Qubits definition

Figure 7.17 (a) Magnetic properties of [LaTb] and [Tb2] in the form of yT versus T plot per mole of Tb(lll). (b) Schematic representation of the qubit definition, weak coupling and asymmetry, as derived from magnetic and heat capacity data. 

In this chapter, we focus on the use of lanthanides as spin-based hardware for QC. The remainder of this introductory section provides some essential concepts and definitions and then it succinctly describes some of the existing proposals for QC. The second section provides a brief overview of results obtained with spin-based systems other than lanthanides. The following two sections review experiments made on qubits and quantum gates, respectively, based on lanthanides, highlighting their specific properties and advantages for QC applications. 

Definition of Qubits, Qugates, Timescales and Essential Requirements... 

A similar study, including detailed EPR experiments, also provides evidence for a proper definition of qubit states at low temperatures for the Er(III) and Ce(III) ions in [LaEr] and [CeY], respectively [139]. 

The studies on [LaTb], [TbLu], [LaEr] and [CeY] established that the individual ions ofthe molecules [Tb2(HL)2(H2L)Cl(py)(H20)] and [CeEr(HL)2(H2L)(N03) (py)(H20)] exhibit isolated, well-defined ground state doublets, thus leading to proper definitions of qubit states. The next step is to prove the existence of a weak coupling within each molecule conducive to the appropriate energy level spectrum for the realization of quantum gate operations. 

Lanthanide ions offer several salient properties that make them especially attractive as qubit candidates (i) their magnetic states provide proper definitions of the qubit basis (ii) they show reasonably long coherence times (iii) important qubit parameters, such as the energy gap AE and the Rabi frequency 2R, can be chemically tuned by the design of the lanthanide co-ordination shell and (iv) the same molecular structure can be realized with many different lanthanide ions (e.g. with or without nuclear spin), thus providing further versatility for the design of spin qubits or hybrid spin registers. 

Other simple codes exist such as the phase flip code, which protects information against phase flip (see below for the definition of the phase flip) and can be simply derived from the bit flip code. Merging these two codes, Peter Shor proposed a code which protects one qubit of information against the action of arbitrary single qubit errors (bit and phase flips) this code involves nine physical qubits and shows the same schematic structure as the previous example. Its publication renewed the interest of physicists for the domain and gave hope that quantum errors are correctable. 

Many systems are being studied to manipulate quantum information. Some make use of individual atoms cold trapped ions, neutral atoms in optical lattices, atoms in crystals. Other involve particle spins or photons in cavity QED or nonlinear optical setups as well as more exotic ones where geometric combinations of elementary excitations are defined as qubits, such as in topological quantum computing [8]. However, none of these systems has yet emerged as a definitive way to build a quantum information processor. A reason for this is that there is an essential dichotomy we need... 

It is important to notice that the definition of entanglement for mixed states is more complicated than for pure states. Whereas product states are always non-entangled pure states, the same is not true for mixed states [15]. For a two-partite system, an non-entangled mixed state p is characterized by the existence of a set of probabilities [pi and one-qubit density matrices p, plfi such that one can write ... 

---