Efficient algorithms for NMR quantum computers with small qubits

Guanru Feng, Yao Lu, Liang Hao +2 more

It is well known that quantum computers are superior to classical computers in efficiently simulating quantum systems. Here we report the first experimental simulation of quantum tunneling through potential barriers, a widespread phenomenon of a unique quantum nature, via NMR techniques. Our experiment is based on a digital particle simulation algorithm and requires very few spin-1/2 nuclei without the need of ancillary qubits. The occurrence of quantum tunneling through a barrier, together with the oscillation of the state in potential wells, are clearly observed through the experimental results. This experiment has clearly demonstrated the possibility to observe and study profound physical phenomena within even the reach of small quantum computers.

Jonathan A. Jones

Noah Linden, Hervé Barjat, Ray Freeman

Ivan S. Oliveira, Tito José Bonagamba, Roberto S. Sarthour +2 more

Jiangfeng Du, Ping Zou, Xinhua Peng +4 more

There has been much recent effort to realize quantum devices in many different physical systems. Among them, nuclear magnetic resonance (NMR) has been the first to demonstrate nontrivial quantum algorithms with small numbers of qubits and hence is a prototype for the key ingredients needed to build quantum computers. An important building block in many quantum applications is the scattering circuit, which can be used as a quantum multimeter to perform various quantum information processing tasks directly without recourse to quantum tomography. We implement in NMR a three-qubit version of the multimeter and also demonstrate a single-qubit fingerprinting.

Mikio Nakahara

The NMR quantum computer is one of the most established systems among many physical realizations of a quantum computer. In spite of its peculiar character associated with mixed states and lack of scalability, it still works as a prototypical quantum computer with at most 10 qubits. We should point out that it is the only quantum computer commercially available at the time of writing this book. For these reasons, an NMR quantum computer is introduced as one of the first examples of a physical system on which we can execute small-scale quantum algorithms. Qubits in this realization are nuclei with spin 1/2. Molecules with a certain number of such nuclei are employed as a quantum register. The system is made of a macroscopic number (∼ 1020) of moleclues in thermal equilibrium, and we have to take care of these aspects in preparation of a state and measurements as explained in this chapter. Our exposition follows [1] and [2]. Other useful review is [3].