Geometric phases are well known to be noise-resilient in quantum evolutions/operations. Holonomic quantum gates provide us with a robust way towards universal quantum computation, asthese quantum gates are actually induced by nonabelian geometric phases. Here we propose and elaborate how to efficiently implement universal nonadiabatic holonomic quantum gates on simpler superconducting circuits, with a single transmon serving as a qubit. In our proposal, an arbitrary single-qubit holonomic gate can be realized in a single-loop scenario, by varying the amplitudes and phase difference of two microwave fields resonantly coupled to a transmon, while nontrivial two-qubit holonomic gates may be generated with a transmission-line resonator being simultaneously coupled to the two target transmons in an effective resonant way. Moreover, our scenario may readily be scaled up to a two-dimensional lattice configuration, which is able to support large scalable quantum computation, paving the way for practically implementing universal nonadiabatic holonomic quantum computation with superconducting circuits.
Implementing holonomic quantum computation is a challenging task as it requires complicated interaction among multilevel systems. Here, we propose to implement nonadiabatic holonomicquantum computation based on dressed-state qubits in circuit QED. An arbitrary holonomic single-qubit gate can be conveniently achieved using external microwave fields and tuning their amplitudes and phases. Meanwhile, nontrivial two-qubit gates can be implemented in a coupled cavities scenario assisted by a grounding SQUID with tunable interaction, where the tuning is achieved by modulating the ac flux threaded through the SQUID. In addition, our proposal is directly scalable, up to a two-dimensional lattice configuration. In our scheme, the dressed states only involve the lowest two levels of each transmon qubits and the effective interactions exploited are all of resonant nature. Therefore, we release the main difficulties for physical implementation of holonomic quantum computation on superconducting circuits.
We present a feasible protocol to mimic topological Weyl semimetal phase in a small one-dimensional circuit-QED lattice. By modulating the photon hopping rates and on-site photon frequenciesin parametric spaces, we demonstrate that the momentum space of this one-dimensional lattice model can be artificially mapped to three dimensions accompanied by the emergence of topological Weyl semimetal phase. Furthermore, via a lattice-based cavity input-output process, we show that all the essential topological features of Weyl semimetal phase, including the topological charge associated with each Weyl point and the open Fermi arcs, can be unambiguously detected in a circuit with four dissipative resonators by measuring the reflection spectra. These remarkable features may open a new prospect in using well-controlled small quantum lattices to mimic and study topological phases.
The concept of flat band plays an important role in strongly-correlated many-body physics. However, the demonstration of the flat band physics is highly nontrivial due to intrinsiclimitations in conventional condensed matter materials. Here we propose a circuit quantum electrodynamics simulator of the 2D Lieb lattice exhibiting a flat middle band. By exploiting the simple parametric conversion method, we design a photonic Lieb lattice with \textit{in situ} tunable hopping strengths in a 2D array of coupled superconducting transmissionline resonators. Moreover, the flexibility of our proposal enables the immediate incorporation of both the artificial gauge field and the strong photon-photon interaction in a time- and site-resolved manner. To unambiguously demonstrate the synthesized flat band, we further investigate the observation of the flat band localization of microwave photons through the pumping and the steady-state measurements of only few sites on the lattice. Requiring only current level of technique and being robust against imperfections in realistic circuits, our scheme can be readily tested in experiments and may pave a new way towards the future realization of exotic photonic quantum Hall fluids including anomalous quantum Hall effect and bosonic fractional quantum Hall states without magnetic fields.
The implementation of holonomic quantum computation generally requires controllable and complicated interaction among addressable multi-level systems, which is challenging on superconductingcircuit. Here, we propose a scalable architecture for non-adiabatic holonomic quantum computation on a circuit QED lattice with hybrid transmon and photon encoding of the logical qubits in a decoherence-free subspace. With proper driven on the transmon, we can obtain tunable resonate interaction between the transmon and each of the resonators, which leads to arbitrary single-qubit operation on the encoded logical qubit. Meanwhile, for a nontrivial two-qubit gate, we only need resonate interactions among the three resonators from the two logical qubits, which can be induced by commonly coupled to a grounding SQUID with ac magnetic driven. More importantly, our scheme is achieved with all resonate interactions among the involved elements, and thus leads to quantum gates with very high fidelity. Therefore, our scheme opens up the possibility of realizing high fidelity universal holonomic quantum computation in solid-state system.
We propose a scheme to realize controllable quantum state transfer and entanglement generation among transmon qubits in the typical circuit QED setup based on adiabatic passage. Throughdesigning the time-dependent driven pulses applied on the transmon qubits, we find that fast quantum sate transfer can be achieved between arbitrary two qubits and quantum entanglement among the qubits also can also be engineered. Furthermore, we numerically analyzed the influence of the decoherence on our scheme with the current experimental accessible systematical parameters. The result shows that our scheme is very robust against both the cavity decay and qubit relaxation, the fidelities of the state transfer and entanglement preparation process could be very high. In addition, our scheme is also shown to be insensitive to the inhomogeneous of qubit-resonator coupling strengths.
We propose to implement tunable interaction of superconducting flux qubits with cavity-assisted interaction and strong driving. The qubits have a three-level Lambda configuration, andthe decay of the excited state will be greatly suppressed due to the effective large detuning. The implemented interaction is insensitive to the cavity field state and can be controlled by modulating the phase difference of the driving fields of the qubits. In particular, our scheme is based on the typical circuit QED setup and thus will provide a simple method towards the tunable interaction of superconducting qubits. Finally, we consider the generation of two and four qubits entangled states with the constructed interaction under the influence of typical decoherence effects.
In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that thecoupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where the qubit degree of freedom can be adiabatically eliminated, and thus results in the enhanced coupling between the two resonators. Therefore, our work opens up the possibility of studying quantum nonlinear effect in circuit electromechanics.
We propose a scheme of investigating topological photonics in superconducting quantum circuits. There are two major ingredients. The first is the synthesization of an artificial gaugefield on a circuit quantum electrodynamics lattice through the developed dynamic modulation approach. The flexibility of such parametric method leads to the effective \textit{in situ} tunable magnetic field for photons on a square lattice. The second, which is the main new ingredient of this paper, considers the detection of the topological phases of the photons. Our idea employs the exotic properties of the edge state modes which result in novel steady states of the lattice under the driving-dissipation competition. Through the pumping and the photon-number measurements of merely few sites, not only the spatial and the spectral characters, but also the momentums and even the integer topological quantum numbers of the edge states can be directly probed, which reveal unambiguously the topological nature of the photons on the proposed lattice. The physical implementation of our scheme is discussed in detail, where our results pinpoint the feasibility based on current level of experimental technology.
To implement a universal set of quantum logic gates based on non-Abelian geometric phases, one needs quantum systems that are beyond two levels. However, this is extremely difficultfor superconducting qubits, and thus the recent experiment has only realized single qubit gates [A. A. Abdumalikov Jr et al., Nature 496, 482 (2013)]. Here, we propose to implement non-adiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where we only use two levels in transmon qubits, and require minimal resources for the decoherence-free subspace encoding. In this way, our scheme avoids difficulties in previous works while still can achieve considerable large effective coupling strength and thus leads to high fidelity quantum gates. Therefore, our scheme presents a promising way for robust quantum computation on superconducting circuits.