Everything about Qubit totally explained
:
A qubit isn't to be confused with a cubit, which is an ancient measure of length.
A
quantum bit, or
qubit (sometimes
qbit) ['kju.bɪt]
or [k'bɪt] is a unit of
quantum information. That
information 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.
Benjamin Schumacher discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a state, and storing the information on a smaller number of states. This is now known as Schumacher compression. In the acknowledgments of his paper (Phys. Rev. A 51, 2738), Schumacher states that the term qubit was invented in jest, during his conversations with
Bill Wootters.
Bit versus qubit
A
bit is the base of computer information. Regardless of its physical representation, it's always read as either a 0 or a 1. An analogy to this is a light switch–the down position can represent 0 (normally equated to
off) and the up position can represent 1 (normally equated to
on).
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.
Representation
The states a qubit may be measured in 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').
The French
Commissariat à l'Énergie Atomique have created a representation of the superposition.
(External Link
)
Qubit states
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 only lie on one of the poles. An
n-qubit register space has 2
n+1 − 2 degrees of freedom. This is much larger than 2
n, which is what one would expect classically with no
entanglement (for example using the cartesian product instead of the tensor product for combining the qubit states.)
Entanglement
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
»
(Note that in this state, there are equal probabilities of measuring either or .)
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, for example if she measured a
, Bob must measure the same, as
is the only state where Alice's qubit is a
.
Entanglement also allows multiple states (such as are 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 can't 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's unique to quantum computation.
Quantum register
A number of entangled qubits taken together is a
qubit register.
Quantum computers perform calculations by manipulating qubits within a register.
Variations of the qubit
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.
Physical representation
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 (for example, 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.
This is an incomplete list of physical implementation of qubits:
Further Information
Get more info on 'Qubit'.
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