We introduce a hybrid qubit-boson beam-splitter gate in which a microwave cavity mode couples to an exchange-dressed two-level subsystem of an interacting two-qubit system in the presence of Kerr nonlinearity. Starting from a general circuit quantum electrodynamics (cQED) model, we derive the corresponding hybrid qubit-cavity interaction, develop its open-system description including photon- and qubit-sector-bath-induced dissipation and obtain in the weak-dissipation regime an analytical expression for the average gate fidelity. We further identify carbon-nanotube circuit QED as a concrete platform for implementing and controlling the gate, provide a representative operating regime and perform noiseless and noisy numerical simulations to study the gate dynamics and benchmark the analytical results. Beyond this implementation route, the proposed hybrid primitive provides a natural building block for many-body dynamics, including quantum-cellular-automaton (QCA) and lattice-gauge-inspired architectures and, through its collision-model reformulation, also suggests connections to noisy QCA, non-Markovian extensions and reservoir-style quantum information processing.
We introduce a hybrid qubit-boson beam-splitter gate in which a microwave cavity mode couples to an exchange-dressed two-level subsystem of an interacting two-qubit system in the presence of Kerr nonlinearity. Starting from a general circuit quantum electrodynamics (cQED) model, we derive the corresponding hybrid qubit-cavity interaction, develop its open-system description including photon- and qubit-sector-bath-induced dissipation and obtain in the weak-dissipation regime an analytical expression for the average gate fidelity. We further identify carbon-nanotube circuit QED as a concrete platform for implementing and controlling the gate, provide a representative operating regime and perform noiseless and noisy numerical simulations to study the gate dynamics and benchmark the analytical results. Beyond this implementation route, the proposed hybrid primitive provides a natural building block for many-body dynamics, including quantum-cellular-automaton (QCA) and lattice-gauge-inspired architectures and, through its collision-model reformulation, also suggests connections to noisy QCA, non-Markovian extensions and reservoir-style quantum information processing.
Abstract In hybrid circuit quantum electrodynamics (QED) architectures containing both ancilla qubits and bosonic modes, a controlled beam splitter (cBS) gate is a powerful resource. It can be used to create (up to a controlled-parity operation) an ancilla-controlled SWAP gate acting on two bosonic modes. This is the essential element required to execute the ‘swap test’ for purity, prepare quantum non-Gaussian entanglement and directly measure nonlinear functionals of quantum states. It also constitutes an important gate for hybrid discrete/continuous-variable quantum computation. We propose a new realization of a hybrid cSWAP utilizing ‘Kerr-cat’ qubits—anharmonic oscillators subject to strong two-photon driving. The Kerr-cat is used to generate a controlled-phase beam splitter operation. When combined with an ordinary beam splitter one obtains a cBS and from this a cSWAP. The strongly biased error channel for the Kerr-cat has phase flips which dominate over bit flips. This yields important benefits for the cSWAP gate which becomes non-destructive and transparent to the dominate error. Our proposal is straightforward to implement and, based on currently existing experimental parameters, should achieve cBS gates with high fidelities comparable to current ordinary beam-splitter operations available in circuit QED.
Coupling on-chip microwave cavities to superconducting microcircuits has provided a new platform to study the light/matter interaction at the most elementary level [1]. The recent generalization of this architecture to more complex open nanocircuits [2,3,4] offers the possibility to go beyond standard cavity quantum electrodynamics experiments usually performed with closed two level systems. A wide variety of experiments can be envisioned, with different types of hybrid nanocircuits combining nanoconductors such as carbon nanotubes or semiconducting nanowires, and metallic electrodes made out from normal metals, superconductors, or ferromagnets. Circuit Quantum Electrodynamics represents a promising method to gain more information on the behavior of electrons in these hybrid nanocircuits. In the first part of this talk, I will discuss the coupling of a Cooper pair splitter to a cavity [5,6]. I will show that a measurement of the cavity dispersive shift provides a rich access to the electronic spectroscopy and dynamics in the Cooper pair splitter [7]. In the second part of this talk, I will discuss the coupling of Majorana quasiparticles (in a semiconducting nanowire) to a cavity [8]. These exotic bound states can cause a significant cavity frequency shift and a strong cavity nonlinearity leading for instance to light squeezing. I will show that the dependence of these effects on the nanowire gate voltages should give direct signatures of the unique properties of Majorana fermions, such as their self-adjoint character and their exponential confinement. References [1] A., Wallraff et al., Nature 431, 162 (2004). [2] M.R. Delbecq et al., Phys. Rev. Lett. 107, 256804 (2011). [3] T. Frey et al., Phys. Rev. Lett. 108, 046807 (2012). [4] K.D. Petersson et al., Nature 490, 380 (2012). [5] A. Cottet, T. Kontos, A. Levy Yeyati, Phys. Rev. Lett. 108, 166803 (2012). [6] A. Cottet, Phys. Rev. B 86, 075107 (2012). [7] A. Cottet et al., in preparation. [8] A. Cottet, T. Kontos, and B. Douçot, arXiv:1307.4185 (2013).
