Theory of decoherence-free fault-tolerant universal quantum computation

By Julia Kempe, D. Bacon, Daniel A. Lidar, K. Birgitta Whaley. 2000

412 citations recorded by the source corpus.

Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this stabilizer formalism. Two possible collective decoherence mechanisms arising from permutation symmetries of the system-bath coupling are examined within this framework. It is shown that in both cases universal quantum computation which always preserves the DFS (natural fault-tolerant computation) can be performed using only two-body interactions. This is in marked contrast to standard error correcting codes, where all known constructions using one- or two-body interactions must leave the code space during the on-time of the fault-tolerant gates. A further consequence of our universality construction is that a single exchange Hamiltonian can be used to perform universal quantum computation on an encoded space whose asymptotic coding efficiency is unity. The exchange Hamiltonian, which is naturally present in many quantum systems, is thus asymptotically universal.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/c2e810ec14adb173f8806c16011e2a68b1a79a56

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum memories at finite temperature (2014, background): “…subsystems was introduced to find a unifying language for decoherence free subspaces (Beige et al., 2000; Duan and Guo, 1997; Lidar et al., 1998; Pachos and Beige, 2004; Palma et al., 1996; Zanardi and Rasetti, 1997) and noiseless subsystems (Kempe et al., 2001; Knill et al., 2000; Zanardi, 2000).”
Scalable noise estimation with random unitary operators (2005, background): “Moreo ver, in the case of quantum devices capable of universal cont rol, knowledge of specific characteristics of the noise enables t h election and optimization of passive and active error-p evention strategies [3, 4, 5, 6, 7, 8].”
Universal quantum computation with the exchange interaction (2000, methodology): “In addition, the general theory [22,21,8, 10 ] shows that”
Decoherence-Free Subspaces and Subsystems (2003, methodology): “They can be used both to further improve the performance of DFS encoded qubits for quantum memory applications, and also in implementations of quantum computation with DFS encodings [36].”