Efficient Quantum Circuits for Square-Root and Inverse Square-Root
Srijit Dutta, Yaswanth Tavva, Debjyoti Bhattacharjee, Anupam Chattopadhyay · 2020
In recent years, rapid advancements in quantum technologies have resulted in heightened research activity, particularly in the domain of efficient implementation of computationally intensive kernels from prominent quantum algorithms. This is partly addressed by increasingly sophisticated synthesis techniques for quantum circuits. In this paper, we study the efficient Clifford +T circuit realization of two kernels, namely square root and inverse square root for different number formats. Quantum algorithms for solving Toeplitz system of linear equations, numerical methods for solving Poisson equation and in general for scientific computing require such kernels with customizable trade-off points for accuracy and performance. We present an efficient circuit design, obtained via detailed exploration of design choices in terms of accuracy and quantum costs. The manual circuits designed provide upto $50 \times $ reduction in qubit count for high precision circuits. Furthermore, a detailed benchmarking of state-of-the-art synthesis tools is undertaken for these kernels along with detailed comparison against manually-implemented designs.