We use NMR quantum simulators to study antiferromagnetic Ising spin chains undergoing quantum phase transitions. Taking advantage of the sensitivity of the systems near criticality, we detect the critical points of the transitions using a direct measurement of the Loschmidt echo. We test our simulators for spin chains of even and odd numbers of spins, and compare the experimental results to theoretical predictions.

We implement an iterative quantum state transfer exploiting the natural dipolar couplings in a spin chain of a liquid-crystal NMR system. During each iteration, a finite part of the amplitude of the state is transferred and, by applying an external operation on only the last two spins, the transferred state is made to accumulate on the spin at the end point. The transfer fidelity reaches one asymptotically through increasing the number of iterations. We also implement the inverted version of the scheme which can transfer an arbitrary state from the end point to any other position of the chain and entangle any pair of spins in the chain, acting as a full quantum data bus.

We demonstrate coherent control of two logical qubits encoded in a decoherence free subspace (DFS) of four dipolar-coupled protons in an NMR quantum information processor. A pseudopure fiducial state is created in the DFS, and a unitary logical qubit entangling operator evolves the system to a logical Bell state. The four-spin molecule is partially aligned by a liquid crystal solvent, which introduces strong dipolar couplings among the spins. Although the system Hamiltonian is never fully specified, we demonstrate high fidelity control over the logical degrees of freedom. In fact, the DFS encoding leads to higher fidelity control than is available in the full four-spin Hilbert space.

This paper describes recent progress using nuclear magnetic resonance (NMR) as a platform for implementing quantum information processing (QIP) tasks. The basic ideas of NMR QIP are detailed, examining the successes and limitations of liquid and solid state experiments. Finally, a future direction for implementing quantum processors is suggested,utilizing both nuclear and electron spin degrees of freedom.

The growing importance of solid-phase peptide synthesis (SPPS) has necessitated the development of spectroscopic experiments that can be used to obtain structural and conformational information on resin-bound peptides. Despite the utility of two-dimensional high-resolution magic angle spinning (HRMAS) NMR experiments that provide homonuclear shift correlations, experiments that provide heteronuclear shift correlations are necessary for complex conformational and structural elucidatory problems. Here we report the optimization and implementation of non-gradient inverse NMR experiments for acquiring the 1H-13C shift correlations of resin-bound peptides. The use of non-gradient experiments is advantageous as many magic angle spinning (MAS) probes do not possess gradient coils. An HRMAS BIRD-HMQC experiment with a reduced 1JCH constant has proven very suitable for obtaining one-bond correlations. Long-range correlations can be interpolated by using a non-gradient HRMAS CT-HMBC-1 experiment where the resulting data is processed with forward linear prediction. It has been shown that removing the effects of 1H-1H J-modulation is crucial in order to view cross peaks that correspond to long-range correlations. Additionally, both experiments prove extremely useful over routine one-dimensional 13C HRMAS experiments for extracting carbon chemical shift data. The non-gradient HRMAS BIRD-HMQC and CT-HMBC-1 experiments can be used to assist in conformational analysis and to identify and deconvolute situations where accidental equivalence and seemingly correlated isochronous signals arise.

Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is based on a three-bit quantum error correcting code carried out on a three-qubit nuclear magnetic resonance (NMR) quantum information processor. Utilizing both engineered and natural noise, the degree of correlations present in the noise affecting a two-qubit subsystem was determined. We measured a correlation factor of c=0.5+/-0.2 using the error correction protocol, and c=0.3+/-0.2 using a standard NMR technique based on coherence pathway selection. Although the error correction method demands precise control, the results demonstrate that the required precision is achievable in the liquid-state NMR setting.

In this Letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or a 12-qubit pseudopure cat state) and decode it into an 11 qubit plus one qutrit pseudopure state using liquid state nuclear magnetic resonance quantum information processors.