Solovay–Kitaev Theorem
A foundational theorem in quantum computing stating that any single-qubit unitary operation can be efficiently approximated by a polynomial-depth circuit drawn from a finite universal gate set, providing a theoretical guarantee for the universality of quantum circuits.
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The Solovay–Kitaev theorem states that any single-qubit unitary operation can be efficiently approximated to polynomial depth by a universal gate set, with the approximation depth growing polylogarithmically with precision.
The gate sequence length given by the Solovay–Kitaev theorem is O(log^c(1/ε)), where the constant c is approximately 3.97, and subsequent work has improved this to near 1.
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The Solovay–Kitaev theorem states that any single-qubit unitary operation can be efficiently approximated to polynomial depth by a universal gate set, with the approximation depth growing polylogarithmically with precision.
50%UnverifiedThe gate sequence length given by the Solovay–Kitaev theorem is O(log^c(1/ε)), where the constant c is approximately 3.97, and subsequent work has improved this to near 1.
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