TY - JOUR
T1 - Approximate quantum error correction for correlated noise
AU - Ben-Aroya, Avraham
AU - Ta-Shma, Amnon
N1 - Funding Information:
Manuscript received December 26, 2009; revised October 22, 2010; accepted November 15, 2010. Date of current version May 25, 2011. The work of A. Ben-Aroya is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities, and by the European Commission IST project “Quantum Computer Science” QCS 25596. The work of A. Ta-Shma is supported by the European Commission IST project “Quantum Computer Science” QCS 25596.
PY - 2011/6
Y1 - 2011/6
N2 - Most of the research on quantum error-correcting codes studies an error model in which each noise operator acts on a bounded number of qubits. In this paper we study a different noise model where the noise operators act on all qubits together, but are otherwise restricted in their action. One example to such an operator is a controlled bit-flip operator, where the control depends on all qubits, i.e., we allow restricted, highly correlated noise. We show both positive and negative results. On the positive side, we show that even though controlled bit-flip errors cannot be perfectly corrected, they can be approximately corrected with a subconstant approximation error. On the negative side, we show that no nontrivial quantum error-correcting code can approximately correct controlled phase error with a subconstant approximation error.
AB - Most of the research on quantum error-correcting codes studies an error model in which each noise operator acts on a bounded number of qubits. In this paper we study a different noise model where the noise operators act on all qubits together, but are otherwise restricted in their action. One example to such an operator is a controlled bit-flip operator, where the control depends on all qubits, i.e., we allow restricted, highly correlated noise. We show both positive and negative results. On the positive side, we show that even though controlled bit-flip errors cannot be perfectly corrected, they can be approximately corrected with a subconstant approximation error. On the negative side, we show that no nontrivial quantum error-correcting code can approximately correct controlled phase error with a subconstant approximation error.
KW - Approximate quantum error-correcting codes
KW - highly correlated quantum noise
KW - quantum error-correcting codes
UR - http://www.scopus.com/inward/record.url?scp=79957635643&partnerID=8YFLogxK
U2 - 10.1109/TIT.2011.2134410
DO - 10.1109/TIT.2011.2134410
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AN - SCOPUS:79957635643
SN - 0018-9448
VL - 57
SP - 3982
EP - 3988
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
M1 - 5773012
ER -