Simulation of the four-body interaction in a nuclear magnetic resonance quantum information processor

Abstract

The four-body interaction plays an important role in many-body systems, and it can exhibit interesting phase transition behaviors. In this letter, we report the experimental demonstration of a four-body interaction in a four-qubit nuclear magnetic resonance quantum information processor. The strongly modulating pulse is used to implement spin selective excitation. The results show a good agreement between theory and experiment.NMR quantum computer, four-body interaction, quantum simulation, four qubits Quantum computers have advantages over the classical counterparts in simulating quantum systems [1] and solving some hard problems, such as factoring large number and searching unsorted databases [2][3][4] . Among various candidates for implementing the large-scale quantum computer in the future and demonstrating quantum algorithms to corroborate existing theories, nuclear magnetic resonance (NMR) has been proven to be a convenient and practical method to learn lessons for the other physical systems [5][6][7][8][9][10][11][12][13][14][15][16] , though it has been a powerful tool in biology and chemistry research as well [17,18] . NMR quantum computer is an Ising-type computer [19] where two-body interactions take the form of π 2Pauli matrix of the i-th spin, and J ij denotes the strength of coupling between the two spins.Besides two-body interactions, many-body interactions are valuable sources for quantum information processors. For example, the three-spin interactions can speed up the quantum state transfer in the Heisenberg spin chain [20] . Four-body interactions have attracted much interest recently [21][22][23][24][25][26][27] . The systems with manybody interactions can exhibit interesting phase transition behaviors [21][22][23][24][25][26][27][28][29] . The three spin-interactions in the spin chain can induce the quantum criticality that cannot be measured by concurrence, because three-spin interactions generate three-qubit entanglement [28,29] . Four-body interactions play important roles in phase transitions in condensed matters [21][22][23][24][25][26][27] , and relate to four-body entanglement, which is still an open problem currently. Simulation of quantum system is one of the main applications of future quantum computers. Practical factoring and searching applications of quantum computer usually require hundreds, or even thousands of qubits. However, the simulation of quantum systems may require only a few dozens of qubits. Simulating quantum systems is surely the initial practical application of the early practical quantum computer with a few qubits. It is helpful to locate problems and gather experiences for large scale quantum computers in future. In previous work, three-body interactions were well simulated in NMR quantum computers [20,30,31] . It is a reasonable assumption that the four-spin interactions relate to fourqubit entanglement, which is still unclear for us currently. In this paper we focus on implementing the four-spin interactions in an NMR quantum computer. Our work is

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