Changhun Oh

While quantum computing can accomplish tasks that are classically intractable, the presence of noise may destroy this advantage in the absence of fault tolerance. In this work, we present a quasi-polynomial-time classical algorithm for simulating quantum circuits under local depolarization noise, thereby ruling out their quantum advantage in these settings. Our algorithm leverages a property called approximate Markov property to sequentially sample from the measurement outcome distribution of noisy circuits. We establish approximate Markov property in a broad range of circuits: (1) we prove that it holds for any circuit when the noise rate exceeds a constant threshold, and (2) we provide strong analytical and numerical evidence that it holds for random quantum circuits subject to any constant noise rate, including non-unital noises. These regimes include previously known classically simulable cases as well as new ones, such as shallow random circuits and random circuits under non-unital noise, where anticoncentration does not hold and prior algorithms fail. Taken together, our results significantly extend the boundary of classical simulability and suggest that noise generically enforces approximate Markov property and classical simulability, thereby highlighting the limitation of noisy quantum circuits in demonstrating quantum advantage.

We present a sample- and time-efficient algorithm to learn any bosonic Fock state acted upon by an arbitrary Gaussian unitary. As a special case, this algorithm efficiently learns states produced in Fock state BosonSampling, thus resolving an open question put forth by Aaronson and Grewal (Aaronson, Grewal 2023). We further study a hierarchy of classes of states beyond Gaussian states that are specified by a finite number of their higher moments. Using the higher moments, we find a full spectrum of invariants under Gaussian unitaries, thereby providing necessary conditions for two states to be related by an arbitrary (including active, e.g.~beyond linear optics) Gaussian unitary.