In quantum computing, a qubit()or quantum bit(sometimes qbit) is the basic unit of quantum informationthe 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 superpositionof both states/levels simultaneously, a property which is fundamental to quantum mechanics and quantum computing.

The coining of the term qubit is attributed to Benjamin Schumacher.[1] 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.

A binary digit, characterized as 0 and 1, is used to represent information in classical computers. 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 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 qubitusually 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 superpositionof both.[2] 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 2n1 complex numbers.[3]

In quantum mechanics, the general quantum state of a qubit can be represented by a linear superposition of its two orthonormal basis states (or basis vectors). These vectors are usually denoted as | 0 = [ 1 0 ] {displaystyle |0rangle ={bigl [}{begin{smallmatrix}1\0end{smallmatrix}}{bigr ]}} and | 1 = [ 0 1 ] {displaystyle |1rangle ={bigl [}{begin{smallmatrix}0\1end{smallmatrix}}{bigr ]}} . They are written in the conventional Diracor “braket”notation; the | 0 {displaystyle |0rangle } and | 1 {displaystyle |1rangle } are pronounced “ket 0” and “ket 1”, respectively. These two orthonormal basis states, { | 0 , | 1 } {displaystyle {|0rangle ,|1rangle }} , together called the computational basis, are said to span the two-dimensional linear vector (Hilbert) space of the qubit.

Qubit basis states can also be combined to form product basis states. For example, two qubits could be represented in a four-dimensional linear vector space spanned by the following product basis states: | 00 = [ 1 0 0 0 ] {displaystyle |00rangle ={biggl [}{begin{smallmatrix}1\0\0\0end{smallmatrix}}{biggr ]}} , | 01 = [ 0 1 0 0 ] {displaystyle |01rangle ={biggl [}{begin{smallmatrix}0\1\0\0end{smallmatrix}}{biggr ]}} , | 10 = [ 0 0 1 0 ] {displaystyle |10rangle ={biggl [}{begin{smallmatrix}0\0\1\0end{smallmatrix}}{biggr ]}} , and | 11 = [ 0 0 0 1 ] {displaystyle |11rangle ={biggl [}{begin{smallmatrix}0\0\0\1end{smallmatrix}}{biggr ]}} .

In general, n qubits are represented by a superposition state vector in 2n-dimensional Hilbert space.

A pure qubit state is a coherent superposition of the basis states. This means that a single qubit can be described by a linear combination of | 0 {displaystyle |0rangle } and | 1 {displaystyle |1rangle } :

where and are probability amplitudes and can in general both be complex numbers.When we measure this qubit in the standard basis, according to the Born rule, the probability of outcome | 0 {displaystyle |0rangle } with value “0” is | | 2 {displaystyle |alpha |^{2}} and the probability of outcome | 1 {displaystyle |1rangle } with value “1” is | | 2 {displaystyle |beta |^{2}} . Because the absolute squares of the amplitudes equate to probabilities, it follows that {displaystyle alpha } and {displaystyle beta } must be constrained by the equation

Note that a qubit in this superposition state does not have a value in between “0” and “1”; rather, when measured, the qubit has a probability | | 2 {displaystyle |alpha |^{2}} of the value 0 and a probability | | 2 {displaystyle |beta |^{2}} of the value “1”. In other words, superposition means that there is no way, even in principle, to tell which of the two possible states forming the superposition state actually pertains. Furthermore, the probability amplitudes, {displaystyle alpha } and {displaystyle beta } , encode more than just the probabilities of the outcomes of a measurement; the relative phase of {displaystyle alpha } and {displaystyle beta } is responsible for quantum interference, e.g., as seen in the two-slit experiment.

It might, at first sight, seem that there should be four degrees of freedom in | = | 0 + | 1 {displaystyle |psi rangle =alpha |0rangle +beta |1rangle ,} , as {displaystyle alpha } and {displaystyle beta } are complex numbers with two degrees of freedom each. However, one degree of freedom is removed by the normalization constraint ||2 + ||2 = 1. This means, with a suitable change of coordinates, one can eliminate one of the degrees of freedom. One possible choice is that of Hopf coordinates:

Additionally, for a single qubit the overall phase of the state ei has no physically observable consequences, so we can arbitrarily choose to be real (or in the case that is zero), leaving just two degrees of freedom:

where e i {displaystyle e^{iphi }} is the physically significant relative phase.

