Magic state distillation is a method for creating more accuratequantum states from multiple noisy ones, which is important^[1] for buildingfault tolerant quantum computers. It has also been linked^[2] toquantum contextuality, a concept thought to contribute to quantum computers' power.^[3]

The technique was first proposed byEmanuel Knill in 2004,^[4]and further analyzed by Sergey Bravyi andAlexei Kitaev the same year.^[5]

Thanks to theGottesman–Knill theorem, it is known that some quantum operations (operations in theClifford group) can be perfectly simulated inpolynomial time on a classical computer. In order to achieve universal quantum computation, a quantum computer must be able to perform operations outside this set. Magic state distillation achieves this, in principle, by concentrating the usefulness of imperfect resources, represented bymixed states, into states that are conducive for performing operations that are difficult to simulate classically.

A variety of qubit magic state distillation routines^[6][7] and distillation routines for qubits^[8][9][10] with various advantages have been proposed.

TheClifford group consists of a set of${\displaystyle n}$-qubit operations generated by the gates{H,S,CNOT} (whereH isHadamard andS is) called Clifford gates. The Clifford group generates stabilizer states which can be efficiently simulated classically, as shown by the Gottesman–Knill theorem. This set of gates with a non-Clifford operation is universal for quantum computation.^[5]

Magic states are purified from${\displaystyle n}$ copies of amixed state${\displaystyle \rho }$.^[6] These states are typically provided via an ancilla to the circuit. A magic state for the${\displaystyle \pi /6}$ rotation operator is${\displaystyle |M⟩=\cos (\beta /2)|0⟩+e^{i\frac{\pi }{4}}\sin (\beta /2)|1⟩}$ where${\displaystyle \beta =\arccos \left(\frac{1}{\sqrt{3}}\right)}$. A non-Clifford gate can be generated by combining (copies of) magic states with Clifford gates.^[5] Since a set of Clifford gates combined with a non-Clifford gate is universal for quantum computation, magic states combined with Clifford gates are also universal.

The first magic state distillation algorithm, invented bySergey Bravyi andAlexei Kitaev, is as follows.^[5]

Input: Prepare 5 imperfect states.

Output: An almost pure state having a small error probability.

repeat

Apply the decoding operation of thefive-qubit error correcting code and measure the syndrome.

If the measured syndrome is${\displaystyle |0000⟩}$, the distillation attempt is successful.

else Get rid of the resulting state and restart the algorithm.

until The states have been distilled to the desired purity.

• Magic (quantum information)

• Quantum computing
• Algorithms

• CS1 errors: missing periodical
• Articles with short description
• Short description is different from Wikidata