution.

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### 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. Its study is also relevant to disciplines such as cognitive science, psychology and neuroscience. Its main focus is in extracting information from matter at the microscopic scale. Observation in science is one of the most important ways of acquiring information and measurement is required in order to quantify the observation, making this crucial to the scientific method. In quantum mechanics, due to the uncertainty principle, non-commuting observables cannot be precisely measured simultaneously. The act of measurement disturbs the state of the system. Hence, it is impossible to make a perfect measurement in microscopic or quantum systems.

Information is something that is encoded in the state of a quantum system, it is physical. While quantum mechanics deals with examining properties of matter at the microscopic level, quantum information science focuses on extracting information from those properties, and quantum computation manipulates and processes information – performs logical operations – using quantum information processing techniques.

Quantum information, like classical information, can be processed using digital computers, transmitted from one location to another, manipulated with algorithms, and analyzed with computer science and mathematics. Just like the basic unit of classical information is the bit, quantum information deals with qubits. Quantum information can be measured using Von Neumann entropy.

Recently, the field of quantum computing has become an active research area because of the possibility to disrupt modern computation, communication, and cryptography.

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### Quantum information science

Quantum information science is an area of study about information science related to quantum effects in physics. It includes theoretical issues in computational models as well as more experimental topics in quantum physics including what can and cannot be done with quantum information. The term quantum information theory is also used, but it fails to encompass experimental research in the area and can be confused with a subfield of quantum information science that studies the processing of quantum information.

Quantum teleportation, quantum entanglement and the manufacturing of quantum computer hardware are just physical and engineering studies. They require serious understanding of quantum physics and engineering. Compared to before the 2010s, there was some remarkable progress in manufacturing quantum computers. Google and IBM are investing heavily in quantum computer hardware research. A quantum computer with more than 100 qubits is possible today. The error occurrence is so serious that we cannot say that we have a material suitable for quantum computers yet. Majorana fermions may be one of the key materials.

Devices for quantum cryptography have been commercialized already. There is an old cipher called a one time pad, which was widely used among the spies in the Cold War era. It uses a long sequence of random keys. If two people exchanged same random keys safely, it is impossible to decrypt one time pad except by accident, but key exchanging is not easy. However, the key exchanging problems can be solved by exchanging quantum entangled particle pairs. Quantum mechanical laws such as no cloning theorem and wave function collapse provide secure exchange of random keys. So, manufacturing devices that can transport quantum entangled particles is an important scientific and engineering problem.

Programming languages for quantum computers are also needed. Q Sharp and Qiskit are popular quantum programming languages

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### 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.

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### Quark

A quark (/kwɔːrk, kwɑːrk/) is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly observable matter is composed of up quarks, down quarks and electrons. Due to a phenomenon known as color confinement, quarks are never found in isolation; they can be found only within hadrons, which include baryons (such as protons and neutrons) and mesons, or in quark–gluon plasmas. For this reason, much of what is known about quarks has been drawn from observations of hadrons.

Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin. They are the only elementary particles in the Standard Model of particle physics to experience all four fundamental interactions, also known as fundamental forces (electromagnetism, gravitation, strong interaction, and weak interaction), as well as the only known particles whose electric charges are not integer multiples of the elementary charge.

There are six types, known as flavors, of quarks: up, down, charm, strange, top, and bottom. Up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay: the transformation from a higher mass state to a lower mass state. Because of this, up and down quarks are generally stable and the most common in the universe, whereas strange, charm, bottom, and top quarks can only be produced in high energy collisions (such as those involving cosmic rays and in particle accelerators). For every quark flavor there is a corresponding type of antiparticle, known as an antiquark, that differs from the quark only in that some of its properties (such as the electric charge) have equal magnitude but opposite sign.

The quark model was independently proposed by physicists Murray Gell-Mann and George Zweig in 1964. Quarks were introduced as parts of an ordering scheme for hadrons, and there was little evidence for their physical existence until deep inelastic scattering experiments at the Stanford Linear Accelerator Center in 1968. Accelerator experiments have provided evidence for all six flavors. The top quark, first observed at Fermilab in 1995, was the last to be discovered.

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### Quark–gluon plasma

Quark–gluon plasma or QGP is an interacting localized assembly of quarks and gluons at thermal (local kinetic) and (close to) chemical (abundance) equilibrium. The word plasma signals that free color charges are allowed. In a 1987 summary, Léon van Hove pointed out the equivalence of the three terms: quark gluon plasma, quark matter and a new state of matter. Since the temperature is above the Hagedorn temperature—and thus above the scale of light u,d-quark mass—the pressure exhibits the relativistic Stefan-Boltzmann format governed by fourth power of temperature and many practically mass free quark and gluon constituents. We can say that QGP emerges to be the new phase of strongly interacting matter which manifests its physical properties in terms of nearly free dynamics of practically massless gluons and quarks. Both quarks and gluons, must be present in conditions near chemical (yield) equilibrium with their colour charge open for a new state of matter to be referred to as QGP.

Quark–gluon plasma filled the entire Universe before matter was created. Theories predicting the existence of quark–gluon plasma were developed in the late 1970s and early 1980s. Discussions around heavy ion experimentation followed suit and the first experiment proposals were put forward at CERN and BNL in the following years. Quark–gluon plasma was detected for the first time in the laboratory at CERN in the year 2000.