The possible quantum states for a single qubit can be visualised using a Bloch sphere (see diagram). Represented on such a 2-sphere, a classical bit could only be at the “North Pole” or the “South Pole”, in the locations where | 0 {displaystyle |0rangle } and | 1 {displaystyle |1rangle } are respectively. This particular choice of the polar axis is arbitrary, however. The rest of the surface of the Bloch sphere is inaccessible to a classical bit, but a pure qubit state can be represented by any point on the surface. For example, the pure qubit state ( ( | 0 + i | 1 ) / 2 ) {displaystyle ((|0rangle +i|1rangle )/{sqrt {2}})} would lie on the equator of the sphere at the positive y axis. In the classical limit, a qubit, which can have quantum states anywhere on the Bloch sphere, reduces to the classical bit, which can be found only at either poles.

The surface of the Bloch sphere is a two-dimensional space, which represents the state space of the pure qubit states. This state space has two local degrees of freedom, which can be represented by the two angles {displaystyle phi } and {displaystyle theta } .

A pure state is one fully specified by a single ket, | = | 0 + | 1 , {displaystyle |psi rangle =alpha |0rangle +beta |1rangle ,,} a coherent superposition as described above. Coherence is essential for a qubit to be in a superposition state. With interactions and decoherence, it is possible to put the qubit in a mixed state, a statistical combination or incoherent mixture of different pure states. Mixed states can be represented by points inside the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the angles {displaystyle phi } and {displaystyle theta } , as well as the length r {displaystyle r} of the vector that represents the mixed state.

There are various kinds of physical operations that can be performed on pure qubit states.

An important distinguishing feature between qubits and classical bits is that multiple qubits can exhibit quantum entanglement. Quantum entanglement is a nonlocal property of two or more qubits that allows a set of qubits to express higher correlation than is possible in classical systems.

The simplest system to display quantum entanglement is the system of two qubits. Consider, for example, two entangled qubits in the | + {displaystyle |Phi ^{+}rangle } Bell state:

In this state, called an equal superposition, there are equal probabilities of measuring either product state | 00 {displaystyle |00rangle } or | 11 {displaystyle |11rangle } , as | 1 / 2 | 2 = 1 / 2 {displaystyle |1/{sqrt {2}}|^{2}=1/2} . In other words, there is no way to tell if the first qubit has value 0 or 1 and likewise for the second qubit.

Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtainingwith equal probabilitieseither | 0 {displaystyle |0rangle } or | 1 {displaystyle |1rangle } , i.e., she can not tell if her qubit has value 0 or 1. Because of the qubits’ entanglement, Bob must now get exactly the same measurement as Alice. For example, if she measures a | 0 {displaystyle |0rangle } , Bob must measure the same, as | 00 {displaystyle |00rangle } is the only state where Alice’s qubit is a | 0 {displaystyle |0rangle } . In short, for these two entangled qubits, whatever Alice measures, so would Bob, with perfect correlation, in any basis, however far apart they may be and even though both can not tell if their qubit has value 0 or 1 a most surprising circumstance that can not be explained by classical physics.

Controlled gates act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the controlled NOT gate (or CNOT or cX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is | 1 {displaystyle |1rangle } , and otherwise leaves it unchanged. With respect to the unentangled product basis { | 00 {displaystyle {|00rangle } , | 01 {displaystyle |01rangle } , | 10 {displaystyle |10rangle } , | 11 } {displaystyle |11rangle }} , it maps the basis states as follows:

A common application of the CNOT gate is to maximally entangle two qubits into the | + {displaystyle |Phi ^{+}rangle } Bell state. To construct | + {displaystyle |Phi ^{+}rangle } , the inputs A (control) and B (target) to the CNOT gate are:

1 2 ( | 0 + | 1 ) A {displaystyle {frac {1}{sqrt {2}}}(|0rangle +|1rangle )_{A}} and | 0 B {displaystyle |0rangle _{B}}

After applying CNOT, the output is the | + {displaystyle |Phi ^{+}rangle } Bell State: 1 2 ( | 00 + | 11 ) {displaystyle {frac {1}{sqrt {2}}}(|00rangle +|11rangle )} .

The | + {displaystyle |Phi ^{+}rangle } Bell state forms part of the setup of the superdense coding, quantum teleportation, and entangled quantum cryptography algorithms.

