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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.


Related in: MedlinePlus

(Color online) (a) The infinite-size quantum phase transition of the model (11) manifests itself as a crossover in a minimal lattice of two plaquettes. Here we have prepared the initial product state shown in the inset, and swept the parameters as , , with a constant speed . When the effect of qubit decay is considered, the spin on the common link [corresponding to the “order parameter”  in this minimal case] decays at a rate , thereby reducing the value of  for large . (b) Effect of disorder in a minimal lattice of two plaquettes. When the qubit frequencies take random values between , the transition becomes less visible. Here we have taken , and plotted the average  (solid line) and standard deviation (dashed lines) over 10000 realizations. The figure shows that, with uncertainties in the qubit frequencies of this magnitude, the crossover can still be observed. Here we have prepared the initial product state shown in the inset of Fig. 12(a), and swept the parameters as , , with a constant speed .
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f000060: (Color online) (a) The infinite-size quantum phase transition of the model (11) manifests itself as a crossover in a minimal lattice of two plaquettes. Here we have prepared the initial product state shown in the inset, and swept the parameters as , , with a constant speed . When the effect of qubit decay is considered, the spin on the common link [corresponding to the “order parameter” in this minimal case] decays at a rate , thereby reducing the value of for large . (b) Effect of disorder in a minimal lattice of two plaquettes. When the qubit frequencies take random values between , the transition becomes less visible. Here we have taken , and plotted the average (solid line) and standard deviation (dashed lines) over 10000 realizations. The figure shows that, with uncertainties in the qubit frequencies of this magnitude, the crossover can still be observed. Here we have prepared the initial product state shown in the inset of Fig. 12(a), and swept the parameters as , , with a constant speed .

Mentions: In Fig. 12(a) we show how the infinite-size quantum phase transition of the model (11) manifests itself on a lattice of two plaquettes, captured by the average magnetization of the central spin between both plaquettes. Here we start with the product state [c.f. Fig. 11 and the inset of Fig. 12(a)], which can be experimentally prepared by first cooling the system to the ground state  [56] and then applying a simultaneous pulse on the appropriate links. We notice that this state is the ground state of the Hamiltonian (11) for , , and that the large energy scale ensures that the Gauss law is satisfied. In Fig. 12(a) we calculate when the parameters are varied with time as , , which, given a constant speed , and amplitudes , , approximately follows the functional form shown in Fig. 7(c). Neglecting qubit decay, increases from to 0. At finite relaxation rates, reaches a maximum at a finite value of and then decreases due to qubit decay. For standard relaxation rates []  [9,10], and superconducting-circuit parameters, the behavior of in the presence of qubit decay approximates well the one shown by the Hamiltonian dynamics, thereby allowing us to characterize the transition.


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) The infinite-size quantum phase transition of the model (11) manifests itself as a crossover in a minimal lattice of two plaquettes. Here we have prepared the initial product state shown in the inset, and swept the parameters as , , with a constant speed . When the effect of qubit decay is considered, the spin on the common link [corresponding to the “order parameter”  in this minimal case] decays at a rate , thereby reducing the value of  for large . (b) Effect of disorder in a minimal lattice of two plaquettes. When the qubit frequencies take random values between , the transition becomes less visible. Here we have taken , and plotted the average  (solid line) and standard deviation (dashed lines) over 10000 realizations. The figure shows that, with uncertainties in the qubit frequencies of this magnitude, the crossover can still be observed. Here we have prepared the initial product state shown in the inset of Fig. 12(a), and swept the parameters as , , with a constant speed .
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

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

f000060: (Color online) (a) The infinite-size quantum phase transition of the model (11) manifests itself as a crossover in a minimal lattice of two plaquettes. Here we have prepared the initial product state shown in the inset, and swept the parameters as , , with a constant speed . When the effect of qubit decay is considered, the spin on the common link [corresponding to the “order parameter” in this minimal case] decays at a rate , thereby reducing the value of for large . (b) Effect of disorder in a minimal lattice of two plaquettes. When the qubit frequencies take random values between , the transition becomes less visible. Here we have taken , and plotted the average (solid line) and standard deviation (dashed lines) over 10000 realizations. The figure shows that, with uncertainties in the qubit frequencies of this magnitude, the crossover can still be observed. Here we have prepared the initial product state shown in the inset of Fig. 12(a), and swept the parameters as , , with a constant speed .
Mentions: In Fig. 12(a) we show how the infinite-size quantum phase transition of the model (11) manifests itself on a lattice of two plaquettes, captured by the average magnetization of the central spin between both plaquettes. Here we start with the product state [c.f. Fig. 11 and the inset of Fig. 12(a)], which can be experimentally prepared by first cooling the system to the ground state  [56] and then applying a simultaneous pulse on the appropriate links. We notice that this state is the ground state of the Hamiltonian (11) for , , and that the large energy scale ensures that the Gauss law is satisfied. In Fig. 12(a) we calculate when the parameters are varied with time as , , which, given a constant speed , and amplitudes , , approximately follows the functional form shown in Fig. 7(c). Neglecting qubit decay, increases from to 0. At finite relaxation rates, reaches a maximum at a finite value of and then decreases due to qubit decay. For standard relaxation rates []  [9,10], and superconducting-circuit parameters, the behavior of in the presence of qubit decay approximates well the one shown by the Hamiltonian dynamics, thereby allowing us to characterize the transition.

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.


Related in: MedlinePlus