Limits...
Two-dimensional lattice gauge theories with superconducting quantum circuits.

Marcos D, Widmer P, Rico E, Hafezi M, Rabl P, Wiese UJ, Zoller P - Ann Phys (N Y) (2014)

Bottom Line: Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well.We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories.The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

View Article: PubMed Central - PubMed

Affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria.

ABSTRACT

A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

No MeSH data available.


(Color online) Action of the ring-exchange Hamiltonian on flippable plaquettes. (a) Flow of electric flux through the links of the lattice. (b) Dimer covering. (c) Spin  representation.
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4263216&req=5

f000010: (Color online) Action of the ring-exchange Hamiltonian on flippable plaquettes. (a) Flow of electric flux through the links of the lattice. (b) Dimer covering. (c) Spin representation.

Mentions: In quantum dimer models, the degrees of freedom account for the presence or absence of a dimer on each link. According to the dimer covering constraint, two dimers cannot touch each other, but can be located at opposite links of a lattice plaquette. The short-range dimer Hamiltonian can be written as  [51](7) where and denote states with two dimers located vertically and horizontally, respectively, on opposite links of a plaquette. The relation between the dimer model and the spin QLM can be established by identifying the presence of a dimer with the state and the absence with the state . With this identification, the Hamiltonian is recast into the form (8)Hdimer=−J∑□(B□−λB□2), where , and which, using , corresponds to the quantum link model Hamiltonian (6) [c.f. Fig. 2 for the action of the ring-exchange interaction in lattice gauge theories, quantum dimer models, and quantum link models]. Although the QLM and the dimer model share the same Hamiltonian, they differ in the realization of the Gauss law constraint, which for the dimer model is given by (9)Qm=eim+ekm+emj+emℓ=−1. This constraint ensures that exactly one dimer touches each lattice site. On the square lattice, around each site there are three links without a valence bond and just one link that carries a dimer. For , the square lattice quantum dimer model exists in a confining columnar phase that extends to the Rokhsar–Kivelson point at , a deconfined critical point at zero temperature.


Two-dimensional lattice gauge theories with superconducting quantum circuits.

Marcos D, Widmer P, Rico E, Hafezi M, Rabl P, Wiese UJ, Zoller P - Ann Phys (N Y) (2014)

(Color online) Action of the ring-exchange Hamiltonian on flippable plaquettes. (a) Flow of electric flux through the links of the lattice. (b) Dimer covering. (c) Spin  representation.
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4263216&req=5

f000010: (Color online) Action of the ring-exchange Hamiltonian on flippable plaquettes. (a) Flow of electric flux through the links of the lattice. (b) Dimer covering. (c) Spin representation.
Mentions: In quantum dimer models, the degrees of freedom account for the presence or absence of a dimer on each link. According to the dimer covering constraint, two dimers cannot touch each other, but can be located at opposite links of a lattice plaquette. The short-range dimer Hamiltonian can be written as  [51](7) where and denote states with two dimers located vertically and horizontally, respectively, on opposite links of a plaquette. The relation between the dimer model and the spin QLM can be established by identifying the presence of a dimer with the state and the absence with the state . With this identification, the Hamiltonian is recast into the form (8)Hdimer=−J∑□(B□−λB□2), where , and which, using , corresponds to the quantum link model Hamiltonian (6) [c.f. Fig. 2 for the action of the ring-exchange interaction in lattice gauge theories, quantum dimer models, and quantum link models]. Although the QLM and the dimer model share the same Hamiltonian, they differ in the realization of the Gauss law constraint, which for the dimer model is given by (9)Qm=eim+ekm+emj+emℓ=−1. This constraint ensures that exactly one dimer touches each lattice site. On the square lattice, around each site there are three links without a valence bond and just one link that carries a dimer. For , the square lattice quantum dimer model exists in a confining columnar phase that extends to the Rokhsar–Kivelson point at , a deconfined critical point at zero temperature.

Bottom Line: Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well.We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories.The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

View Article: PubMed Central - PubMed

Affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria.

ABSTRACT

A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

No MeSH data available.