Kadanoff Seminar: Quantum circuit and novel quantum state preparation from spacetime duality. - Yizhi You, Northeasten

The preparation of quantum states with long-range correlations and topological entanglement is a key objective for quantum simulators and processors. A common approach is the Sequential Quantum Circuit, which applies local unitary transformations to sub-regions of a system sequentially with linear depth. An alternative strategy, the measurement and feedback (MF) circuit, avoids high-depth circuits by using finite-depth unitaries, measurements, and outcome-dependent feedback to prepare states in constant depth.

In this talk, I show how these two methods—sequential circuits and MF protocols—are unified through spacetime duality. This framework interprets nonlocal operators and observables in MF circuits as auto-correlators in sequential circuits. The duality also has broader implications, including insights into non-invertible symmetries in quantum circuits and the interplay between unitary and measurement errors in quantum computation.