Constructing Functional Braids for Low-Leakage Topological Quantum Computing

We discuss how to significantly reduce leakage errors in topological quantum computation by introducing an irrelevant error in phase, using the construction of a CNOT gate in the Fibonacci anyon model as a concrete example. To be specific, we construct a functional braid in a six-anyon Hilbert space that exchanges two neighboring anyons while conserving the encoded quantum information. The leakage error is $\sim$$10^{-10}$ for a braid of $\sim$100 interchanges of anyons. Applying the braid greatly reduces the leakage error in the construction of generic controlled-rotation gates.Comment: 5 pages, 4 figures, updated, accepeted by Phys. Rev.

Chip-based photonic sensors for metrology and applications

Photonic sensors are of crucial importance in modern science and technology. They can be designed to be ultra-sensitive to certain physical quantities, while robust against other physical parameters. Many photonic sensors are compatible with CMOS technology and can be integrated on chips for use as highly sensitive, small scale and low cost sensors, such as ring resonator, disk resonator, Mach-Zehnder interferometer, photonic crystal, directional coupler, grating, etc. In this thesis we focus on two types of photonic sensors, micro-ring resonator and high contrast grating membrane, including their fabrication, theoretical basis, experimental characterizations, and their applications to the measurement of two fundamental physical quantities: temperature and length. We study chip-based micro-ring resonators, and show that ring resonator temperature sensors can be used to detect temperature differences as small as 80 μK, a 13-fold improved on previously reported results. We study a mirror-in-the-middle system with a high-reflectivity sub-wavelength grating. We show how the mode structure rapidly changes near the points where the left cavity and the right cavity simultaneously come into resonance, and suggest that this is best understood via a perturbation theory starting from unit reflectivity, in contrast to the usual dispersive regime for membrane-in-the-middle work. In addition, the spectral signatures of the system allow more detailed study of the losses than is possible in a simple cavity, and we quantify the reflection, transmission, absorption and scattering losses in the context of a simple model. We use the mirror-in-the-middle system as a platform for high resolution absolute displacement measurement. This technique is based on radio frequency measurement without an optical reference. We have achieved a resolution of 4x10-14 m at a sampling rate of 10 Hz. This displacement sensing is used to analyze the stability and slow movement of the grating membrane in the mirror-in-the-middle cavity system. We also study theoretically two types of buckling transitions due to the optomechanical interaction between light and a grating membrane, which can be observed using our displacement sensing technique

Exploiting Geometric Degrees of Freedom in Topological Quantum Computing

In a topological quantum computer, braids of non-Abelian anyons in a (2+1)-dimensional space-time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to create and exploit redundant geometric degrees of freedom to improve the theoretical accuracy of topological single- and two-qubit quantum gates. We demonstrate the power of the idea using explicit constructions in the Fibonacci model. We compare its efficiency with that of the Solovay-Kitaev algorithm and explain its connection to the leakage errors reduction in an earlier construction [Phys. Rev. A 78, 042325 (2008)].Comment: 5 pages, 2 figures, accepted for publication in Phys. Rev.

Nonreciprocal Amplification Transition in a Driven-Dissipative Quantum Network

We study the transport properties of a driven-dissipative quantum network, where multiple bosonic cavities such as photonic microcavities are coupled through a nonreciprocal bus with unidirectional transmission. For short-range coupling between the cavities, the occurrence of nonreciprocal amplification can be linked to a topological phase transition of the underlying dynamic Hamiltonian. However, for long-range coupling, we find that the nonreciprocal amplification transition deviates drastically from the topological phase transition. Nonetheless, we show that the nonreciprocal amplification transition can be connected to the emergence of zero-energy edge states of an auxiliary Hamiltonian with chiral symmetry even in the long-range coupling limit. We also investigate the stability, the crossover from short to long-range coupling, and the bandwidth of the nonreciprocal amplification. Our work has potential application in signal transmission and amplification, and also opens a window to non-Hermitian systems with long-range coupling and nontrivial boundary effects.Comment: 5 pages, 4 figure

Entangled X-ray Photon Pair Generation by Free Electron Lasers

Einstein, Podolsky and Rosen's prediction on incompleteness of quantum mechanics was overturned by experimental tests on Bell's inequality that confirmed the existence of quantum entanglement. In X-ray optics, entangled photon pairs can be generated by X-ray parametric down conversion (XPDC), which is limited by relatively low efficiency. Meanwhile, free electron laser (FEL) has successfully lased at X-ray frequencies recently. However, FEL is usually seen as a classical light source, and its quantum effects are considered minor corrections to the classical theory. Here we investigate entangled X-ray photon pair emissions in FEL. We establish a theory for coherently amplified entangled photon pair emission from microbunched electron pulses in the undulator. We also propose an experimental scheme for the observation of the entangled photon pairs via energy and spatial correlation measurements. Such an entangled X-ray photon pair source is of great importance in quantum optics and other X-ray applications.Comment: 13 pages, 3 figure