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.
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.
Superconducting quantum circuits are a promising approach for realizations of large scale quantum information processing and quantum simulations. The Josephson junction, which forms the basis of superconducting circuits, is the only known nonlinear non-dissipative circuit element, and its inherent nonlinearities have found many different applications. In this thesis I discuss specific implementations of these circuits. I show that strong two-photon nonlinearities can be induced by coupling photons in the microwave domain to Josephson nonlinearities. I then propose a method to simulate a parent Hamiltonian that can potentially be used to observe fractional quantum Hall states of light. I will also explore how superconducting circuits can be used to modify system-bath couplings to emulate a chemical potential for photons. Finally, I consider the limitations of devising a scheme to couple superconducting circuits to trapped ions, and consider the challenges for such hybrid approaches.
The latest technological progress of achieving the ultrastrong-coupling regime in circuit quantum electrodynamics (QED) systems has greatly promoted the developments of quantum physics, where novel quantum optics phenomena and potential computational benefits have been predicted. Here, we propose a scheme to accelerate the nontrivial two-qubit phase gate in a circuit QED system, where superconducting flux qubits are ultrastrongly coupled to a transmission line resonator (TLR), and two more TLRs are coupled to the ultrastrongly-coupled system for assistant. The nontrivial unconventional geometric phase gate between the two flux qubits is achieved based on close-loop displacements of the three-mode intracavity fields. Moreover, as there are three resonators contributing to the phase accumulation, the requirement of the coupling strength to realize the two-qubit gate can be reduced. Further reduction in the coupling strength to achieve a specific controlled-phase gate can be realized by adding more auxiliary resonators to the ultrastrongly-coupled system through superconducting quantum interference devices. We also present a study of our scheme with realistic parameters considering imperfect controls and noisy environment. Our scheme possesses the merits of ultrafastness and noise-tolerance due to the advantages of geometric phases.
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is, the controlled-phase (c-phase) gate on two microwave-photon resonators and the controlled-controlled phase (cc-phase) gates on three resonators, resorting to quantum resonance operations, without any drive field. Compared with previous works, our universal quantum gates have the higher fidelities and shorter operation times in theory. The numerical simulation shows that the fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our cc-phase gate is 99.25% within about 73.3 ns.
Strong nonlinear coupling of superconducting qubits and/or photons is a critical building block for quantum information processing. Because of the perturbative nature of the Josephson nonlinearity, linear coupling is often used in the dispersive regime to approximate nonlinear coupling. However, this dispersive coupling is weak and the underlying linear coupling mixes the local modes, which, for example, distributes unwanted self-Kerr nonlinearity to photon modes. Here, we use the quarton to yield purely nonlinear coupling between two linearly decoupled transmon qubits. The quarton's zero ϕ^{2} potential enables an ultrastrong gigahertz-level cross-Kerr coupling, which is an order of magnitude stronger compared to existing schemes, and the quarton's positive ϕ^{4} potential can cancel the negative self-Kerr nonlinearity of qubits to linearize them into resonators. This ultrastrong cross-Kerr coupling between bare modes of qubit-qubit, qubit-photon, and even photon-photon is ideal for applications such as single microwave photon detection, ultrafast two-qubit gates, and readout.
In the last decade, the field of Quantum Optics has been enriched with a completely new platform: superconducting quantum circuits, also known as circuit-QED. This platform builds on the original designs of superconducting qubits, that is few-level systems made of superconducting islands and Josephson junctions, but adds to it a new ingredient, microwave photons. In this talk I will review circuit-QED with a focus on two complementary lines of research: ultrastrong light-matter coupling and strongly correlated propagating photons. The first topic deals with novel designs of superconducting qubits, engineering their coupling to the microwave radiation field to reach Rabi frequencies that approach the qubit and photon frequencies. In this regime, known as ”ultrastrong coupling”, the rotating wave approximation from Quantum Optics is no longer valid, the vacuum may spontaneously polarize, producing photons that get bound to the qubit, and novel physics is expected to emerge. I will review recent experiments on this topic, together with various theoretical proposals to tame this ultrastrong coupling. The second topic revolves around the notion of ”propagating” photons in these circuits. Most experiments in circuit-QED so far adopted the typical configuration of artificial atoms (qubits) interacting with artificial cavities (LC resonators). This proved useful in order to reach the strong coupling regime, demonstrating Rabi oscillations and developing a variety of protocols for quantum information, tomograhy, entanglement, etc. However, recent experiments have shown that it is possible to also work with propagating photons, replacing the LC resonators with open transmission lines, and studying the scattering properties of those artificial atoms. In this context we have worked on developing new technology to detect and control these photons, engineering single-photon detectors, quantum metamaterials and photonic crystals, or even new nonlinear media based on coupled cavities.
We theoretically explore the applications of a nonlinear circuit QED system, where a charge qubit is inductively coupled to an LC resonator, in the photonic engineering and ultrastrong-coupling multiphoton quantum optics. An arbitrary Fock-state pulsed maser, where the artificial qubit plays the gain-medium role, is achieved via simply sweeping the gate-voltage bias. The resonantly pumped parametric qubit-resonator interface leads to a squeezed intraresonator field, which is utilizable for the quantum-limited microwave amplification. Moreover, upwards and downwards multiphoton quantum jumps may be observed in the driving-free steady-state system.