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Fault-tolerant quantum computation with long-range correlated noise
Dorit Aharonov1, Alexei Kitaev, John Preskill
1School of Computer Science and Engineering, Hebrew University, Jerusalem, Israel.
Physical Review Letters
|February 21, 2006
Summary
This study introduces a new quantum accuracy threshold theorem for non-Markovian noise. It shows reliable quantum computation is possible even with spatially correlated noise if it weakens with distance.
Area of Science:
- Quantum Information Science
- Theoretical Computer Science
- Condensed Matter Physics
Background:
- Quantum computations are sensitive to noise, which can limit their reliability.
- Existing quantum accuracy threshold theorems often assume Markovian noise, which is not always realistic.
Purpose of the Study:
- To develop a new quantum accuracy threshold theorem applicable to non-Markovian noise.
- To establish conditions under which reliable quantum computation is possible despite spatially correlated noise.
Main Methods:
- The study employs a novel mathematical framework to analyze the impact of non-Markovian noise on quantum computations.
- It focuses on perturbations acting collectively on pairs of qubits and the environment.
- The analysis considers noise with algebraically decaying spatial correlations in D spatial dimensions.
Main Results:
- A new version of the quantum accuracy threshold theorem is proven.
- It is demonstrated that reliable quantum computation is achievable for arbitrarily long durations.
- This holds true if the noise perturbation is sufficiently weak and decays spatially faster than 1/r(D).
Conclusions:
- The findings extend the applicability of quantum accuracy threshold theorems to more realistic noise models.
- This research provides theoretical underpinnings for building fault-tolerant quantum computers in the presence of complex noise.
- The results suggest that spatial correlations in noise do not necessarily prevent reliable quantum computation.
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