Xiao Yuan

Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, or other domains. Quantum computing provides an alternative to the perturbation paradigm, yet current quantum processors with few noisy qubits are of limited practical utility. In this talk, we introduce perturbative quantum simulation, which combines the complementary strengths of the two approaches, enabling the solution of large quantum problems using limited intermediate-scale quantum hardware. The use of a quantum processor alleviates the need to identify a solvable unperturbed Hamiltonian, while the introduction of perturbative coupling permits a quantum processor to simulate systems with larger sizes. We present an explicit perturbative expansion that mimics the Dyson series expansion and involves only local unitary operations. We then discuss its optimality over other expansions under certain conditions. This perturbative approach is benchmarked by simulating the interacting dynamics of representative quantum systems.

Quantum algorithms promise transformative speedups, yet their practical impact is often limited by prohibitively deep circuits, with two recurring sources of depth: costly preparation of structured input states and the execution of subroutines based on truncated series approximations. We introduce a unified, resource-efficient paradigm that uses classical randomness as an algorithmic primitive to improve accuracy–depth trade-offs. For realistic states with hierarchical amplitude structure, we propose a randomized state-preparation protocol that probabilistically amplifies small amplitudes using ensembles of low-complexity circuits, reducing the number of amplitudes that must be encoded and achieving up to 99% reductions in CNOT and T-gate counts in simulations on LiH wavefunctions and power-law decay states. Target quantum algorithms, we develop Randomized Truncated Series, a generic acceleration principle for any quantum algorithm built from truncated series, which quadratically suppresses truncation error while enabling continuous tuning of the effective truncation order via random mixing of shallow circuits. Together, these results broaden the regime where end-to-end quantum advantage is feasible on near-term and early fault-tolerant hardware.