Discrete and continuous systems of logic in nuclear magnetic resonance

We implement several non-binary logic systems using the spin dynamics of nuclear spins in nuclear magnetic resonance (NMR). The NMR system is a suitable test system because of its high degree of experimental control; findings from NMR implementations are relevant for other computational platforms exploiting particles with spin, such as electrons or photons. While we do not expect the NMR system to become a practical computational device, it is uniquely useful to explore strengths and weaknesses of unconventional computational approaches, such as non-binary logic

Quantum Computing

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future.Comment: 26 pages, 7 figures, 291 references. Early draft of Nature 464, 45-53 (4 March 2010). Published version is more up-to-date and has several corrections, but is half the length with far fewer reference

Implementing quantum logic gates with GRAPE: principles and practicalities

We briefly describe the use of GRAPE pulses to implement quantum logic gates in NMR quantum computers, and discuss a range of simple extensions to the core technique. We then consider a range of difficulties which can arise in practical implementations of GRAPE sequences, reflecting non-idealities in the experimental systems used.Comment: 15 pages rspublic including 4 figures. This is the original manuscript preprint form which differs slightly from the final accepted version (Phil Trans Roy Soc A in press

Geometric quantum computation with NMR

The experimental realisation of the basic constituents of quantum information processing devices, namely fault-tolerant quantum logic gates, requires conditional quantum dynamics, in which one subsystem undergoes a coherent evolution that depends on the quantum state of another subsystem. In particular, the subsystem may acquire a conditional phase shift. Here we consider a novel scenario in which this phase is of geometric rather than dynamical origin. As the conditional geometric (Berry) phase depends only on the geometry of the path executed it is resilient to certain types of errors, and offers the potential of an intrinsically fault-tolerant way of performing quantum gates. Nuclear Magnetic Resonance (NMR) has already been used to demonstrate both simple quantum information processing and Berry's phase. Here we report an NMR experiment which implements a conditional Berry phase, and thus a controlled phase shift gate. This constitutes the first elementary geometric quantum computation.Comment: Minor additions at request of referees. 4 pages revtex including 2 figures (1 eps). Nature in pres