Spin-based qubits

Lanthanide ions have emerged as a very promising category of chemically accessible realizations of spin-based qubits. Their suitability for this task, which results from their physical, chemical and quantum mechanical properties, is discussed in the following sections. 

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. 

Gershenfeld and Chuang s two-qubit system [101] uses an NMR machine and the protons in 25. They demonstrated a nonlinear interaction between spins, a prerequisite for quantum logic gates. This was realized through the controlled-NOT operation (CNOT) which conditionally flips one spin based on the value of another [102], This gate can be considered as a quantum XOR gate. 

The final section deals with known examples of molecular spin qubits based on lanthanide SIMs. Distinction is made between single-qubit molecules and molecules which embody more than one qubit. This section includes some comments about decoherence in these molecular systems and strategies to control it. 

J., van Slageren, J., Coronado, E. and Luis, F. (2012) Gd-based single-ion magnets with tunable magnetic anisotropy molecular design of spin qubits. Phys. Rev. Lett., 108, 247213. 

Baldovi, J.J., Cardona-Serra, S., Clemente-Juan, J.M., Coronado, E., Gaita-Arino, A. and Palii, A. (2012) Rational design of single ion magnets and spin qubits based on mononuclear lanthanide complexes. Inorg. Chem., 51, 12565-12574. 

H. (2013) Coherent manipulation of spin qubits based on polyoxometa-lates the case of the single ion magnet [GdW30P5On0]14-. Chem. Commun.,... 

Finally, a physical application to the rubidium atom has been suggested. One qubit of information is encoded on the spin states of the atom whereas the orbital part plays the role of the ancilla. A realistic physical setting has been considered in particular, we have suggested a projection process based on the spontaneous emission. 

To create a quantum computation system based on a qubit ensemble and to decrease the required magnetic field and its gradient the modification of the cluster structure was proposed [1,2]. It consists in utilization of nuclear spin chains on the steps of the silicon surface which serve as the qubit ensemble. Resonance frequencies of a magnetic isotope nucleus 29Si are divided between neighboring chains. In this case the efficiency of quantum computation is determined by the decoherence rate for a quantum state. The decoherence rate depends on the number of nucleus in a qubit and on the time of transverse relaxation of nuclear spin polarization. The aim of the present work is calculation of the decoherence rate of the quantum state of the qubit ensemble built on the basis of these nuclei. 

The decoherence rate calculated for the 29Si atom chain is limited by quantum coherence order at a fixed number of spins in the chain. It is decreasing from 14 to 1 ms 1 with the decrease of the number of atoms in the chain from 800 to 10. The range of ratio of decoherence and relaxation rates narrows significantly from 0.3 to 0.005 when the number of atoms in the chain increases from 10 to 800. Therefore, a choice of the decoherence rate may be based on measuring possibility of the quantum qubit state. It was shown that the decoherence rate for magnetic isotope 29Si is smaller than the relaxation rate for nuclear polarization in the qubit chains. 

Cold gases of polar molecules can be used to construct in a natural way a complete toolbox for any permutation symmetric two spin-1 /2 (qubit) interaction, based on techniques of interaction engineering discussed in the previous sections. 

Various schemes for hybrid quantum processors based on molecular ensembles as quantum memories and optical interfaces have been proposed. In Ref. [17], a hybrid quantum circuit using ensembles of cold polar molecules with solid-state quantum processors is discussed. As described above, the quantum memory is realized by collective spin states (ensemble qubit), which are coupled to a high-Q stripline cavity via microwave Raman processes. This proposal combines both molecular ensemble and stripline resonator ideas. A variant of this scheme using collective excitations of rotational and spin states of an ensemble of polar molecules prepared in a dipolar... 

In order to conclude this brief discussion on the NMR implementations of qubits, let us mention the direct dipolar coupled spins. This spin system is becoming quite important in NMR QIP, since many of the candidate approaches to produce scalable NMR quantum computers (see Chapter 7), are based on spin 1 /2 systems in solid-state materials, where... 

We propose a nuclear spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that a MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids (a) preparation of the ground-state, (b) one- and two-qubit quantum logic gates, and (c) a measurement of the final state. — G.P. Berman, G.D. Doolen, RC. Hammel, V.L Tsifrinovich [Rhys. Rev. B 61 (2000) 14694]... 

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]. 

FIGURE 2 Diagram of a silicon-based quantum computer architecture. Single nuclear spins are the qubits mobile electrons are used to manipulate the nuclear-spin states and move quantum information within the computer. Voltage pulses applied to metal gates on the top of the structure control the positions of electrons inside the silicon. 

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