Recent Advancements in Quantum Error Mitigation and Quantum Simulation

Quantum simulation is a key near-term application of quantum computing. I will present several recent advancements in quantum simulation techniques and error mitigation. I will discuss error mitigation strategies for estimating expectation values of local observables, where we introduce a new Probabilistic Error Cancellation (PEC) estimator leveraging light-cone structures to drastically reduce sampling overhead. I will also describe our 'shaded lightcone' approach, which combines classical bounds on error channel influence on the expectation values to optimize the bias-variance trade-off, achieving up to a two-order-of-magnitude runtime reduction for circuits like 127-qubit Trotter circuits. Finally, I will introduce an algorithm for simulating geometrically local Hamiltonians under small perturbations using the Magnus expansion in an interaction frame, avoiding the need for ancillary qubits. This algorithm's efficient computation is guaranteed by the Lieb-Robinson bound, making it appealing for near-term and early-fault-tolerant quantum devices. This seminar is a hybrid event at NC State.