Logic Synthesis for Quantum Computing

Today’s rapid advances in the physical implementation of quantum computers call for scalable synthesis methods to map practical logic designs to quantum architectures. We present a synthesis framework to map logic networks into quantum circuits for quantum computing. The synthesis framework is based on LUT networks (lookup-table networks), which play a key role in state-of-the-art conventional logic synthesis. Establishing a connection between LUTs in a LUT network and reversible single-target gates in a reversible network allows us to bridge conventional logic synthesis with logic synthesis for quantum computing—despite several fundamental differences. As a result, our proposed synthesis framework directly benefits from the scientific achievements that were made in logic synthesis during the past decades. We call our synthesis framework LUT-based Hierarchical Reversible Logic Synthesis (LHRS). Input to LHRS is a classical logic network, e.g., represented as Verilog description; output is a quantum network (realized in terms of Clifford+T gates, the most frequently used gate library in quantum computing). The framework offers to trade-off the number of qubits for the number of quantum gates. In a first step, an initial network is derived that only consists of single-target gates and already completely determines the number of qubits in the final quantum network. Different methods are then used to map each singletarget gate into Clifford+T gates, while aiming at optimally using available resources. We demonstrate the effectiveness of our method in automatically synthesizing IEEE compliant floating point networks up to double precision. As many quantum algorithms target scientific simulation applications, they can make rich use of floating point arithmetic components. But due to the lack of quantum circuit descriptions for those components, it can be difficult to find a realistic cost estimation for the algorithms. Our synthesized benchmarks provide cost estimates that allow quantum algorithm designers to provide the first complete cost estimates for a host of quantum algorithms. Thus, the benchmarks and, more generally, the LHRS framework are an essential step towards the goal of understanding which quantum algorithms will be practical in the first generations of quantum computers.