Abstract
We propose a new scheme for transforming a general quantum circuit into a geometrically local quantum circuit with polynomial qubit overhead and constant circuit depth overhead.We show that our scheme preserves fault-tolerance of the input quantum circuit under local stochastic noise. As a corollary, we show that our scheme can be used as a black box to transform any fault-tolerance construction involving non-local operations into one which only involves geometrically local operations. More generally, our transformation dispenses with the need for considering the locality of operations when designing schemes for fault-tolerant quantum information processing. Applied to recent fault-tolerance constructions, this gives a fault-tolerance threshold theorem for universal quantum computations with local operations, a polynomial qubit overhead and a quasi-polylogarithmic depth overhead. A key element for our construction is a parallel repetition theorem for fault-tolerant long-range entanglement generation.