Adaptive circuit knitting for simulating quantum dynamics

Simulating quantum dynamics is one of the most promising applications of quantum processors. Yet many classically intractable, interesting quantum dynamics occur at system sizes too large to fit on today's noisy intermediate-scale quantum (NISQ) processors or imminent fault-tolerant quantum computers (FTQC). To address this, circuit knitting techniques allow large quantum systems to be broken into smaller, manageable sub-circuits that can be executed on limited-size quantum processors (QPUs). While the straightforward application of this approach comes with an exponential cost in runtime, an adaptive circuit knitting (ACK) strategy could significantly reduce this cost by identifying and cutting through low-entanglement boundaries in the quantum circuit. Building on this, we introduce a hybrid quantum-classical algorithm that leverages tensor-network contractions to compile the time evolution circuit, allowing quantum dynamics simulations to reach longer time scales via ACK. We demonstrate the power of this approach by simulating the dynamics of a disordered quantum Ising model, achieving a significant improvement in sample complexity.