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2008

C3, Semi-Clifford and Generalized Semi-Clifford Operations

Beigi, Salman, Shor, Peter W.

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Fault-tolerant quantum computation is a basic problem in quantum computation, and teleportation is one of the main techniques in this theory.

Using teleportation on stabilizer codes, the most well-known quantum codes, Pauli gates and Clifford operators can be applied fault-tolerantly.
Indeed, this technique can be generalized for an extended set of gates, the so called ${\mathcal{C}}_k$ hierarchy gates, introduced by Gottesman and Chuang (Nature, 402, 390-392).
${\mathcal{C}}_k$ gates are a generalization of Clifford operators, but our knowledge of these sets is not as rich as our knowledge of Clifford gates.

C3, Semi-Clifford and Generalized Semi-Clifford Operations · Around

Built on

Loo-Keng Hua, On the Automorphisms of the Symplectic Group Over Any Field
1948
Earlier work this paper cites.
D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
1999
Earlier work this paper cites.

Similar

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information
2000
Cited alongside, same era.
Jeroen Dehaene, Bart De Moor, The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
2003
Cited alongside, same era.

Then

Bei Zeng, Xie Chen, Isaac L. Chuang, Semi-Clifford operations, structure of 𝒞 k {\mathcal{C}}_{k} hierarchy, and gate complexity for fault-tolerant quantum computation
2008
Closest in time.
D. Gross and M. Van den Nest, The LU-LC conjecture, diagonal local operations and quadratic forms over GF(2)
2008
Closest in time.

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