Kernkonzepte
Quantum maximum likelihood decoding (QMLD) for the surface code is NP-hard.
Zusammenfassung
The content discusses the complexity of decoding the surface code with Pauli noise, focusing on quantum error correction. It presents a reduction from SAT to QMLD, showing that QMLD is NP-hard. The reduction involves gadgets simulating boolean circuits, such as AND, OR, NOT, and FAN-OUT gates, to convert a boolean formula into a QMLD problem instance. The reduction ensures that the maximum probability error corresponds to a satisfying assignment of the boolean formula, if one exists.
- Introduction to quantum error correction and the surface code.
- Reduction from SAT to QMLD for the surface code.
- Overview of the reduction process and the gadgets involved.
- Detailed explanation of the gadgets used in the reduction.
- Analysis of the noise model and syndromes outputted by the conversion.
- Hypothetical examples of errors corresponding to satisfying and unsatisfying assignments.
Statistiken
"Quantum maximum likelihood decoding (QMLD) for the surface code with independent non-identically distributed Pauli noise is NP-hard."
Zitate
"Real quantum computers will not be subject to simple noise such as depolarizing noise, but rather more complicated noise that may be different for each qubit."
"Decoding the surface code is known to be closely related to computing partition functions of Ising models, which is known to be #P-hard."