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.


Circuit lattice to engineer the Rokhsar–Kivelson model and different four-body spin interactions. Every plaquette of the two-dimensional lattice contains one qubit (e.g. a transmon) on each link. These are mutually coupled via a capacitor in parallel with a two-Josephson-junction loop. When this loop is biased with a quantum flux from a central LC circuit, interactions of the type  are enabled perturbatively (see main text for details).
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f000040: Circuit lattice to engineer the Rokhsar–Kivelson model and different four-body spin interactions. Every plaquette of the two-dimensional lattice contains one qubit (e.g. a transmon) on each link. These are mutually coupled via a capacitor in parallel with a two-Josephson-junction loop. When this loop is biased with a quantum flux from a central LC circuit, interactions of the type are enabled perturbatively (see main text for details).

Mentions: Different gauge invariant interactions can be engineered by slightly modifying the complexity of the circuit lattice shown in Fig. 5. A particularly interesting example is the Rokhsar–Kivelson (RK) model  [51]—a paradigm of dimer physics, which describes resonant valence bond dynamics, relevant in the context of high-temperature superconductivity  [46]. This model can be simulated with the circuit shown in Fig. 8, where we draw a basic plaquette of the two-dimensional lattice. Although this circuit is similar to the architecture of Fig. 5, here the squids coupling neighboring transmons are biased with a quantum flux from an LC resonator located at the center of the plaquette. Following a similar derivation to Section  3, the model describing this circuit can be written as (33) Here for spins on horizontal links of the lattice, while for vertical links. The sum involves nearest-neighbor lattice sites, and the sum involves nearest-neighbor links around a plaquette. For equal transmons, and in the limit , , the coupling constants are given by (34)V′=Ω−Ω′,Ω′=U2EJ□EJcos(πϕextΦ0),μ=ε2(EJ□EJcos(πϕextΦ0)−CQC)−Ω′,β′=U2EJ□EJsin(πϕextΦ0),η=ε2EJ□EJsin(πϕextΦ0)−β′. In the derivation of the Hamiltonian (33) we have assumed that, on top of the quantum flux from the resonator, consecutive squids are biased with external classical fields of alternating signs. Furthermore, we notice that, under realistic experimental conditions, the constants and will be reduced by a factor determined by the fraction of the LC-resonator flux biasing the squid.


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)

Circuit lattice to engineer the Rokhsar–Kivelson model and different four-body spin interactions. Every plaquette of the two-dimensional lattice contains one qubit (e.g. a transmon) on each link. These are mutually coupled via a capacitor in parallel with a two-Josephson-junction loop. When this loop is biased with a quantum flux from a central LC circuit, interactions of the type  are enabled perturbatively (see main text for details).
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

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

f000040: Circuit lattice to engineer the Rokhsar–Kivelson model and different four-body spin interactions. Every plaquette of the two-dimensional lattice contains one qubit (e.g. a transmon) on each link. These are mutually coupled via a capacitor in parallel with a two-Josephson-junction loop. When this loop is biased with a quantum flux from a central LC circuit, interactions of the type are enabled perturbatively (see main text for details).
Mentions: Different gauge invariant interactions can be engineered by slightly modifying the complexity of the circuit lattice shown in Fig. 5. A particularly interesting example is the Rokhsar–Kivelson (RK) model  [51]—a paradigm of dimer physics, which describes resonant valence bond dynamics, relevant in the context of high-temperature superconductivity  [46]. This model can be simulated with the circuit shown in Fig. 8, where we draw a basic plaquette of the two-dimensional lattice. Although this circuit is similar to the architecture of Fig. 5, here the squids coupling neighboring transmons are biased with a quantum flux from an LC resonator located at the center of the plaquette. Following a similar derivation to Section  3, the model describing this circuit can be written as (33) Here for spins on horizontal links of the lattice, while for vertical links. The sum involves nearest-neighbor lattice sites, and the sum involves nearest-neighbor links around a plaquette. For equal transmons, and in the limit , , the coupling constants are given by (34)V′=Ω−Ω′,Ω′=U2EJ□EJcos(πϕextΦ0),μ=ε2(EJ□EJcos(πϕextΦ0)−CQC)−Ω′,β′=U2EJ□EJsin(πϕextΦ0),η=ε2EJ□EJsin(πϕextΦ0)−β′. In the derivation of the Hamiltonian (33) we have assumed that, on top of the quantum flux from the resonator, consecutive squids are biased with external classical fields of alternating signs. Furthermore, we notice that, under realistic experimental conditions, the constants and will be reduced by a factor determined by the fraction of the LC-resonator flux biasing the squid.

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.