Physics (Internal)

Experimental Realization of Spin Liquids in a Programmable Quantum Device

This event is part of the Preliminary Oral Exam.

Quantum spin liquids (QSL) have a long history. They were first proposed in the 1970s by Anderson [1] as an alternative to the spin 1/2 N´eel antiferromagnetic state, and later as candidates for the insulating parent state of the high-temperature superconductors[2]. QSLs are closely related to lattice gauge models in particle physics, also dating to the 1970s [3–5]. Today, a QSL model known as the toric code is a potential platform for topological computing [6]. There have been many proposed materials, but to-date gapped QSLs have not been unambiguously observed in nature [7]. Since they are so hard to find in materials, a more recent idea is to build a QSL synthetically out of superconducting circuits [8–10]. In this talk I will take these ideas one step further and show that, in principle, a programmable device can be used to emulate QSL phases so far unreachable by other means, a step towards realizing logical topological qubits in these same devices. We build and probe a Z2 spin liquid in a programmable quantum device, the D-Wave DW-2000Q. To realize this state of matter, we design a Hamiltonian with combinatorial gauge symmetry [11] using only pairwise-qubit interactions and a transverse field, i.e., interactions which are accessible in this quantum device. The combinatorial gauge symmetry remains exact along the full quantum annealing path, landing the system onto the classical 8-vertex model at the endpoint of the path. The output configurations from the device allows us to directly observe the loop structure of the model. Moreover, we deform the Hamiltonian so as to vary the weights of the 8 vertices and show that we can selectively attain the 6-vertex (ice model), or drive the system into a ferromagnetic state. We present studies of the phase diagram of the system as function of the 8-vertex deformations and effective temperature, which we control by varying the relative strengths of the programmable couplings, and we show that the experimental results are consistent with theoretical analysis. Finally, we identify additional capabilities that, if added to these quantum devices, would allow us to realize Z2 quantum spin liquids on which to build topological qubits.

[1] P. Anderson, “Resonating valence bonds: A new kind of insulator?” Materials Research Bulletin 8, 153 – 160 (1973).

[2] P. W. Anderson, “The resonating valence bond state in La2CuO4 and superconductivity,” Science 235, 1196–1198 (1987).

[3] F. J. Wegner, “Duality in generalized Ising models and phase transitions without local order parameters,” J. Math. Phys. 12, 2259–2272 (1971).

[4] J. B. Kogut, “An introduction to lattice gauge theory and spin systems,” Rev. Mod. Phys. 51, 659–713 (1979).

[5] E. Fradkin and L. Susskind, “Order and disorder in gauge systems and magnets,” Phys. Rev. D 17, 2637–2658 (1978).

[6] A. Y. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303, 2–30 (2003).

[7] L. Savary and L. Balents, “Quantum spin liquids: a review,” Reports on Progress in Physics 80, 016502 (2016).

[8] L. B. Ioffe, M. V. Feigel’man, A. Ioselevich, D. Ivanov, M. Troyer, and G. Blatter, “Topologically protected quantum bits using Josephson junction arrays,” Nature 415, 503–506 (2002).

[9] L. B. Ioffe and M. V. Feigel’man, “Possible realization of an ideal quantum computer in Josephson junction array,” Phys. Rev. B 66, 224503 (2002).

[10] C. Chamon and D. Green, “A superconducting circuit realization of combinatorial gauge symmetry,” (2020), arXiv:2006.10060.

[11] C. Chamon, D. Green, and Z.-C. Yang, “Constructing quantum spin liquids using combinatorial gauge symmetry,” Phys. Rev. Lett. 125, 067203 (2020).

Time: Dec 11, 2020 10:30 AM Eastern Time (US and Canada)

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