Towards the Design Automation of Quantum Circuits

Quantum mechanics based computing systems are expected to have high capabilities and are considered good candidates to replace classical cryptography and supercomputing systems. Among many implementations, quantum optics systems provide a promising platform to implement universal quantum computers, since they link quantum computation and quantum communication in the same framework. Recently, several quantum gates, circuits, and protocols have been experimentally realized using optics. Despite the fact that big advances in building the physical quantum computers were achieved, there are no currently available industrial computer aided tools that can perform the modeling, analysis, and verification of optical quantum computing systems. In this thesis, we tackle the idea of design automation for quantum circuits, where we use a sound language, higher order logic, to model and reason about quantum circuits formally. In particular, we propose a framework for the hierarchical modeling and automated verification of quantum computing circuits. The modeling approach captures quantum models built hierarchically from quantum gates, which models are readily available in a library. The analysis and verification of composed circuits is done seamlessly based on dedicated mathematical foundations formalized in the theorem prover. Specifically, the tensor product and linear projection are used to extract the quantum circuit outputs. Subsequently, a rich library of quantum gates which includes 1-qubit, 2-qubit, and 3-qubit gates is formalized. In order to automate the analysis process, we developed a decision procedure to eliminate the need of user guidance throughout the formal proofs. To demonstrate the effectiveness of the proposed framework, we conduct the formal analysis of a benchmark of quantum circuits including the Shor's integer factorization algorithm, the Grover's oracle, and the quantum full adder

Integrated design for integrated photonics: from the physical to the circuit level and back

Silicon photonics is maturing rapidly on a technology basis, but design challenges are still prevalent. We discuss these challenges and explain how design of photonic integrated circuits needs to be handled on both the circuit as on the physical level. We also present a number of tools based on the IPKISS design framework

Teaching photonic integrated circuits with Jupyter notebooks : design, simulation, fabrication

At Ghent University, we have built a course curriculum on integrated photonics, and in particular silicon photonics, based on interactive Jupyter Notebooks. This has been used in short workshops, specialization courses at PhD level, as well as the M.Sc. Photonics Engineering program at Ghent University and the Free University of Brussels. The course material teaches the concepts of on-chip waveguides, basic building blocks, circuits, the design process, fabrication and measurements. The Jupyter notebook environment provides an interface where static didactic content (text, figures, movies, formulas) is mixed with Python code that the user can modify and execute, and interactive plots and widgets to explore the effect of changes in circuits or components. The Python environment supplies a host of scientific and engineering libraries, while the photonic capabilities are based on IPKISS, a commercial design framework for photonic integrated circuits by Luceda Photonics. The IPKISS framework allows scripting of layout and simulation directly from the Jupyter notebooks, so the teaching modules contain live circuit simulation, as well as integration with electromagnetic solvers. Because this is a complete design framework, students can also use it to tape out a small chip design which is fabricated through a rapid prototyping service and then measured, allowing the students to validate the actual performance of their design against the original simulation. The scripting in Jupyter notebooks also provides a self-documenting design flow, and the use of an established design tool guarantees that the acquired skills can be transferred to larger, real-world design projects

Photonic integrated circuit design in a foundry+fabless ecosystem

A foundry-based photonic ecosystem is expected to become necessary with increasing demand and adoption of photonics for commercial products. To make foundry-enabled photonics a real success, the photonic circuit design flow should adopt known concepts from analog and mixed signal electronics. Based on the similarities and differences between the existing photonic and the standardized electronics design flow, we project the needs and evolution of the photonic design flow, such as schematic driven design, accurate behavioral models, and yield prediction in the presence of fabrication variability

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Benchmarking of Gaussian boson sampling using two-point correlators

Gaussian boson sampling is a promising scheme for demonstrating a quantum computational advantage using photonic states that are accessible in a laboratory and, thus, offer scalable sources of quantum light. In this contribution, we study two-point photon-number correlation functions to gain insight into the interference of Gaussian states in optical networks. We investigate the characteristic features of statistical signatures which enable us to distinguish classical from quantum interference. In contrast to the typical implementation of boson sampling, we find additional contributions to the correlators under study which stem from the phase dependence of Gaussian states and which are not observable when Fock states interfere. Using the first three moments, we formulate the tools required to experimentally observe signatures of quantum interference of Gaussian states using two outputs only. By considering the current architectural limitations in realistic experiments, we further show that a statistically significant discrimination between quantum and classical interference is possible even in the presence of loss, noise, and a finite photon-number resolution. Therefore, we formulate and apply a theoretical framework to benchmark the quantum features of Gaussian boson sampling under realistic conditions