Towards Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers

Dynamic simulations of materials are one of the most promising applications for noisy intermediate-scale quantum (NISQ) computers. The difficulty in carrying out such simulations is that a quantum circuit must be executed for each time-step, and these circuits tend to grow in size with increasing time-step. NISQ computers, however, can only produce high-fidelity results for circuits up to a given size due to gate error rates and qubit decoherence times, limiting the duration of simulations that can be performed. Here, we present work towards developing constant-depth circuits for dynamic simulations under special classes of Hamiltonians. Specifically, we show that simulations of one-dimensional, time-dependent, N-spin transverse-field Ising models require quantum circuits with only N(N-1) CNOT gates for all time-steps, providing orders of magnitude depth reduction when compared with previous circuit generation methods. Such constant-depth circuits allow for simulations of arbitrary duration, enabling simulations of long-time dynamics which are often required to observe interesting and important atomic-level events.