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 buselement. 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.
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 basedon 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.
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-fieldXY 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.
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-equilibriumquantum 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.
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 modelis 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.