Engineering spin-1 chains within the Haldane phase on a qudit quantum processor by Murray Batchelor
The Haldane phase is a paradigmatic example of a symmetry protected topological (SPT) phase found in the spin-1 Heisenberg chain. The Haldane phase has several characteristic features. In addition to symmetry protection and the presence of an energy gap there are also fractionalised spin-1/2 edge states, which are hosted at the ends of the chain when the spin chain has open boundaries. This is a form of symmetry fractionalization, where the bulk spin-1 symmetry breaks into SU(2) components at the edges.
A group of researchers in Austria, Spain, Switzerland and Australia have obtained an experimental realization of the spin-1 Haldane phase using qutrits in a trapped-ion quantum processor [1]. This is achieved by combining a scalable state-preparation technique based on sequentially coupling neighbouring spins to an auxiliary system, with a flexible quantum computing platform based on multilevel qudits.
Two different states from the Haldane phase are realised and explored from condensed matter and quantum information perspectives. Namely the well known spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) chain [2] created in qutrits and a spin-1/2 cluster state created in qubits. The results demonstrate the essential nonclassical features of the Haldane phase, most notably, the bulk-boundary relation emerging from the SPT nature of the phase. The experiment clearly shows spin fractionalization of the physical spin-1 particles into effective qubits at the chain edges. The long-range string order is also verified.
Looking further ahead the realization of Haldane physics on a qudit quantum processor along with scalable preparation procedures opens the door to the exploration of other interesting higher spin systems. One such challenge would be the exploration of the rich range of physics in the more general spin-1 bilinear-biquadratic model. As highlighted by the authors further possibilities involve the preparation of more general matrix product states and the overarching goal to extend the study of SPT phases beyond one spatial dimension on quantum processors using hardware-efficient qudit encodings.
References
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C.L. Edmunds et al., Symmetry-protected topological Haldane phase on a qudit quantum processor. PRX Quantum 6, 020349 (2025)
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I. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki, Rigorous results on valence bond ground states in antiferromagnets. Phys. Rev. Lett. 59, 799 (1987)
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Pham Van Ky, Nonstatic Reissner-Nordström metric in the perturbative f(R) theory: embedding in the background of the FLRW cosmology, uniqueness of solutions, the TOV equation. Eur. Phys. J. C 85(2), 170 (2025)
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