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### Quasiparticle

In physics, quasiparticles and collective excitations (which are closely related) are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For example, as an electron travels through a semiconductor, its motion is disturbed in a complex way by its interactions with other electrons and with atomic nuclei. The electron behaves as though it has a different effective mass travelling unperturbed in vacuum. Such an electron is called an electron quasiparticle. In another example, the aggregate motion of electrons in the valence band of a semiconductor or a hole band in a metal behave as though the material instead contained positively charged quasiparticles called electron holes. Other quasiparticles or collective excitations include the phonon (a particle derived from the vibrations of atoms in a solid), the plasmons (a particle derived from plasma oscillation), and many others.

These particles are typically called quasiparticles if they are related to fermions, and called collective excitations if they are related to bosons, although the precise distinction is not universally agreed upon. Thus, electrons and electron holes (fermions) are typically called quasiparticles, while phonons and plasmons (baryons) are typically called collective excitations.

The quasiparticle concept is important in condensed matter physics because it can simplify the many-body problem in quantum mechanics.

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### Qubit

In quantum computing, a qubit (/ˈkjuːbɪt/) or quantum bit (sometimes qbit) is the basic unit of quantum information—the quantum version of the classical 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. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states simultaneously, a property which is fundamental to quantum mechanics and quantum computing.

Etymology

The coining of the term qubit is attributed to Benjamin Schumacher. In the acknowledgments of his 1995 paper, Schumacher states that the term qubit was created in jest during a conversation with William Wootters. The paper describes a way of compressing states emitted by a quantum source of information so that they require fewer physical resources to store. This procedure is now known as Schumacher compression.

Bit versus qubit

A binary digit, characterized as 0 and 1, is used to represent information in classical computers. When averaged over both of its states (0,1), a binary digit can represent up to one bit of Shannon information, where a bit is the basic unit of information. However, in this article, the word bit is synonymous with a binary digit.

In classical computer technologies, a processed bit is implemented by one of two levels of low DC voltage, and whilst switching from one of these two levels to the other, a so-called forbidden zone must be passed as fast as possible, as electrical voltage cannot change from one level to another instantaneously.

There are two possible outcomes for the measurement of a qubit—usually taken to have the value “0” and “1”, like a bit or binary digit. However, whereas the state of a bit can only be either 0 or 1, the general state of a qubit according to quantum mechanics can be a coherent superposition of both. Moreover, whereas a measurement of a classical bit would not disturb its state, a measurement of a qubit would destroy its coherence and irrevocably disturb the superposition state. It is possible to fully encode one bit in one qubit. However, a qubit can hold more information, e.g. up to two bits using superdense coding.

For a system of n components, a complete description of its state in classical physics requires only n bits, whereas in quantum physics it requires 2n complex numbers.

Physical implementations

Any two-level quantum-mechanical system can be used as a qubit. Multilevel systems can be used as well, if they possess two states that can be effectively decoupled from the rest (e.g., ground state and first excited state of a nonlinear oscillator). There are various proposals. Several physical implementations that approximate two-level systems to various degrees were successfully realized. Similarly to a classical bit where the state of a transistor in a processor, the magnetization of a surface in a hard disk and the presence of current in a cable can all be used to represent bits in the same computer, an eventual quantum computer is likely to use various combinations of qubits in its design.

The following is an incomplete list of physical implementations of qubits, and the choices of basis are by convention only.

Photon Polarization encoding Polarization of light Horizontal Vertical

Number of photons Fock state Vacuum Single photon state

Time-bin encoding Time of arrival Early Late

Coherent state of light Squeezed light Quadrature[clarification needed] Amplitude-squeezed state Phase-squeezed state

Electrons Electronic spin Spin Up Down

Electron number Charge No electron One electron

Nucleus Nuclear spin addressed through NMR Spin Up Down

Optical lattices Atomic spin Spin Up Down

Josephson junction Superconducting charge qubit Charge Uncharged superconducting island (Q=0) Charged superconducting island (Q=2e, one extra Cooper pair)

Superconducting flux qubit Current Clockwise current Counterclockwise current

Superconducting phase qubit Energy Ground state First excited state

Singly charged quantum dot pair Electron localization Charge Electron on left dot Electron on right dot

Quantum dot Dot spin Spin Down Up

Gapped topological system Non-abelian anyons Braiding of Excitations Depends on specific topological system Depends on specific topological system

van der Waals heterostructure Electron localization Charge

Qubit storage

In a paper entitled “Solid-state quantum memory using the 31P nuclear spin”, published in the October 23, 2008, issue of the journal Nature, a team of scientists from the U.K. and U.S. reported the first relatively long (1.75 seconds) and coherent transfer of a superposition state in an electron spin “processing” qubit to a nuclear spin “memory” qubit. This event can be considered the first relatively consistent quantum data storage, a vital step towards the development of quantum computing. Recently, a modification of similar systems (using charged rather than neutral donors) has dramatically extended this time, to 3 hours at very low temperatures and 39 minutes at room temperature. Room temperature preparation of a qubit based on electron spins instead of nuclear spin was also demonstrated by a team of scientists from Switzerland and Australia.

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