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13:30   MS5: Numerical Mathematics on Quantum Computers (Part 2) Chair: Matthias Möller 13:30 25 mins SurfBraid: A concept tool for preparing and resource estimating quantum circuits protected by the surface code Alexandru Paler Abstract: The first generations of quantum computers will execute fault-tolerant quantum circuits, and it is very likely that such circuits will use surface quantum error correcting codes. To the best of our knowledge, no complete design automation tool for such circuits is currently available. This is to a large extent because such circuits have three dimensional layouts (e.g. two dimensional hardware and time axis as a third dimension) and their optimisation is still ongoing research. This work introduces SurfBraid, a tool for the automatic design of surface code protected quantum circuits -- it includes a complete workflow that compiles an arbitrary quantum circuit into an intermediary Clifford+T equivalent representation which is further synthesised and optimised to surface code protected structures (for the moment, braided defects). SurfBraid is arguably the first flexible (modular structure, extensible through user provided scripts) and interactive (automatically updating the results based on user interaction, browser based) tool for such circuits. One of the prototype's methodological novelty is its capability to automatically estimate the resources necessary for executing large fault-tolerant circuits. A prototype implementation and the corresponding source code are available at https://alexandrupaler.github.io/quantjs/. 13:55 25 mins Quantum error correction for near-term and long-term quantum processors Lingling Lao, Carmen G. Almudever Abstract: Quantum computing can solve problems that are not tractable by classical computers. However, qubits are fragile as they tend to decohere extremely quickly and quantum operations are faulty, making reliable computation very difficult. Therefore, quantum error correction (QEC) and fault-tolerant mechanisms are required to protect quantum states from errors and make quantum computing fault-tolerant (FT). Quantum error correction is inspired by classical error correction in which a more reliable unit of quantum information called logical qubit is encoded into several noisy physical qubits. In addition, errors are detected by performing error syndrome measurement (ESM) with the help of ancilliary qubits. These qubits are measured at the end of the ESM and their binary measurement results or error syndromes are forwarded to a decoding algorithm that identifies highly probable errors. The number of errors that can be corrected is determined by the code distance d which is defined by the minimum number of physical operations required to perform a logical operation. One of the most promising QEC codes is surface code. It can be used for FT implementation of large-scale quantum algorithms. However, many physical qubits are required to encode one logical qubits, which makes it unfeasible for demonstrating fault tolerance in near-term quantum processors that consist of small number of noisy qubits (e.g. tens of qubits). Such a processors are also called Noisy-Intermediate-Scale Quantum (NISQ) devices. Therefore, quantum error correction with low qubit overhead needs to be designed. In this talk, I will first introduce the basics of quantum error correction. Then I will briefly discuss topological QEC codes that can be applied to long-term quantum processors such as surface codes. Afterwards, I will focus more on small QEC codes for NISQ processors such as the Steane code with flag and bridge qubits. 14:20 25 mins LibKet: A C++ expression template library for rapid prototyping of practical quantum algorithms Matthias Möller, Merel Schalkers Abstract: The development of practically usable quantum computers is in full swing with global players like Google, IBM, and Microsoft and specialists in this field like Rigetti Computing competing for technology lead and, at the end of the day, simply the raw number of qubits integrated in their quantum processing units (QPUs) which can be either true quantum computers or simulators running on classical computer hardware. This situation resembles the very early days of GPU-accelerated computing when the first generation of programmable graphics cards became available but their productive use was largely hindered by the non-availability of software development kits (SDKs) and, even more severe, the lack of standardized non-proprietary programming languages that would lower the dependence on a particular hardware vendor. Basically all vendors of quantum computing solutions are nowadays offering proprietary SDKs which are typically written in Python and target at developing quantum algorithms for a specific QPU. The current situation makes it thus difficult to create a generally accepted benchmark suite of quantum algorithms that would allow a fair performance comparison between different QPUs. Moreover, the non-standardization of quantum programming languages leads to the repeated re-implementation of quantum algorithms and computational building blocks thereby limiting the speed of scientific progress. In this talk we present our Kwantum expression template library LibKet (https://gitlab.com/mmoelle1/LibKet) - Kwantum is Dutch for Quantum - which is a non-proprietary open-source framework for developing quantum-accelerated scientific applications in C++. Inspired by projects like Eigen (http://eigen.tuxfamily.org), LibKet is designed to formulate quantum algorithms as lightweight expressions that can be evaluated for the different QPU backends. Next to a growing collection of quantum algorithms and common building blocks like the Quantum Fourier transformation, LibKet in particular focusses on using QPUs as special-purpose accelerators in larger scientific applications. LibKet therefore implements arithmetic types for integer and real-valued data together with basic mathematical operations and, as near-future goal, aims at becoming a C++ toolbox for quantum-accelerated numerical linear algebra applications. 14:45 25 mins Quantum Inspire – The European cloud based quantum computing platform Richard Versluis Abstract: In September 2018 QuTech launched Quantum Inspire, a platform for cloud based quantum computing providing free access to QX, an efficient quantum simulator backend. Currently the system is being upgraded to provide access to hardware backends based on multiple qubit technologies, such as spin qubits, superconducting qubits, NV centers and ion traps. Circuit based quantum algorithms can be created through a graphical user interface for novice users or through the Python-based Quantum Inspire SDK, providing a backend for the projectQ framework and the Qiskit framework. Quantum Inspire provides a knowledge base with user guides and some example algorithms. In this talk I will highlight the most recent progress on Quantum Inspire, such as recent improvements in the quantum simulator, the use of real hardware backends and some physical aspects of near term quantum computers that need to be considered for algorithm development.