Quantum entanglement also allows multiple states (such as the Bell state mentioned above) to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer. Many of the successes of quantum computation and communication, such as quantum teleportation and superdense coding, make use of entanglement, suggesting that entanglement is a resource that is unique to quantum computation.[4] A major hurdle facing quantum computing, as of 2018, in its quest to surpass classical digital computing, is noise in quantum gates that limits the size of quantum circuits that can be executed reliably.[5]

A number of qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits within a register. A qubyte (quantum byte) is a collection of eight qubits.[6]

Similar to the qubit, the qutrit is the unit of quantum information that can be realized in suitable 3-level quantum systems. This is analogous to the unit of classical information trit of ternary computers. Note, however, that not all 3-level quantum systems are qutrits.[7] The term “qu-d-it” (quantum d-git) denotes the unit of quantum information that can be realized in suitable d-level quantum systems.[8]

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.

In a paper entitled “Solid-state quantum memory using the 31P nuclear spin”, published in the October 23, 2008, issue of the journal Nature,[9] 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.[10] 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.[11]

Here is the original post:

Qubit – Wikipedia

- For a Split Second, a Quantum Computer Made History Go ... - May 13th, 2019
- Noisy Quantum Computers Could Be Good for Chemistry Problems ... - April 11th, 2019
- What is a Quantum Computer? - Definition from Techopedia - April 11th, 2019
- What Is a Quantum Computer? | JSTOR Daily - April 11th, 2019
- Measuring Quantum Computer Power With IBM Quantum Volume ... - April 9th, 2019
- Explainer: What is a quantum computer ... - March 24th, 2019
- What Can We Do with a Quantum Computer? | Institute for ... - March 7th, 2019
- Quantum computer | computer science | Britannica.com - January 10th, 2019
- IBMs new quantum computer is a symbol, not a breakthrough - January 9th, 2019
- IBM unveils the world's first quantum computer that ... - January 9th, 2019
- Were Close to a Universal Quantum Computer, Heres Where We're At - November 28th, 2018
- Schrdinger's Killer App: Race to Build the World's First ... - August 7th, 2018
- How Quantum Computers Work - May 3rd, 2018
- This is what a 50-qubit quantum computer looks like - January 15th, 2018
- Inside Microsofts quantum computing world | InfoWorld - January 1st, 2018
- Microsoft Takes Path Less Traveled to Build a Quantum ... - December 13th, 2017
- Researchers create new type of quantum computer | Harvard Gazette - December 12th, 2017
- Microsoft releases quantum computing development kit preview ... - December 12th, 2017
- Intel moves towards production quantum computing with new 17 ... - October 11th, 2017
- Quantum computer a possibility in 10 years - News.com.au - NEWS.com.au - September 7th, 2017
- Scientists Propose a New Kind of Quantum Computer, But What ... - Gizmodo - September 7th, 2017
- Quantum detectives in the hunt for the world's first quantum computer - Phys.Org - September 7th, 2017
- Scientists Just Found A Use For The Hashtag In Quantum Computing - Gizmodo Australia - September 4th, 2017
- The Future of AI: From Quantum Computing to the Internet of Things - Outer Places - September 4th, 2017
- We're About to Cross The 'Quantum Supremacy' Limit in Computing - ScienceAlert - September 2nd, 2017
- Explaining the Most Recent Record for Quantum Computing: A 51-Qubit Quantum Computer Array - All About Circuits - September 2nd, 2017
- USRA Upgrades D-Wave Quantum Computer to 2000 Qubits - insideHPC - September 1st, 2017
- Quantum encrypted box hints at unhackable communication - Wired.co.uk - September 1st, 2017
- Quantum Computer Programming: What You Need to Learn to Get ... - TrendinTech - September 1st, 2017
- Google's John Martinis Believes Quantum Computing Threat to Be Long Way Off - Bitcoin News (press release) - August 31st, 2017
- Australian quantum computing outfit goes commercial - Networks Asia - August 31st, 2017
- Elusive Majorana Particle Takes Major Step Towards Quantum Computing - IEEE Spectrum - August 29th, 2017
- Australia gets quantum computing company - ACS (registration) - August 28th, 2017
- Quantum Computing and Financial Trading - LeapRate - August 28th, 2017
