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Introduction to Quantum Computing and Quantum Information - What is a qubit ?

Aravind Babu N.
04 Aug 0 0

The classical two-state system can have two possible states either 1 or 0 whereas a qubit can be in a superposition between 0 and 1

Qubit is generically represented as liner superposition of basis states

                        |Ψ> = α|0>+β|1>

      Where alpha and beta are amplitudes(complex)

                       |α|2 +|β|2 = 1

Properties of qubit

Superposition & quantum parallelism

The main implication of states like that of equation (above) is that a single state contains the potential

for the system to be in either basis state. In some sense, the system, say an electron characterized by its spin value, simultaneously exists in both states until measured. Physically this does not seem to make sense to our classical minds unless we say that the electron has not decided which of the two possible states it should be in, until forced into one of them by measurement. This feature is exploited in quantum computation to implement what is called quantum parallelism: an operation that acts on a bit can now simultaneously act on both possible values of the bit if the input is a qubit in a quantum superposition.

 

Size of Computational space

If we want to do an n-bit computation, Classically the “space" available for computation is of size n. In terms of a quantum system of n qubits, the number of possible basis states is 2n, and this is the size of the space available for computation. The size of the space of states available for computation grows exponentially with the number of bits. This is the power we wish to exploit in quantum computation.

 

Entanglement and quantum correlation

Multiple qubit systems can exist in superposition states that are known as entangled states. These states possess intrinsic correlations between the component systems that are different from classical correlations. These correlations can survive even if the component systems are taken physically far apart from each other. For example, 2-qubit states are in general linear superpositions of |00>, |01>, |10> and |11>. Look at the state |00> + |11>. In such a state, the first and second systems are correlated quantum mechanically: the value of the second qubit is always equal to that of the first qubit, irrespective of what measurement we make on which bit and when. Such a state is called “entangled" because of this correlation. Quantum correlations can be exploited to generate new methods of processing, increasing the efficiency by allowing controlled operations to be performed. These correlations are an invaluable resource in quantum information theory, and we will see their basic applications in quantum state teleportation and secure information transfer over a distance.

 

Measurement and state collapse

Though a qubit could exist in a superposition of basis states, a measurement of the qubit would give one of the two basis states alone. Measurement of a quantum system causes it to collapse into one of the basis states, which destroys the superposition, including any information that may be encoded in the probability amplitudes. Some authors express this property as a qubit existing in a superposition not having a definite state. Measurement results can be predicted with 100% certainty in definite" states, and the system exists in a basis state. When a system is not in a definite state, measurement disturbs the system and one can never know the original state exactly. It is a quantitative and in-depth study of quantum measurements that has uncovered new laws of quantum information.

Unitary evolution and reversibility

Quantum dynamical laws governing the evolution of an isolated quantum system are what are known as unitary evolutions. Thus, the functioning of a quantum computer is necessarily via unitary transformations of the initial quantum state. Unitary operations are fully reversible and, from a large body of study on the energetics of computation, are said to lead to greater energy efficiency.

No cloning theorem

This is another peculiar property of generic quantum state: quantum states that are not basis states cannot be perfectly cloned or copied. The fact that classical states can be copied and kept aside for further processing is often taken for granted. When implementing a function in a classical circuit, we often send copies of a certain input to different parts of the circuit. Such an operation is no longer possible in quantum computing. This changes the way we look at a quantum computation. And on the upside, this also makes it possible to exchange information securely since tapping a quantum line disturbs the system irrevocably

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