Circuit quantum electrodynamics has received an increasing amount of attention over the last decade in light of its potential use in quantum information processing. The underlying principle of this architecture is the coherent coupling between microwave photons stored in superconducting resonators and superconducting qubits made from non-linear, non-dissipative electrical circuits. This architecture can be extended to other solid-state systems with transition frequencies in the microwave regime, such as nuclear and electron spins or Andreev bound states. These hybrid devices would allow the coherent exchange of information between such systems and superconducting qubits mediated by a microwave resonator. This could lead to advances in quantum information processing and new insights in the physics governing these interacting systems. In this dissertation experimental work with different types of hybrid quantum circuits is presented. A first experiment investigates the coherent coupling of microwave photons with a spin ensemble in a correlated and uncorrelated state. The coupling strength and magnetic resonance is studied as a function of temperature and magnetic field direction. A pronounced temperature dependent anisotropy of the magnetic resonance is observed, which can be attributed to the onset of antiferromagnetic correlations in the spin ensemble when cooled below T=4 K. A simple one-dimensional model gives a good description of this anisotropy. A next experiment studies the transport characteristics of carbon nanotubes electrically accessed with normal and superconducting contacts. These devices were characterised using both DC and RF reflectometry techniques. The carbon nanotube devices with superconducting contacts exhibit transport characteristics of Josephson junctions with critical currents of up to Ic~18 nA, as well as multiple Andreev reflections. These semiconductor-superconductor hybrid Josephson junctions are then used to realise a carbon-nanotube-based superconducting qubit with voltage tunable transition frequency using a local electrostatic gate. Strong coupling (g~100 MHz) to a coplanar waveguide resonator is demonstrated via a resonator frequency shift dependent on applied gate voltage. Qubit parameters are extracted from spectroscopy and correspond well to the DC measurements of the carbon nanotube Josephson junctions. Qubit relaxation and coherence times in the range 10-100 ns are observed. The hybrid devices investigated in this work present potential building blocks for more extensive hybrid architectures for quantum information processing.
Hybrid circuit quantum electrodynamics (QED) involves the study of coherent quantum physics in solid state systems via their interactions with superconducting microwave circuits.Here we present a crucial step in the implementation of a hybrid superconducting qubit that employs a carbon nanotube as a Josephson junction.We realise the junction by contacting a carbon nanotube with a superconducting Pd/Al bi-layer, and implement voltage tunability of the quantum circuit's frequency using a local electrostatic gate.We demonstrate a strong dispersive coupling to a coplanar waveguide resonator by investigating the gate-tunable resonator frequency.We extract qubit parameters from spectroscopy using dispersive readout and find qubit relaxation and coherence times in the range of 10 -200 ns.
Hybrid qubits have recently drawn intense attention in quantum computing. We here propose a method to implement a universal controlled-phase gate of two hybrid qubits via two three-dimensional (3D) microwave cavities coupled to a superconducting flux qutrit. For the gate considered here, the control qubit is a microwave photonic qubit (particle-like qubit), whose two logic states are encoded by the vacuum state and the single-photon state of a cavity, while the target qubit is a cat-state qubit (wave-like qubit), whose two logic states are encoded by the two orthogonal cat states of the other cavity. During the gate operation, the qutrit remains in the ground state; therefore, decoherence from the qutrit is greatly suppressed. The gate realization is quite simple, because only a single basic operation is employed and neither classical pulse nor measurement is used. Our numerical simulations demonstrate that with current circuit quantum electrodynamics technology, this gate can be realized with a high fidelity. The generality of this proposal allows implementing the proposed gate in a wide range of physical systems, such as two 1D or 3D microwave or optical cavities coupled to a natural or artificial three-level atom. Finally, this proposal can be applied to create a novel entangled state between a particle-like photonic qubit and a wave-like cat-state qubit.
One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.