- Russians Lead the Quantum Computer Race With 51-Qubit Machine - Edgy Labs (blog) - August 28th, 2017
- Bitcoin vs. The NSAs Quantum Computer Bitcoin Not Bombs - August 26th, 2017
- qBitcoin: A Way of Making Bitcoin Quantum-Computer Proof? - IEEE Spectrum - August 26th, 2017
- Hype and cash are muddying public understanding of quantum ... - Phys.Org - August 26th, 2017
- Silicon Quantum Computing launched to commercialise UNSW ... - ZDNet - August 23rd, 2017
- IEEE Approves Standards Project for Quantum Computing ... - Business Wire (press release) - August 23rd, 2017
- Introducing Australia's first quantum computing hardware company - CIO Australia - August 23rd, 2017
- What is quantum computer? - Definition from WhatIs.com - August 22nd, 2017
- Hype and cash are muddying public understanding of quantum computing - The Conversation AU - August 22nd, 2017
- Finns chill out quantum computers with qubit refrigerator to cut out errors - ZDNet - August 22nd, 2017
- UNSW joins with government and business to keep quantum computing technology in Australia - The Australian Financial Review - August 22nd, 2017
- 'Tools of DESTRUCTION' Quantum computers WILL wreak havoc ... - Express.co.uk - August 19th, 2017
- Quantum computing comes of age - Alphr - August 14th, 2017
- No, Quantum Teleportation Won't Let Us Send Instant Messages to Alpha Centauri - Air & Space Magazine - August 12th, 2017
- Google on track for quantum computer breakthrough by end of ... - August 11th, 2017
- Closing In On Quantum Computing | WIRED - August 11th, 2017
- World's Leading Physicist Says Quantum Computers Are Tools of Destruction, Not Creation - Futurism - August 10th, 2017
- Will you be able to trust a quantum computer? - Digital Journal - August 9th, 2017
- New Methods of Controlling Electrons Could be Major in Quantum Computing - TrendinTech - August 5th, 2017
- Exactly what could quantum computers do? - Electronics Weekly - August 4th, 2017
- What is quantum computing and why does the future of Earth depend on it? - Alphr - August 2nd, 2017
- The Age of Quantum Computers is upon us! - Gizbot - August 2nd, 2017
- Ultracold molecules hold promise for quantum computing | MIT News - MIT News - August 1st, 2017
- Clarifiying complex chemical processes with quantum computers - Phys.Org - August 1st, 2017
- When Will Quantum Computers Be Consumer Products? - Futurism - August 1st, 2017
- Quantum Computers Just Moved a Step Closer to Reality - NBCNews.com - August 1st, 2017
- A New Breakthrough in Quantum Computing is Set to Transform Our ... - Futurism - August 1st, 2017
- Quantum computers compete for supremacy - Salon - July 10th, 2017
- Quantum Computers Compete for "Supremacy" - Scientific American - July 5th, 2017
- Less is more for Canadian quantum computing researchers - ITworld - July 4th, 2017
- New method could enable more stable and scalable quantum ... - Phys.Org - July 4th, 2017
- Volkswagen buys D-Wave quantum computers which sell for $15 million each - Robotics and Automation News (press release) (registration) - July 2nd, 2017
- 6 Things Quantum Computers Will Be Incredibly Useful For - Singularity Hub - July 1st, 2017
- Quantum Machine Learning Computer Hybrids at the Center of New Start-Ups - TrendinTech - June 20th, 2017
- Israel Enters Quantum Computer Race, Placing Encryption at Ever-Greater Risk - Sputnik International - June 20th, 2017
- Prototype device enables photon-photon interactions at room ... - Phys.Org - June 20th, 2017
- The Quantum Computer Factory That's Taking on Google and IBM - WIRED - June 20th, 2017
- Toward optical quantum computing - MIT News - June 17th, 2017
- Get ahead in quantum computing AND attract Goldman Sachs - eFinancialCareers - June 16th, 2017
- KPN CISO details Quantum computing attack dangers - Mobile World Live - June 16th, 2017
- Quantum Computing Technologies markets will reach $10.7 billion by 2024 - PR Newswire (press release) - June 14th, 2017
- From the Abacus to Supercomputers to Quantum Computers - Duke Today - June 13th, 2017
- Quantum Computers Will Analyze Every Financial Model at Once - Singularity Hub - June 13th, 2017
- Are Enterprises Ready to Take a Quantum Leap? - IT Business Edge - June 13th, 2017
- Scientists May Have Found a Way to Combat Quantum Computer Blockchain Hacking - Futurism - June 13th, 2017
- Microsoft and Purdue work on scalable topological quantum computer - Next Big Future - June 13th, 2017

## Recent Comments