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APS

Quantum Simulation of Dynamical Gauge Field Theories with Superconducting Qubits

D. Crespo Marcos, Peter Rabl, E. Rico, Philippe Widmer, Mohammad Hafezi, U.‐J. Wiese, P. Zoller

Published Mar 1, 2013• 0 citations
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A system which can implement an analog quantum simulation of lattice gauge theories \nhas been proposed. In particular, the Schwinger model is formulated in terms of a lattice \nand superconducting qubit implementation is found which maps onto these dynamics. This \nthesis details the design of the superconducting circuit implementation of the model. The \nHamiltonian of the superconducting circuit is designed to exhibit the gauge invariant dynamics \nof a U(1) symmetry. The gauge invariant set of states corresponds to those that are \nin the subspace of states that are shared by the Hamiltonian and the symmetry. Gauge invariance \nis simulated by looking at the dynamics of those states which obey a lattice version \nof Gauss' law. \nThe device is simulated in an open quantum system and the measurable observables \nare extracted and mapped onto processes which can be observed in the lab. We nd that \nthe dynamics occur over realistic time scales that can be observed with current laboratory \nequipment. These dynamics occur over hundred nanosecond timescales well within the minimum \nresolution of our equipment as well as well within the decoherence times of current \nsuperconducting devices.

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Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating systematically-improvable representations of lattice gauge theory Hamiltonians that are efficient at all values of the gauge coupling. One such candidate representation for SU(2) is the fully gauge-fixed Hamiltonian defined in the mixed basis. This work focuses on the quantum simulation of the smallest non-trivial system: two plaquettes with open boundary conditions. A mapping of the continuous gauge field degrees of freedom to qubit-based representations is developed. It is found that as few as three qubits per plaquette is sufficient to reach per-mille level precision on predictions for observables. Two distinct algorithms for implementing time evolution in the mixed basis are developed and analyzed in terms of quantum resource estimates. One algorithm has favorable scaling in circuit depth for large numbers of qubits, while the other is more practical when qubit count is limited. The latter algorithm is used in the measurement of a real-time observable on IBM's Heron superconducting quantum processor, ibm_fez. The quantum results match classical predictions at the percent-level. This work lays out a path forward for two- and three-dimensional simulations of larger systems, as well as demonstrating the viability of mixed-basis formulations for studying the properties of SU(2) gauge theories at all values of the gauge coupling.

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We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that, despite the presence of decoherence in these systems, distinctive phenomena from condensed-matter and high-energy physics can be visualized with state-of-the-art technology in small superconducting-circuit arrays.
Motivated by recent realizations of two-dimensional (2D) superconducting-qubit lattices, we propose a protocol to simulate Hofstadter butterfly with synthetic gauge fields in superconducting circuits. Based on the existing 2D superconducting-qubit lattices, we construct a generalized Hofstadter model on zigzag lattices, which has a fractal energy spectrum similar to the original Hofstadter butterfly. By periodically modulating the resonant frequencies of qubits, we engineer a synthetic gauge field to mimic the generalized Hofstadter Hamiltonian. A spectroscopic method is used to demonstrate the Hofstadter butterfly from the time evolutions of experimental observables. We numerically simulate the dynamics of the system with realistic parameters, and the results show a butterfly spectrum clearly. Our proposal provides a promising way to realize the Hofstadter butterfly on the latest 2D superconducting-qubit lattices and will stimulate the quantum simulation of novel properties induced by magnetic fields in superconducting circuits.
A system which can implement an analog quantum simulation of lattice gauge theories \nhas been proposed. In particular, the Schwinger model is formulated in terms of a lattice \nand superconducting qubit implementation is found which maps onto these dynamics. This \nthesis details the design of the superconducting circuit implementation of the model. The \nHamiltonian of the superconducting circuit is designed to exhibit the gauge invariant dynamics \nof a U(1) symmetry. The gauge invariant set of states corresponds to those that are \nin the subspace of states that are shared by the Hamiltonian and the symmetry. Gauge invariance \nis simulated by looking at the dynamics of those states which obey a lattice version \nof Gauss' law. \nThe device is simulated in an open quantum system and the measurable observables \nare extracted and mapped onto processes which can be observed in the lab. We nd that \nthe dynamics occur over realistic time scales that can be observed with current laboratory \nequipment. These dynamics occur over hundred nanosecond timescales well within the minimum \nresolution of our equipment as well as well within the decoherence times of current \nsuperconducting devices.
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating systematically-improvable representations of lattice gauge theory Hamiltonians that are efficient at all values of the gauge coupling. One such candidate representation for SU(2) is the fully gauge-fixed Hamiltonian defined in the mixed basis. This work focuses on the quantum simulation of the smallest non-trivial system: two plaquettes with open boundary conditions. A mapping of the continuous gauge field degrees of freedom to qubit-based representations is developed. It is found that as few as three qubits per plaquette is sufficient to reach per-mille level precision on predictions for observables. Two distinct algorithms for implementing time evolution in the mixed basis are developed and analyzed in terms of quantum resource estimates. One algorithm has favorable scaling in circuit depth for large numbers of qubits, while the other is more practical when qubit count is limited. The latter algorithm is used in the measurement of a real-time observable on IBM's Heron superconducting quantum processor, ibm_fez. The quantum results match classical predictions at the percent-level. This work lays out a path forward for two- and three-dimensional simulations of larger systems, as well as demonstrating the viability of mixed-basis formulations for studying the properties of SU(2) gauge theories at all values of the gauge coupling.