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) Upper panel: Flux configurations that obey the Gauss law on a lattice of two plaquettes, and corresponding spin configurations (below). Lower panel: Flux distribution in the ground state for  (left) and  (right). For  we recover the state , while for  the ground state is a superposition of the three gauge invariant states, with the electric flux propagating completely along the edges of the lattice.
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f000055: (Color online) Upper panel: Flux configurations that obey the Gauss law on a lattice of two plaquettes, and corresponding spin configurations (below). Lower panel: Flux distribution in the ground state for (left) and (right). For we recover the state , while for the ground state is a superposition of the three gauge invariant states, with the electric flux propagating completely along the edges of the lattice.

Mentions: In the upper panel of Fig. 11 we show the possible configurations compatible with the Gauss law for a lattice of two plaquettes. Notice, that for a spin representation of the gauge fields, the Gauss law is irremediably broken at the vertices connected to three links. Therefore, in Fig. 11 a charge–anticharge pair with has been created at the vertices 3 and 4. Furthermore, each of the states , , , is degenerate with the state corresponding to simultaneously inverting all the spins, a degeneracy that can be broken by applying a small magnetic field. These states can be initially prepared by locally applying simultaneous pulses on the appropriate qubits. Starting e.g. in , which corresponds to the ground state of the Hamiltonian (11) for , , we can adiabatically switch on the ring-exchange interaction to reach the ground state of the system for a particular ratio . In the lower panel of Fig. 11 we show a simulation of the ground-state flux distribution for , (left) and for , (right). In the former case, the ground state is, as mentioned above, the antiferromagnetic state . However, when the ratio is increased, the ring-exchange term dominates the dynamics and the electric flux propagates from charge to anticharge along the edges of the lattice. In this case, the ground state is no longer a product state, but a quantum superposition of the states , , and .


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) Upper panel: Flux configurations that obey the Gauss law on a lattice of two plaquettes, and corresponding spin configurations (below). Lower panel: Flux distribution in the ground state for  (left) and  (right). For  we recover the state , while for  the ground state is a superposition of the three gauge invariant states, with the electric flux propagating completely along the edges of the lattice.
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

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

f000055: (Color online) Upper panel: Flux configurations that obey the Gauss law on a lattice of two plaquettes, and corresponding spin configurations (below). Lower panel: Flux distribution in the ground state for (left) and (right). For we recover the state , while for the ground state is a superposition of the three gauge invariant states, with the electric flux propagating completely along the edges of the lattice.
Mentions: In the upper panel of Fig. 11 we show the possible configurations compatible with the Gauss law for a lattice of two plaquettes. Notice, that for a spin representation of the gauge fields, the Gauss law is irremediably broken at the vertices connected to three links. Therefore, in Fig. 11 a charge–anticharge pair with has been created at the vertices 3 and 4. Furthermore, each of the states , , , is degenerate with the state corresponding to simultaneously inverting all the spins, a degeneracy that can be broken by applying a small magnetic field. These states can be initially prepared by locally applying simultaneous pulses on the appropriate qubits. Starting e.g. in , which corresponds to the ground state of the Hamiltonian (11) for , , we can adiabatically switch on the ring-exchange interaction to reach the ground state of the system for a particular ratio . In the lower panel of Fig. 11 we show a simulation of the ground-state flux distribution for , (left) and for , (right). In the former case, the ground state is, as mentioned above, the antiferromagnetic state . However, when the ratio is increased, the ring-exchange term dominates the dynamics and the electric flux propagates from charge to anticharge along the edges of the lattice. In this case, the ground state is no longer a product state, but a quantum superposition of the states , , and .

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.