Can Randomized Compilation Enable Efficient Simulation of Linear Non-Unitary Dynamics?
Date:
Abstract：
In this talk, we will introduce random-LCHS, a circuit-efficient randomized-compilation framework for simulating linear non-unitary dynamics based on the linear combination of Hamiltonian simulation (LCHS) method. We present three variants: the general random-LCHS for time-dependent inhomogeneous systems, the observable-driven random-LCHS that directly estimates expectation values of observables at the final time, and the symmetric random-LCHS, a time-independent, symmetry-exploiting reduction. We will show that by randomizing both the outer linear-combination-of-unitaries layer and the deterministic inner Hamiltonian simulation layer, random-LCHS achieves favorable circuit resource overheads for early fault-tolerant devices. Next, we demonstrate that the observable-driven version utilizes an unbiased Monte Carlo estimator to reduce sample complexity, whereas the symmetry-integrated approach yields tighter error bounds and improved empirical accuracy. We will discuss both the theoretical guarantees and numerical results, along with implementation trade-offs for near-term quantum hardware.