AC/DC: Automated Compilation for Dynamic Circuits

Dynamic quantum circuits incorporate mid-circuit measurements and feed-forward operations originally intended to realize Quantum Error Correction. This paradigm has recently been utilized to prepare certain states and long-range entangling gates as well as reduce resource overhead in quantum algorithms such as Quantum Fourier Transformation and Quantum Phase Estimation. In this paper, we present a novel framework for generating dynamic quantum circuits that automatically prepare any state or unitary operator. This procedure is powered by numerical optimization-based circuit synthesis methods. The first contribution is introducing optimization objective functions incorporating mid-circuit measurement and feed-forward operations. The second contribution is incorporating these into a popular open-source quantum circuit synthesis framework. We demonstrate the generation of dynamic circuits for state preparation, long-range entangling gates, circuit optimization, and the application of dynamic circuits to lattice simulations. The resulting circuits are validated through simulation and execution on quantum hardware. Furthermore, we perform noise analysis to explore the impact of different error ratios in mid-circuit measurements and gate errors, identifying scenarios where dynamic circuits offer the most significant benefits. The dynamic circuits generated by our framework show substantial improvements in reducing circuit depth and, in some cases, the number of gates required. To our knowledge, this is the first practical procedure to generate dynamic quantum circuits. Our objective functions are independent of the underlying synthesis framework and can be easily reused. This framework opens new possibilities for circuit generation and optimization methods, highlighting the potential of dynamic circuits to enhance the performance of quantum algorithms on near-term quantum computers.