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Explore a groundbreaking scheme for transforming general quantum circuits into geometrically local quantum circuits with polynomial qubit overhead and constant circuit depth overhead. Learn how this approach preserves fault-tolerance under local stochastic noise and can be used as a black box to transform fault-tolerance constructions involving non-local operations into ones with only geometrically local operations. Discover the implications for designing fault-tolerant quantum information processing schemes without considering operation locality. Examine the application of this transformation to recent fault-tolerance constructions, resulting in a fault-tolerance threshold theorem for universal quantum computations with local operations, polynomial qubit overhead, and quasi-polylogarithmic depth overhead. Delve into the key element of the construction: a parallel repetition theorem for fault-tolerant long-range entanglement generation.
