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Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems

Abstract

Quantum simulators are controllable quantum systems that can reproduce the dynamics of the system of interest in situations that are not amenable to classical computers. Recent developments in quantum technology enable the precise control of individual quantum particles as required for studying complex quantum systems. In particular, quantum simulators capable of simulating frustrated Heisenberg spin systems provide platforms for understanding exotic matter such as high-temperature superconductors. Here we report the analogue quantum simulation of the ground-state wavefunction to probe arbitrary Heisenberg-type interactions among four spin-1/2 particles. Depending on the interaction strength, frustration within the system emerges such that the ground state evolves from a localized to a resonating-valence-bond state. This spin-1/2 tetramer is created using the polarization states of four photons. The single-particle addressability and tunable measurement-induced interactions provide us with insights into entanglement dynamics among individual particles. We directly extract ground-state energies and pairwise quantum correlations to observe the monogamy of entanglement.

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Figure 1: Mimicking an adiabatic quantum evolution with an analogue quantum simulator.
Figure 2: Experimental set-up.
Figure 3: Ground-state energy of the spin-1/2 tetramer.
Figure 4: Density matrices of various spin-1/2 tetramer configurations in the computational basis (|H〉/|V 〉).
Figure 5: Experimentally extracted pairwise Heisenberg energies.
Figure 6: Directly observed pairwise correlation functions of various valence-bond states.

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Acknowledgements

The authors thank F. Verstraete, Č. Brukner, W. Hofstetter, J. Kofler, T. Jennewein, R. Ursin, S. Zotter and S. Barz for discussions. We acknowledge support from the European Commission, project QAP (No 015848), Q-ESSENCE (No 248095), an ERC senior grant (QIT4QAD), the Marie-Curie research training network EMALI, JTF, SFB-FOQUS and the doctoral programme CoQuS of the Austrian Science Foundation (FWF).

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X-s.M. and W.N. designed and carried out experiments, analysed data and wrote the manuscript. B.D. provided the theoretical analysis, analysed data and wrote the manuscript. A.Z. supervised the project and edited the manuscript. P.W. designed experiments, analysed data, wrote the manuscript and supervised the project.

Corresponding author

Correspondence to Philip Walther.

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Ma, Xs., Dakic, B., Naylor, W. et al. Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems. Nature Phys 7, 399–405 (2011). https://doi.org/10.1038/nphys1919

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