Qubit

[1] In the acknowledgments of his 1995 paper, Schumacher states that the term qubit was created in jest during a conversation with William Wootters.

A binary digit, characterized as 0 or 1, is used to represent information in classical computers.

Alternatively and equivalently, the value stored in a qubit can be described as a single point in a 2-dimensional complex coordinate space.

Similarly, a set of n qubits, which is also called a register, requires 2n complex numbers to describe its superposition state vector.

[3][4]: 7–17 [2]: 13–17 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).

, together called the computational basis, are said to span the two-dimensional linear vector (Hilbert) space of the qubit.

For example, two qubits could be represented in a four-dimensional linear vector space spanned by the following product basis states:

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

When we measure this qubit in the standard basis, according to the Born rule, the probability of outcome

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 global phase of the state

[7][b] The possible quantum states for a single qubit can be visualised using a Bloch sphere (see picture).

This state space has two local degrees of freedom, which can be represented by the two angles

a coherent superposition, represented by a point on the surface of the Bloch sphere as described above.

, it maps the basis states as follows: A common application of the CNOT gate is to maximally entangle two qubits into the

Quantum computers perform calculations by manipulating qubits within a register.

[10] A qubit register that can be measured to N states is identical to an N-level qudit.

A rarely used[11] synonym for qudit is quNit,[12] since both d and N are frequently used to denote the dimension of a quantum system.

Qudits are similar to the integer types in classical computing, and may be mapped to (or realized by) arrays of qubits.

Qudits where the d-level system is not an exponent of 2 cannot be mapped to arrays of qubits.

In 2017, scientists at the National Institute of Scientific Research constructed a pair of qudits with 10 different states each, giving more computational power than 6 qubits.

[14] In the same year, researchers at Tsinghua University's Center for Quantum Information implemented the dual-type qubit scheme in trapped ion quantum computers using the same ion species.

[15] Also in 2022, researchers at the University of California, Berkeley developed a technique to dynamically control the cross-Kerr interactions between fixed-frequency qutrits, achieving high two-qutrit gate fidelities.

This is analogous to the unit of classical information trit of ternary computers.

[18] Besides the advantage associated with the enlarged computational space, the third qutrit level can be exploited to implement efficient compilation of multi-qubit gates.

Several physical implementations that approximate two-level systems to various degrees have been 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 2008 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.

In 2013, 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.