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Solovay-Kitaev Theorem

Mathematical Physics

In quantum information and computation, the Solovay-Kitaev theorem states that if a set of single-qubit quantum gates generates a dense subgroup of SU(2), that set can be used to approximate any desired quantum gate with a short sequence of gates that can also be found efficiently. Robert M. Solovay first announced the theorem in 1995, and Alexei Kitaev independently proved it in 1997; Michael Nielsen and Christopher M. Dawson have noted its importance to the field of quantum computation.

Facts
Statement
If a set of single-qubit quantum gates generates a dense subgroup of SU(2), then that set can be used to approximate any desired quantum gate. 1
Proof Year
1997 1
Classification
Statement Form
Existence Theorem 1
Connections

Has Statement Form

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Sources
1. Solovay-Kitaev theorem, Wikipedia
  • Statement
    if a set of single-qubit quantum gates generates a dense subgroup of SU(2), then that set can be used to approximate any desired quantum gate
  • Attribution
    independently proven by Alexei Kitaev in 1997
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