Fundamental units of information |
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In quantum computing, a qubit (pronounced /ˈkʲuːbɪt/) or quantum bit is a unit of quantum information —the quantum analogue of the classical bit —with additional dimensions associated to the quantum properties of a physical atom. The physical construction of a quantum computer is itself an arrangement of entangled atoms, and the qubit represents both the state memory and the state of entanglement in a system. A quantum computation is performed by initializing a system of qubits with a quantum algorithm —"initialization" here referring to some advanced physical process that puts the system into an entangled state.
The qubit is described by a state vector in a two-level quantum-mechanical system, which is formally equivalent to a two-dimensional vector space over the complex numbers.
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A bit is the basic unit of computer information. Regardless of its physical realization, a bit is always understood to be either a 0 or a 1. An analogy to this is a light switch— with the off position representing 0 and the on position representing 1.
A qubit has some similarities to a classical bit, but is overall very different. Like a bit, a qubit can have two possible values—normally a 0 or a 1. The difference is that whereas a bit must be either 0 or 1, a qubit can be 0, 1, or a superposition of both.
The states in which a qubit may be measured are known as basis states (or vectors). As is the tradition with any sort of quantum states, Dirac, or bra-ket notation is used to represent them. This means that the two computational basis states are conventionally written as and (pronounced "ket 0" and "ket 1").
A pure qubit state is a linear superposition of those two states. This means that the qubit can be represented as a linear combination of and :
where α and β are probability amplitudes and can in general both be complex numbers.
When we measure this qubit in the standard basis, the probability of outcome is and the probability of outcome is . Because the absolute squares of the amplitudes equate to probabilities, it follows that α and β must be constrained by the equation
simply because this ensures you must measure either one state or the other.
The state space of a single qubit register can be represented geometrically by the Bloch sphere. This is a two-dimensional space which has an underlying geometry of the surface of a sphere. This essentially means that the single qubit register space has two local degrees of freedom. Represented on such a sphere, a classical bit could lie on only one of the poles.
An important distinguishing feature between a qubit and a classical bit is that multiple qubits can exhibit quantum entanglement. Entanglement is a nonlocal property that allows a set of qubits to express higher correlation than is possible in classical systems. Take, for example, two entangled qubits in the Bell state
In this state, called an equal superposition, there are equal probabilities of measuring either or , as .
Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtaining—with equal probabilities—either or . Because of the qubits' entanglement, Bob must now get the exact same measurement as Alice; i.e., if she measures a , Bob must measure the same, as is the only state where Alice's qubit is a .
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.
A number of entangled qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits within a register. A qubyte is a collection of eight entangled qubits. It was first demonstrated by a team at the Institute of Quantum Optics and Quantum Information at the University of Innsbruck in Austria in December 2005.[1]
Similar to the qubit, a qutrit is a unit of quantum information in a 3-level quantum system. This is analogous to the unit of classical information trit. The term "qudit" is used to denote a unit of quantum information in a d-level quantum system. A quiet qubit refers to a qubit that can be efficiently decoupled from the environment.[2]
Any two-level 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 which 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.
Physical support | Name | Information support | ||
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Single photon (Fock states) | Polarization encoding | Polarization of light | Horizontal | Vertical |
Photon number | Photon number | Vacuum | Single photon state | |
Time-bin encoding | Time of arrival | Early | Late | |
Coherent state of light | Squeezed light | Quadrature | 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 |
In a paper entitled: “Solid-state quantum memory using the 31P nuclear spin,” published in the October 23, 2008 issue of the journal Nature[3], an international team of scientists that included researchers with the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab) reported the first relatively long (1.75 segs.) 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.
The origin of the term qubit is attributed to a paper by Benjamin Schumacher.[4] In the acknowledgments of his paper, Schumacher states that the term qubit was invented in jest (due to its phonological resemblance with an ancient unit of length called cubit), 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.
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