Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Quantum decoherence and quasi-equilibrium in open quantum systems with few degrees of freedom: application to 1H NMR of nematic liquid crystals

Explanation of decoherence and quasi-equilibrium in systems with few degrees of freedom demands a deep theoretical analysis that considers the observed system as an open quantum system. In this work, we study the problem of decoherence of an observed system of quantum interacting particles, coupled to a quantum lattice. Our strategy is based on treating the environment and the system-environment Hamiltonians fully quantum mechanically, which yields a representation of the time evolution operator useful for disentangling the different time scales underlying in the observed system dynamics. To describe the possible different stages of the dynamics of the observed system, we introduce quantum mechanical definitions of essentially isolated, essentially adiabatic, and thermal-contact system-environment interactions. This general approach is then applied to the study of decoherence and quasi-equilibrium in proton nuclear magnetic resonance ((1)H NMR) of nematic liquid crystals. A summary of the original results of this work is as follows. We calculate the decoherence function and apply it to describe the evolution of a coherent spin state, induced by the coupling with the molecular environment, in absence of spin-lattice relaxation. By assuming quantum energy conserving or non-demolition interactions, we identify an intermediate time scale, between those controlled by self-interactions and thermalization, where coherence decays irreversibly. This treatment is also adequate for explaining the buildup of quasi-equilibrium of the proton spin system, via the process we called eigen-selectivity. By analyzing a hypothetical time reversal experiment, we identify two sources of coherence loss which are of a very different nature and give rise to distinct time scales of the spin dynamics: (a) reversible or adiabatic quantum decoherence and (b) irreversible or essentially adiabatic quantum decoherence. Local irreversibility arises as a consequence of the uncertainty introduced by the coupling with an infinite quantum environment. The reversible part can be represented by a semiclassical model, similar to standard line-shape adiabatic models. By exploiting the separation existing between the time scales of the spin coherences and the irreversible decoherence, we present a novel technique to obtain the orientational molecular distribution function for a nematic liquid crystal. The procedure is based on the comparison of the observed coherence time evolution and numerical calculation under the adiabatic quantum decoherence approach. As an example, it is used the experimental free induction decay from a nematic PAA(d6) sample to extract such an orientational distribution. This is the first theoretical description of the experimental liquid crystal NMR signal in the time domain. On the contrary, the irreversible decoherence is intrinsically full-quantum mechanical, as it is governed by the commutation properties of the environment and the spin-lattice Hamiltonians. Consistently, it depends on the molecular correlation in a decisive way, since it vanishes under a mean-field model for the molecular dynamics. The results of this work can contribute to the understanding of the open question of the applicability of the spin-temperature concept in spin systems with few degrees of freedom.

Pseudopure state of a twelve-spin system

Pseudopure states of a system of twelve interacting spins are experimentally demonstrated. The system is a cluster of dipolar-coupled nuclear spins of fully labeled (13)C(6)-benzene in a liquid crystalline matrix. At present, this is the largest and the most complex composite system where individual quantum states have been addressed.

Use of non-adiabatic geometric phase for quantum computing by NMR

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.