Building a scalable quantum computer is one of the greatest challenges of this century. A quantum computer should be able to execute quantum algorithms which promise great speed up in solving certain computational problems. Microwave photons in superconducting circuits offer a promising platform for quantum computing due to their long coherence times, and the ease of their generation and control. Single-qubit quantum gates are implemented with conventional microwave components. However, implementing entangling two-qubit gates for photonic qubits is considerably difficult because photons do not interact with each other naturally. In this thesis, we investigate the effective interactions between photons mediated by superconducting qubits. Especially, the nonlinear effects in the photonic states generated by these interactions are studied. Based on the analysis of the scattering properties of the system, we present a design for a nonlinear phase shifter device, which yields a photon-number-dependent phase shift in the transmitted photons. Furthermore, we show how entangling two-qubit gates can be implemented using the presented nonlinear phase shifter.
Building a scalable quantum computer is one of the greatest challenges of this century. A quantum computer should be able to execute quantum algorithms which promise great speed up in solving certain computational problems. Microwave photons in superconducting circuits offer a promising platform for quantum computing due to their long coherence times, and the ease of their generation and control. Single-qubit quantum gates are implemented with conventional microwave components. However, implementing entangling two-qubit gates for photonic qubits is considerably difficult because photons do not interact with each other naturally. In this thesis, we investigate the effective interactions between photons mediated by superconducting qubits. Especially, the nonlinear effects in the photonic states generated by these interactions are studied. Based on the analysis of the scattering properties of the system, we present a design for a nonlinear phase shifter device, which yields a photon-number-dependent phase shift in the transmitted photons. Furthermore, we show how entangling two-qubit gates can be implemented using the presented nonlinear phase shifter.
Microwave photons in superconducting circuits is a promising approach for quantum computing due to long coherence times and the easy controllability of superconducting devices. However, as the search of the ultimate design of a quantum computer is still ongoing, various suggestions for the realization of a quantum bit, qubit, exist even in the area of superconducting circuits. In this thesis, we study theoretically quantum computing using itinerant microwave photons as qubits. Basic tools for treating the reflection of wave packets and the noise generated by resistive elements in a circuit are derived starting from a widely used model for superconducting transmission lines. We also present simple quantum devices that can act as quantum gates for microwave qubits, including a novel suggestion for a tunable phase shifter. A tunable phase shifter is a useful component in the study of microwave photons in general as well as in quantum computing. The tunable phase shifter consists of three superconducting quantum interference devices (SQUIDs) that can be treated as tunable inductors in the low-power regime. The results of this thesis can be used both in applications related to quantum computing and in the general study of quantum mechanics in circuits. In particular, we conclude that there exist feasible system parameters, for which it should be possible to demonstrate the tunable phase shifter utilizing available experimental techniques. We also show the principle how the possible nonlinearity of the phase shifter can be used in a two-qubit gate providing interactions between microwave photons.
A quantum computer is a promising addition to a classical computer due to increase in performance on certain computational problems. A classical computer computes by manipulating bits, which assume a value either 0 or 1, using logical gates. Similarly, a quantum computation is carried out by manipulating quantum bits, so-called qubits, using quantum gates. The main advantage of qubits is that they can be not only in the states representing 0 and 1, but also in any superposition of these two states. Many different physical realizations for qubits have been proposed. One of the most promising candidates for the hardware of quantum computing are superconducting circuits. Here, the qubit can be represented in number of ways. For example, the two different states can be the direction of current circulating in a superconducting loop, or presence and absence of a photon in a transmission line. In this thesis, we study a tunable phase gate for microwave photons. The gate is implemented by a transmission line interrupted by three superconducting quantum interference devices (SQUIDs), which we model as inductors. We theoretically show that this system fulfills the requirements of a phase gate and that the tunability of the phase shift is frequency dependent. In addition, we consider a non-ideal system by including the effects of the capacitance associated with the SQUIDs. We find that the capacitance has no adverse effects, and in the best case, it may even increase the range of tunability. We also measure the phase shift at frequency of 6.3 GHz and find that the system is well described by the theory. To our knowledge, similar phase gate has not been experimentally studied before.
