Qubit
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- A qubit is not to be confused with a cubit, which is an ancient measure of length.
A quantum bit, or qubit (sometimes qbit) is a unit of quantum information. That information is described by a state in a 2-level quantum mechanical system which is formally equivalent to a two-dimensional vector space over the complex numbers. The two basis states (or vectors) are conventionally written as <math>|0 \rangle </math> and <math>|1 \rangle </math> (pronounced: 'ket 0' and 'ket 1') as this follows the usual bra-ket notation of writing quantum states. Hence a qubit can be thought of as a quantum mechanical version of a classical data bit. A pure qubit state is a linear quantum superposition of those two states. This means that each qubit can be represented as a linear combination of <math>|0 \rangle </math> and <math>|1 \rangle</math>:
- <math>| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle,\,</math>
where α and β are probability amplitudes and can in general be complex. α and β are constrained by the equation
- <math>| \alpha |^2 + | \beta |^2 = 1. \,</math>
The probability that the qubit will be measured in the state <math>|0 \rangle </math> is <math>| \alpha |^2</math> and the probability that it will be measured in the state <math>|1 \rangle</math> is <math>| \beta |^2</math>. Hence the total probability of the system being observed in either state <math>|0 \rangle </math> or <math>|1 \rangle </math> is 1.
In general therefore an indivdual qubit is in a superposition of both the <math>|0 \rangle </math> and the <math>|1 \rangle </math> states. Measurement of the qubit will collapse this superposition in to one or other of the states with the probability discussed above. This is significantly different from the state of a classical bit, which can only take the value 0 or 1.
When qubits are used in a quantum computation the computation must be carried out a number of times such that the appropriate answer is obtained. This is due to the superposition of states that qubit is in; each measurement will give an answer in line with the probabilities associated with each basis state. In order to be confident of the answer obtained, we merely perform the calculation many times and observe the distribution of results.
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 quantum superpositions of different binary strings (01010 and 11111, for example) simultaneously. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer. The use of entanglement in quantum computing has been referred to as "quantum parallelism", and offers a possible explanation for the power of quantum computing: because the state of the computer can be in a quantum superposition of many different classical computational paths, these paths can all proceed concurrently.
A number of qubits taken together is a qubit register. Quantum computers perform calculations by manipulating qubits.
Similarly, a unit of quantum information in a 3-level quantum system is called a qutrit, by analogy with the unit of classical information trit. The term "Qudit" is used to denote a unit of quantum information in a d-level quantum system.
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. Schumacher is also credited with inventing the term qubit.
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. An n-qubit register space has 2n+1 − 2 degrees of freedom. This is much larger than 2n, which is what one would expect classically with no entanglement.
External links
- An update on qubits in the Jan 2005 issue of Scientific American
- An update on qubits in the Oct 2005 issue of Scientific American
- The organization cofounded by one of the pioneers in quantum computation, David Deutsch
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