Adiabatic quantum simulations with driven superconducting qubits

  1. Marco Roth,
  2. Nikolaj Moll,
  3. Gian Salis,
  4. Marc Ganzhorn,
  5. Daniel J. Egger,
  6. Stefan Filipp,
  7. and Sebastian Schmidt
We propose a quantum simulator based on driven superconducting qubits where the interactions are generated parametrically by a polychromatic magnetic flux modulation of a tunable bus
element. Using a time-dependent Schrieffer-Wolff transformation, we analytically derive a multi-qubit Hamiltonian which features independently tunable XX and YY-type interactions as well as local bias fields over a large parameter range. We demonstrate the adiabatic simulation of the ground state of a hydrogen molecule using two superconducting qubits and one tunable bus element. The time required to reach chemical accuracy lies in the few microsecond range and therefore could be implemented on currently available superconducting circuits. Further applications of this technique may also be found in the simulation of interacting spin systems.

Analysis of parametrically driven exchange-type (iSWAP) and two-photon (bSWAP) interactions between superconducting qubits

  1. Marco Roth,
  2. Marc Ganzhorn,
  3. Nikolaj Moll,
  4. Stefan Filipp,
  5. Gian Salis,
  6. and Sebastian Schmidt
A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two and more quantum bits in arrays of coupled qubits. Gates based
on parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we study theoretically and experimentally a superconducting qubit setup with two transmon qubits connected via a capacitively coupled tunable bus. We develop a time-dependent Schrieffer-Wolff transformation and derive analytic expressions for exchange-interaction gates swapping excitations between the qubits (iSWAP) and for two-photon gates creating and annihilating simultaneous two-qubit excitations (bSWAP). We find that the bSWAP gate is generally slower than the more commonly used iSWAP gate, but features favorable scalability properties with less severe frequency crowding effects, which typically degrade the fidelity in multi-qubit setups. Our theoretical results are backed by experimental measurements as well as exact numerical simulations including the effects of higher transmon levels and dissipation.

Signatures of topological quantum phase transitions in driven and dissipative qubit-arrays

  1. Y. L. Dong,
  2. Titus Neupert,
  3. R. Chitra,
  4. and Sebastian Schmidt
We study photonic signatures of symmetry broken and topological phases in a driven, dissipative circuit QED realization of spin-1/2 chains. Specifically, we consider the transverse-field
XY model and a dual model with 3-spin interactions. The former has a ferromagnetic and a paramagnetic phase, while the latter features, in addition, a symmetry protected topological phase. Using the method of third quantization, we calculate the non-equilibrium steady-state of the open spin chains for arbitrary system sizes and temperatures. We find that the bi-local correlation function of the spins at both ends of the chain provides a sensitive measure for both symmetry-breaking and topological phase transitions of the systems, but no universal means to distinguish between the two types of transitions. Both models have equivalent representations in terms of free Majorana fermions, which host zero, one and two topological Majorana end modes in the paramagnetic, ferromagnetic, and symmetry protected topological phases, respectively. The correlation function we study retains its bi-local character in the fermionic representation, so that our results are equally applicable to the fermionic models in their own right. We propose a photonic realization of the dissipative transverse-field XY model in a tunable setup, where an array of superconducting transmon qubits is coupled at both ends to a photonic microwave circuit.

Observation of a Dissipation-Induced Classical to Quantum Transition

  1. James Raftery,
  2. Darius Sadri,
  3. Sebastian Schmidt,
  4. Hakan E. Türeci,
  5. and Andrew A. Houck
The emergence of non-trivial structure in many-body physics has been a central topic of research bearing on many branches of science. Important recent work has explored the non-equilibrium
quantum dynamics of closed many-body systems. Photonic systems offer a unique platform for the study of open quantum systems. We report here the experimental observation of a novel dissipation driven dynamical localization transition of strongly correlated photons in an extended superconducting circuit. Monitoring the homodyne signal reveals this transition to be from a regime of classical oscillations into a macroscopically self-trapped state manifesting revivals, a fundamentally quantum phenomenon. This experiment also demonstrates a new class of scalable quantum simulators with well controlled coherent and dissipative dynamics suited to the study of quantum many-body phenomena out of equilibrium.

Circuit QED lattices: towards quantum simulation with superconducting circuits

  1. Sebastian Schmidt,
  2. and Jens Koch
The Jaynes-Cummings model describes the coupling between photons and a single two-level atom in a simplified representation of light-matter interactions. In circuit QED, this model
is implemented by combining microwave resonators and superconducting qubits on a microchip with unprecedented experimental control. Arranging qubits and resonators in the form of a lattice realizes a new kind of Hubbard model, the Jaynes-Cummings-Hubbard model, in which the elementary excitations are polariton quasi-particles. Due to the genuine openness of photonic systems, circuit QED lattices offer the possibility to study the intricate interplay of collective behavior, strong correlations and non-equilibrium physics. Thus, turning circuit QED into an architecture for quantum simulation, i.e., using a well-controlled system to mimic the intricate quantum behavior of another system too daunting for a theorist to tackle head-on, is an exciting idea which has served as theorists‘ playground for a while and is now also starting to catch on in experiments. This review gives a summary of the most recent theoretical proposals and experimental efforts in this context.