Observation of Time-Invariant Coherence in a Nuclear Magnetic Resonance Quantum Simulator.

The ability to live in coherent superpositions is a signature trait of quantum systems and constitutes an irreplaceable resource for quantum-enhanced technologies. However, decoherence effects usually destroy quantum superpositions. It was recently predicted that, in a composite quantum system exposed to dephasing noise, quantum coherence in a transversal reference basis can stay protected for an indefinite time. This can occur for a class of quantum states independently of the measure used to quantify coherence, and it requires no control on the system during the dynamics. Here, such an invariant coherence phenomenon is observed experimentally in two different setups based on nuclear magnetic resonance at room temperature, realizing an effective quantum simulator of two- and four-qubit spin systems. Our study further reveals a novel interplay between coherence and various forms of correlations, and it highlights the natural resilience of quantum effects in complex systems.

Engineering of an all-heteronuclear 5-qubit NMR quantum computer.

The realization of an all-heteronuclear 5-qubit nuclear magnetic resonance quantum computer is reported, from the design and synthesis of a suitable molecule through the engineering of a prototype 6-channel probe head. Full control over the quantum computer is shown by a benchmark experiment.

Control aspects of quantum computing using pure and mixed states.

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

Nuclear-magnetic-resonance quantum calculations of the Jones polynomial.

The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation, however, involves many known experimental challenges. Here we present experimental results for small-scale approximate evaluation of the Jones polynomial by nuclear magnetic resonance (NMR); in addition, we show how to escape from the limitations of NMR approaches that employ pseudopure states. Specifically, we use two spin-1/2 nuclei of natural abundance chloroform and apply a sequence of unitary transforms representing the trefoil knot, the figure-eight knot, and the Borromean rings. After measuring the nuclear spin state of the molecule in each case, we are able to estimate the value of the Jones polynomial for each of the knots.

Spins swing like pendulums do: an exact classical model for TOCSY transfer in systems of three isotropically coupled spins 1/2.

An exact correspondence is found between the quantum dynamics of three isotropically coupled spins 1/2 and the dynamics of three coupled classical oscillators. This correspondence is demonstrated by experimentally simulating the polarization transfer functions of an isotropic mixing TOCSY experiment with a set of mechanically coupled pendulums. The extend to which the exact correspondence holds is analyzed and it is shown that it breaks down for systems consisting of more than three coupled spins.