The Solovay–Kitaev theorem is a significant result in the field of quantum computing, particularly in the study of quantum circuits. It addresses the problem of approximating a given quantum gate using a finite set of gate operations. Here's an overview of its main points: 1. **Approximation of Quantum Gates**: The theorem states that any single-qubit unitary operation can be approximated to arbitrary precision using an arbitrary universal gate set, provided that the gate set is sufficiently rich.
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For a suitable finite inverse-closed universal quantum gate set, the Solovay--Kitaev theorem approximates a fixed-dimensional unitary to operator norm error with a gate sequence of length polynomial in .