Bound on quantum computation time: Quantum error correction in a critical environment

Details Bound on quantum computation time: Quantum error correction in a critical environment Bound on quantum computation time: Quantum error correction in a critical environment

2010-04-19

arxiv.org/abs/1004.3247v2

Phys. Rev. A 82, 020303(R) (2010)

Physics

Quantum Physics

4 pages (revised title, following PRA request)

Scientific paper

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user.

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