Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventionalcomputers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources which are polynomial in the number of spins and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.
Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universalquantum simulation of fermionic systems is daunting due to their particle statistics, and Feynman left as an open question whether it could be done, because of the need for non-local control. Here, we implement fermionic interactions with digital techniques in a superconducting circuit. Focusing on the Hubbard model, we perform time evolution with constant interactions as well as a dynamic phase transition with up to four fermionic modes encoded in four qubits. The implemented digital approach is universal and allows for the efficient simulation of fermions in arbitrary spatial dimensions. We use in excess of 300 single-qubit and two-qubit gates, and reach global fidelities which are limited by gate errors. This demonstration highlights the feasibility of the digital approach and opens a viable route towards analog-digital quantum simulation of interacting fermions and bosons in large-scale solid state systems.
We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition,and multiqubit gates, be with the use of a quantum bus or direct capacitive couplings. We apply our method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest and next-nearest neighbours. Furthermore, we propose an optimal architecture for this model and discuss the benchmarking of the simulations in realistic circuit quantum electrodynamics setups.
We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular thosewhich are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.
Quantum field theories (QFTs) are among the deepest descriptions of nature. In this sense, different computing approaches have been developed, as Feynman diagrams or lattice gauge theories.In general, the numerical simulations of QFTs are computationally hard, with the processing time growing exponentially with the system size. Nevertheless, a quantum simulator could provide an efficient way to emulate these theories in polynomial time. Here, we propose the quantum simulation of fermionic field modes interacting via a continuum of bosonic modes with superconducting circuits, which are among the most advanced quantum technologies in terms of quantum control and scalability. An important feature of superconducting devices is that, unlike other quantum platforms, they offer naturally a strong coupling of qubits to a continuum of bosonic modes. Therefore, this system is a specially suited platform to realize quantum simulations of scattering processes involving interacting fermionic and bosonic quantum field theories, where access to the continuum of modes is required.
The efficient implementation of many-body interactions in superconducting circuits allows for the realization of multipartite entanglement and topological codes, as well as the efficientsimulation of highly-correlated fermionic systems. We propose the engineering of fast multiqubit interactions with tunable transmon-resonator couplings. This dynamics is obtained by the modulation of magnetic fluxes threading SQUID loops embedded in the transmon devices. We consider the feasibility of the proposed implementation in a realistic scenario and discuss potential applications.
The phenomenon of quantum fluctuations, consisting in virtual particles emerging from vacuum, is central to understanding important effects in nature – for instance, the Lambshift of atomic spectra and the anomalous magnetic moment of the electron. It was also suggested that a mirror undergoing relativistic motion could convert virtual into real photons. This phenomenon, denominated dynamical Casimir effect (DCE), has been observed in recent experiments with superconducting circuits. Here, we show that the physics underlying the DCE may generate multipartite quantum correlations. To achieve it, we propose a circuit quantum electrodynamics (cQED) scenario involving superconducting quantum interference devices (SQUIDs), cavities, and superconducting qubits, also called artificial atoms. Our results predict the generation of highly entangled states for two and three superconducting qubits in different geometric configurations with realistic parameters. This proposal paves the way for a scalable method of multipartite entanglement generation in cavity networks through dynamical Casimir physics.
We propose the implementation of a digital quantum simulator for prototypical spin models in a circuit quantum electrodynamics architecture. We consider the feasibility of the quantumsimulation of Heisenberg and frustrated Ising models in transmon qubits coupled to coplanar waveguide microwave resonators. Furthermore, we analyze the time evolution of these models and compare the ideal spin dynamics with a realistic version of the proposed quantum simulator. Finally, we discuss the key steps for developing the toolbox of digital quantum simulators in superconducting circuits.