We report a generic scheme to implement transmission-type quantum gates for propagating microwave photons, based on a sequence of lumped-element components on transmission lines. By choosing three equidistant superconducting quantum interference devices (SQUIDs) as the components on a single transmission line, we experimentally implement a magnetic-flux-tunable phase shifter and demonstrate that it produces a broad range of phase shifts and full transmission within the experimental uncertainty. Together with previously demonstrated beam splitters, these phase shifters can be utilized to implement arbitrary single-qubit gates. Furthermore, we theoretically show that replacing the SQUIDs by superconducting qubits, the phase shifter can be made strongly nonlinear, thus introducing deterministic photon--photon interactions. These results critically complement the previous demonstrations of on-demand single-photon sources and detectors, and hence pave the way for an all-microwave quantum computer based on propagating photons.
Superconducting circuits provide a suitable platform to build quantum computers with increasing number of quantum bits (qubits). As such the sheer number of qubits, i.e., the quantum mechanical computational units in a quantum computer, cannot be used to determine the computational power of the computer. On the other hand, a large number of qubits is required to execute well-known quantum algorithms with reliable accuracy. To even dream about solving complex tasks with the state-of-the-art quantum circuits, they have to be improved in many ways to achieve a high level of accuracy. An essential part of large quantum systems is the communication between distant computational units. Establishing efficient communication channels between different parts allows building a network of established components. However, the communication has to be resistant to significant levels of background noise. Quantum backscatter communication is particularly interesting communication paradigm that fulfills this requirement. Here, a single photon is generated and divided into an entangled pair of a signal and an idler photon. The idler photon is sent directly to a receiving quantum system whereas the signal photon is scattered from an auxiliary component. The backscattering event introduces a phase shift that carries the information being sent from the backscatterer to the receiving quantum system. The utilization of quantum entanglement improves the signal-to-noise ratio compared with the classical backscatter paradigm. In this thesis, we study a method to generate single signal photons conditioned on a quantum state of a superconducting qubit, which is a prerequisite for quantum backscattering communication. This process involves exciting the quantum bit to its second excited state and driving it with an appropriate pulse frequency such that the qubit evolves back to the ground state of the system while simultaneously generating a single photon. We find that with our current measurement setup, the signal photon is generated with a success rate of 70%. As our research group’s first trial for this type of measurement, the results show great promise for future work with the quantum backscatter project.
Quantum optics in superconducting circuits, known as circuit QED, studies the interaction of photons at microwave frequencies with artificial atoms made of Josephson junctions. Although quite young, remarkable progress has been made in this field over the past decade, especially given the interest in building a quantum computer using superconducting circuits. In this thesis based on the appended papers, we look at generation, engineering and detection of microwave photons using superconducting circuits. We do this by taking advantage of the strong coupling, on-chip tunability and huge nonlinearity available in superconducting circuits. First, we present the strong photon-photon interaction measured experimentally, as shown in the giant cross-Kerr effect. In this work, conditional phase shift of about 20 degrees per photon was measured between two coherent fields at single photon level. Given this strong interaction, we propose and analyze a cascaded setup based on the cross-Kerr effect to detect itinerant microwave photons, a long outstanding problem with only recent experimental realizations. We show that a nondestructive detection of microwave photons is possible with few cascaded transmons. The on-chip tunability of Superconducting Quantum Interference Device (SQUID) is exploited to create a tunable superconducting resonator in the next presented experimental work. Finally, we show that by placing the atom at the end of a transmission line, microwave photons can be generated efficiently and on-demand. We also present a setup that can generate the photons in arbitrary wave packets.
A photonic transistor that can switch or amplify an optical signal with a single gate photon requires strong non-linear interaction at the single-photon level. Circuit quantum electrodynamics provides great flexibility to generate such an interaction, and thus could serve as an effective platform to realize a high-performance single-photon transistor. Here we demonstrate such a photonic transistor in the microwave regime. Our device consists of two microwave cavities dispersively coupled to a superconducting qubit. A single gate photon imprints a phase shift on the qubit state through one cavity, and further shifts the resonance frequency of the other cavity. In this way, we realize a gain of the transistor up to 53.4 dB, with an extinction ratio better than 20 dB. Our device outperforms previous devices in the optical regime by several orders in terms of optical gain, which indicates a great potential for application in the field of microwave quantum photonics and quantum information processing.