Open Access
Structured near-optimal channel-adapted quantum error correction
Andrew S. Fletcher,Peter W. Shor,Moe Z. Win +2 more
- 01 Jan 2008
2
TL;DR: In this article, a class of numerical algorithms which adapt a quantum error correction scheme to a channel model is presented, where each recovery operation begins with a projective error syndrome measurement.
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Abstract: We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement fidelity may be calculated by a semidefinite program (SDP), which is a convex optimization. While optimal, this recovery operation is computationally difficult for long codes. Furthermore, the optimal recovery operation has no structure beyond the completely positive trace preserving (CPTP) constraint. We derive methods to generate structured channel-adapted error recovery operations. Specifically, each recovery operation begins with a projective error syndrome measurement. The algorithms to compute the structured recovery operations are more scalable than the SDP and yield recovery operations with an intuitive physical form. Using Lagrange duality, we derive performance bounds to certify near-optimality.
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Citations
Quantum error correction and reversible operations
Carlton M. Caves
- 01 Jan 1998
TL;DR: A pedagogical account of Shor's nine-bit code for correcting arbitrary errors on single qubits is given and work that determines when it is possible to maintain quantum coherence by reversing the deleterious effects of open-system quantum dynamics is reviewed.
36
•Posted Content
Efficient Entanglement Distillation for Quantum Channels with Polarization Mode Dispersion
TL;DR: In this paper, the authors proposed a recurrence QED algorithm for photonic qubit pairs affected by polarization mode dispersion (PMD)degraded channels. And the algorithm achieves the optimal fidelity as well as the optimal success probability in every round of distillation.
2
References
Mixed State Entanglement and Quantum Error Correction
Charles H. Bennett,Charles H. Bennett,Charles H. Bennett,David P. DiVincenzo,David P. DiVincenzo,David P. DiVincenzo,John A. Smolin,John A. Smolin,John A. Smolin,William K. Wootters,William K. Wootters,William K. Wootters +11 more
TL;DR: It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication.
6K
Scheme for reducing decoherence in quantum computer memory
TL;DR: In the mid-1990s, theorists devised methods to preserve the integrity of quantum bits\char22{}techniques that may become the key to practical quantum computing on a large scale.
4.9K
Completely positive linear maps on complex matrices
TL;DR: A linear map from M n to M m is completely positive iff it admits an expression Φ(A)=Σ i V ∗ i AV i where Vi are n×m matrices as mentioned in this paper.
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Good quantum error-correcting codes exist
A. R. Calderbank,Peter W. Shor +1 more
TL;DR: The techniques investigated in this paper can be extended so as to reduce the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions.
Error Correcting Codes in Quantum Theory.
TL;DR: It is shown that a pair of states which are, in a certain sense, “macroscopically different,” can form a superposition in which the interference phase between the two parts is measurable, providing a highly stabilized “Schrodinger cat” state.
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