Quantum Information Processing Using Molecular Nanomagnets As Qubits

Abstract

The idea that the superposition of quantum states could be utilized as a way of performing computation seems, at least on the surface, almost self-contradictory. However in 1994 Shor proposed an algorithm that would allow a quantum computer to factorize numbers much faster than a classical computer, and, shortly afterwards, Grover proposed an algorithm that would lead to much faster database searching with a quantum computer. As a result of these proposals much effort has been expended on finding physical systems that could be used in quantum information processing (QIP). One of the most promising systems—and one where chemists can make a very significant contribution through the synthesis of appropriate molecules—involves using molecular nanomagnets. The initial proposal was made in 2001 by Leuenberger and Loss, when they showed that the Grover algorithm could be implemented using a single molecule of the dodecanuclear manganese cluster [Mn12O12(O2CMe)12(H2O)4]. [4] The physical implementation of the experiment proposed looks extremely challenging. However, this proposal has inspired further schemes to implement QIP with molecular nanomagnets. The majority of these proposals look to implement the Shor algorithm, which is in itself probably more valuable than the Grover algorithm as factorizing large numbers is the method used to encode much data in the modern world using, in general, the RSA code (so named after its inventors Rivest, Shamir, and Adleman). The first proposal to use a molecular system to implement the Shor algorithm came from the Loss group, with further schemes proposed by Troiani et al. The core idea is, at one level, remarkably simple to understand. If a cage complex can be made which has an S= =2 ground state, that spin ground state can be regarded as a two-level system, which is the first criterion for a “qubit”; a “qubit” plays the same role in QIP that a “bit” plays in a classical computer. The two-level system arises from regarding the spin as “up” in one level and “down” in the other. An S= =2 system is a qubit because of superposition of the spin-up/spin-down states. Controlled interaction of the qubits then allows QIP. For QIP to be possible there are several further criteria that have to be met by individual qubits. Firstly, the ground state has to be a “pure” S= =2 state. If there are significant admixtures of higher spin states, then the two-level system is lost, which brings in the second consideration; that the energy gap to the first excited state must be reasonably large. If the gap is too small, other values of S would have to be considered in describing the system. Thirdly, it must be possible to populate one state in preference to the other without inducing significant loss of population to the higher S states. For an S= =2 state this is simply achieved by introducing a magnetic field; Zeeman splitting will lead to this separation and a population increase in the lower energy state. The major advantage electron spin has over nuclear spin is that the electron Zeeman splitting is much larger and hence offers a greater possibility of making usable devices. In principle, many molecules can satisfy these criteria. In practice, studies have thus far been restricted by concerns about the next challenge—described by Stamp as the “most formidable”—which is the problem of decoherence, that is, loss of information stored before it is processed. For QIP to work, the “two-level” system has to encode the information without losing that information to the surroundings. Two major potential sources of decoherence can be foreseen for any molecular system. Interaction between molecules could induce decoherence due to dipolar coupling—essentially one S= =2 qubit interacting in an uncontrolled way with another. Secondly, interaction of the electron spin with nuclear spins within the molecule—the hyperfine interaction—could also induce decoherence. The more atoms (and hence nuclei) a molecule contains, the greater the possibility of hyperfine coupling and hence the faster the decoherence. The rate of decoherence is best quantified by a coherence time, which is essentially equivalent to the spin–spin relaxation time as measured in EPR or NMR spectroscopy. Yet for some time there has been some evidence that decoherence in complex molecules, such as molecular nanomagnets, might not be such a severe problem. Firstly, pulsed electron paramagnetic resonance (EPR) spectroscopy is increasingly used to characterize the active sites of metalloenzymes and other proteins. For this method to work at all, relaxation times must be reasonably long. Secondly, theoretical work from Katsnelson and co-workers suggested that coherence times in a {V15} polyoxometallate (POM) [12] could [*] Prof. R. E. P. Winpenny The Lewis Magnetism Laboratory, The School of Chemistry The University of Manchester Oxford Road, Manchester, M13 9PL (UK) Fax: (+44)161-275-4616 E-mail: richard.winpenny@manchester.ac.uk Highlights