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) (a) Setup for a minimal experiment to verify ring-exchange dynamics. This system consists of a single plaquette on the lattice of Fig. 5, where four superconducting qubits (whose spin degree of freedom is represented by the arrows) are mutually coupled via a Josephson junction in parallel with a capacitor. (b) Energy levels of the microscopic Hamiltonian (13) [see  Appendix A]. Five different sets of states (distinguished by the total number of excitations on the plaquette) are separated by the energy scale  (qubit frequency). Within the two-excitation subspace, a large energy scale  separates states corresponding to different Gauss law sectors. Finally, the lower energy scales  and  provide an energy splitting (in the one- and two-excitation subspaces, respectively). The numbers on the right indicate the level degeneracy.
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

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

f000045: (Color online) (a) Setup for a minimal experiment to verify ring-exchange dynamics. This system consists of a single plaquette on the lattice of Fig. 5, where four superconducting qubits (whose spin degree of freedom is represented by the arrows) are mutually coupled via a Josephson junction in parallel with a capacitor. (b) Energy levels of the microscopic Hamiltonian (13) [see  Appendix A]. Five different sets of states (distinguished by the total number of excitations on the plaquette) are separated by the energy scale (qubit frequency). Within the two-excitation subspace, a large energy scale separates states corresponding to different Gauss law sectors. Finally, the lower energy scales and provide an energy splitting (in the one- and two-excitation subspaces, respectively). The numbers on the right indicate the level degeneracy.

Mentions: A minimal setup for studying ring-exchange interactions is a circuit with four superconducting qubits forming a single plaquette [see Fig. 9]. The approach described in the previous section can then be used to engineer an effective ring-exchange interaction within the two-excitation subspace of the four spins on the plaquette. In this minimal instance, the only non-vanishing coupling is between the states and , i.e.,  (37)〈↓↑↓↑/H/↑↓↑↓〉=−J. Note that for a single plaquette the Ising-type coupling commutes with the ring-exchange interaction, and a competition between both terms in the Hamiltonian (11) appears only in systems consisting of two or more plaquettes.


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) (a) Setup for a minimal experiment to verify ring-exchange dynamics. This system consists of a single plaquette on the lattice of Fig. 5, where four superconducting qubits (whose spin degree of freedom is represented by the arrows) are mutually coupled via a Josephson junction in parallel with a capacitor. (b) Energy levels of the microscopic Hamiltonian (13) [see  Appendix A]. Five different sets of states (distinguished by the total number of excitations on the plaquette) are separated by the energy scale  (qubit frequency). Within the two-excitation subspace, a large energy scale  separates states corresponding to different Gauss law sectors. Finally, the lower energy scales  and  provide an energy splitting (in the one- and two-excitation subspaces, respectively). The numbers on the right indicate the level degeneracy.
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

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

f000045: (Color online) (a) Setup for a minimal experiment to verify ring-exchange dynamics. This system consists of a single plaquette on the lattice of Fig. 5, where four superconducting qubits (whose spin degree of freedom is represented by the arrows) are mutually coupled via a Josephson junction in parallel with a capacitor. (b) Energy levels of the microscopic Hamiltonian (13) [see  Appendix A]. Five different sets of states (distinguished by the total number of excitations on the plaquette) are separated by the energy scale (qubit frequency). Within the two-excitation subspace, a large energy scale separates states corresponding to different Gauss law sectors. Finally, the lower energy scales and provide an energy splitting (in the one- and two-excitation subspaces, respectively). The numbers on the right indicate the level degeneracy.
Mentions: A minimal setup for studying ring-exchange interactions is a circuit with four superconducting qubits forming a single plaquette [see Fig. 9]. The approach described in the previous section can then be used to engineer an effective ring-exchange interaction within the two-excitation subspace of the four spins on the plaquette. In this minimal instance, the only non-vanishing coupling is between the states and , i.e.,  (37)〈↓↑↓↑/H/↑↓↑↓〉=−J. Note that for a single plaquette the Ising-type coupling commutes with the ring-exchange interaction, and a competition between both terms in the Hamiltonian (11) appears only in systems consisting of two or more plaquettes.

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.