NMR quantum computation

Here we will focus on electron spin qubits and thus we will not be discussing NMR quantum computing, where molecules played a key role in the early successes of quantum information processing. 

As of this writing, 3-, 5- and 7-qubit NMR quantum computers have been realized. The latter is capable of carrying out Shor s algorithm to factor the number 15, thus equalling the computational ability of a first-grade elementary school student. 

So we have defined mixed states. How are they used in NMR quantum computation in the liquid state ... 

R394 J. A. Jones, NMR Quantum Computation , Los Alamos Natl. Lab., Prepr. Arch., Quantum Phys., [preprint] 1 Sep. 2000, 1, arXiv quant-ph/ 0009002, URL http //xxx.lanl.gOv/pdf/quant-ph/0009002... 

The enormous improvement in the nuclear spin polarization achievable by these optical approaches has great potential to impact conventional NMR smdies in a variety of ways. Besides simply increasing the detection sensitivity of NMR, the enhanced nuclear spin polarization may be useful for obtaining enhanced spectral selectivity (e.g., for some spatial, structural, or dynamical feature of a sample) enhanced contrast and resolution in MRI and improved density matrix purity (e.g., for NMR quantum computation). Finally, it is worth noting that the optical fields used in some of these methods can be gated, thereby permitting time-resolved studies that would not be possible with conventional NMR approaches. 

Cory, Introduction to NMR Quantum Information Processing , p. 411 R 281 Y. Yamamoto, T.D. Ladd, J.R. Goldman and F. Yamaguchi, Solid-State Crystal Lattice NMR Quantum Computation , p. 441... 

HP xenon has also been used to enhance the polarization of a two-qubit NMR quantum computer using the C-enriched chloroform.Using the SPINOE transfer mechanism, this approach led to a polarization enhancement of the chloroform that was approximately 10 times the thermal values for H and Temporal spin-labeling methods along with measurements of the deviation density matrix were used to observe the formation of a pure spin state. The authors then demonstrated their approach by implementing a 2-qubit Grover s search algorithm. 

The use of a rubidium-xenon polarization unit has enabled the measurement of both Rb and Xe polarization. Three-dimensional Rb NMR imaging has been applied to pig hearts. Cs chemical shifts have been studied in binary melts of Cs+/M+-[02CCF3]- M = Li+, Na+, K+, Tl+. JC Cs F) = 54.9 Hz has been observed in the Cs+ complex of (4). Cs NMR spectra of the liquid crystalline medium have been examined for NMR quantum computing. NMR data have also been reported for potassium hydrido iodide,... 

Mawhiimey and Schreckenbach performed the relativistic DFT ZORA calculations to obtain theoretical results for chemical shifts and spin-spin coupling constants in compoimds currently used in NMR quantum computing experiments. The quantum computors demand the general design criteria that (1) the differences in chemical shifts of the nuclei should be as large as possible and (2) spin spin coupling between nuclei should be large. 

The first concrete proposal for a NMR scalable quantum computer was made by Kane in 1998 [32], He showed that an array of atoms (nuclear spin 1/2) embedded in a Silicon lattice, with the hyperfine field and interaction between nuclei controlled by electric gates, could work as a scalable NMR quantum computer. Difficulties with Kane original approach were raised by Koiller and co-workers [33], Afterwards, Skinner, Davenport and Kane [34] proposed an alternative scheme in which such difficulties could be circumvented. 

A very interesting proposal using Magnetic Resonance Force Microscopy (MRFM) was made by Berman and co-workers in 2000 [35], In that paper it is shown that through single-spin electron measurement and electron-nucleus hyperfine coupling, NMR quantum computation could be implemented, including the steps of initial state preparation, unitary transformations and final readout. 

In 2002, Ladd and co-workers [36] proposed an architecture for a Silicon scalable quantum computer. In this scheme, arrays of Si atoms (nuclear spin 1 /2) lay on the steps of a Si superlattice (nuclear spin zero). The NMR frequencies are determined by a magnetic field gradient generated by a Dy-based micromagnet, and spin-spin interactions by the dipole fields. Upon initial polarization beyond a threshold, the scheme becomes scalable and could be used in a NMR quantum computer. 

L.M.K. Vandersypen, C.S. Yannoni, I.L. Chuang, Liquid state NMR quantum computing, in D.M. Grant, R.K. Harris (Eds.), Encyclopedia of Nuclear Magnetic Resonance (John Wiley Sons, Chichester, 2002), pp. 687-397. 

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... 

---