Quantum bits

The classical information unit is the binary digit, or bit. One bit can assume the logical values 0 or 1 . In the computers, bits are physically represented by the presence or absence of electrical currents, travelling through the electronic components inside the chips. The presence of the current indicates that the bit is in the logical state 1 and its absence indicates that the bit is the logical state 0 . Obviously, a bit cannot be at two logical states at the same time [7]. 

Analogously, the unit of information in Quantum Information and Quantum Computation is the quantum bit, or qubit, for short. A qubit can assume the logical values 0 or 1. However, it can also be in a logical state containing any linear combination of them, thanks to laws of quantum mechanics [8], Physically, qubits can be represented by any quantum object with two well defined and distinct eigenstates. Examples of qubits are the photon polarization states, electrons in two-level atoms (as an approximation) and nuclear spins under the influence of a magnetic field. 

The set 0), 11) forms a two dimensional basis in Hilbert s space of one qubit, and is called computational basis. For the case of spin 1/2 particle, the logical state 0 can be represented by the spin up state ( 0) = t ), whereas the logical state 1 can be represented by the spin down state (11) = ),)). Other orthonormal basis can be built from the computational basis, such as - -) and -)  

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The basic element of a quantum computer is the quantum bit or qubit. It is the QC counterpart of the Boolean bit, a classical physical system with two well-defined states. A material realization of a qubit is a quantum two-level system, with energy eigenstates, 0) and 1), and an energy gap AE, which can be in any arbitrary superposition cp) = cos(d/2) 0) + exp(i0)sin(0/2) l).These pure superposition states can be visualized by using a Bloch sphere representation (see Figure 7.1). 

In this equation, C andT refer to control and target qubits, respectively. The resulting state (output of the qugate) is said to be an entangled state of the two qubits, that is, a state that cannot be written as a product of states for each qubit [30]. The occurrence of such entangled states is another characteristic trait of QC, at the basis of secure quantum communication or cryptography. It also implies that, as opposed to what happens with a classical bit, an arbitrary quantum bit cannot be copied (the COPY classical operation is, in fact, based on the application of a succession of classical CNOT gates) [4]. 

Experimental realization of a quantum computer requires isolated quantum systems that act as the quantum bits (qubits), and the presence of controlled unitary interactions between the qubits. As pointed out by many authors [97-99], if the qubits are not sufficiently isolated from outside influences, decoherences can destroy the quantum interferences that actually form the computation. 

Such an entity represents the basic unit of information in a quantum computer—a quantum bit or qubit. Unlike a classical bit, which can store only a single value—a 0 or 1—a qubit can store both 0 and 1 at the same time. The state of a two-qubit register could be written... 

This work has been supported by the Russian Foundation for Basic Research grant 08-02-99042-r-ofi, a grant of the Program "Quantum Nanostructures" of the Presidium of RAS and a grant "Quantum bit on base of micro- and nanostructures with metal conductivity" of the Program "Technology Basis of New Computing Methods" of ITCS department of RAS. 

Keywords Quantum bit, Josephson junction, d-wave superconductors. 

Vandersypen L. M. K. et al., Quantum computing and quantum bits in mesoscopic systems, (Kluwer, New York, 2003). 

The spin-spin relaxation T2, or the experimentally determined phase memory time Tm, is a parameter of interest in molecular magnetism, because it is the time available for a quantum computation. It was recognized several years ago that MNMs may be used to implement quantum bits [137, 138]. There are currently essentially three proposals for using MNMs for quantum information processing [21, 139, 140]. The first is an elaborate scheme to use high-spin MNMs, such as... 

In spite of impressive experimental demonstrations of basic quantum information effects in a number of different mesoscopic solid state systems, such as quantum dots in semiconductor microcavities, cold ions in traps, nuclear spin systems, Josephson junctions, etc., their concrete implementation is still at the proof-of-principle stage [1]. The development of materials that may host quantum coherent states with long coherence lifetimes is a critical research problem for the nearest future. There is a need for the fabrication of quantum bits (qubits) with coherence lifetimes at least three-four orders of magnitude longer than it takes to perform a bit flip. This would involve entangling operations, followed by the nearest neighbor interaction over short distances and quantum information transfer over longer distances. 

This entangled state is named quantum bit or q-bit. It replaces the bits 0 and T of the classical computer. 

The individual unit of classical information is the bit an object that can take either one of two values, say 0 or 1. The corresponding unit of quantum information is the quantum bit or qubit. It describes a state in the simplest possible quantum system [1,2]. The smallest nontrivial Hilbert space is two-dimensional, and we may denote an orthonormal basis for the vector space as 0> and 11 >. A single bit or qubit can represent at most two numbers, but qubits can be put into infinitely many other states by a superposition ... 

Representative SMS spectra of ferropericlase ((Mgo.75,Feo.25)0) as a function of pressure at room temperature (a) [23] and along with a stainless steel (SS) for CS measurements (b). Dots Experimental measurements black lines modeled spectra with the MOTIF program. The quantum bits at 0, 13, and 45 GPa are generated from the QS of the high-spin Fe " " in the sample, whereas the flat feature of the spectra at 70,79, and 92 GPa indicates disappearance of the QS and the occurrence of the low-spin Fe +. 

The superdense coding is a process, in which two bits of classical information are transmitted using only one quantum bit. Here the example of exchange of information between two parties Alice and Bob, is described. Suppose that initially Alice and Bob share qubits in an entangled cat state ... 

Within the past decade much progress has also been made in experimental realizations of quantum computing hardware. Many architectures have been proposed based on a variety of physical hardware. On a small scale, quantum information has been stored and manipulated in superconducting quantum bits (qubits) [4,5], trapped ions [6,7], electron spins [8-11], nuclear spins in the liquid or solid state [12], and other systems. On the theoretical side, new quantum algorithms have recently been found, exhibiting significant pol momial speedups on quantum computers for solution of sparse linear equations or differential equations [13,14], quantum Monte Carlo problems [15], and classical simulated annealing problems [16]. 

Q executes the conditional not on two quantum bits x,y. Therefore, (P gi 2) may entangle qbits qi and Q2. But if qi is entangled to qo, and 2 is entangled to qs, then (P q 2) also entangles qo to <73 This simplistic example shows that the classical binder, A, is not well suited to deal with quantmn bits and more generally with global references. 

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